United Stilts
                   Environmental Protection
                   Agency
Off ice of
Toxic Substances
Washington, DC 20460
EPA 560/7-81-005
August 1981
                   Toxic Substances
v>EPA
                   The Relevance of
                   Multiple Criteria  Decision Making to
                   Priorities for Chemical Regulations:
                   An Annotated  Bibliography

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                                                     OlS-IlC REFORI FILE
       The Relevance of Multiple Criteria Decision Making.
to Priorities for Chemical Regulation:  An Annotated Bibliography
                          Prepared by:
                       Tracor Jitco, Inc.
                   1776 East Je'fferson Street
                   Rockville, Maryland  20852
                     Contract No.  68-01-6021
                      Technical Directive 9
                             Authors
                          Steve Wilhelm
                 Environmental Protection Agency

                        Patricia Foreman
                          Tracor Jitco

                         Project Officer
                          Doug Sellers
                          August, 1981
                          Prepared for
                 Environmental  Protection Agency
                   Office of Toxic Substances
                     Washington,  D.C.   20460

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This report has been reviewed by the Office of
Toxic Substances, EPA, and approved for
publication.  Approval does not signify that the
contents necessarily reflect the views and
policies of the Environmental Protection Agency,
nor does mention of trade names or commercial
products constitute endorsement or recommendation
for use.

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              ABSTRACT
This bibliography contains one hundred and
thirteen references and original abstracts on
multiple criteria decision making and
multi-attribute utility theory.  It is a
selection of representative articles and reviews
rather than an exhaustive review of the
literature.  This report was prepared in
cooperation with the Office of Toxics Integration
within the Office of Toxic Substances.

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         TABLE OF CONTENTS






Abstract	 C




Introduction	 i




Bibliography	 1

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                               The Relevance of
                     Multiple Criteria Decision.Making  to
                     Priorities for Chemical Regulations;
                           An Annotated Bibliography
Introduction
This  bibliography  contains one  hundred and  thirteen references  and original
abstracts  on multiple  criteria  decision  making  and multi-attribute  utility
theory.  It  is  a selection of representative articles and  reviews rather than
an exhaustive review of the literature.

MAUT

Many  articles cited describe multi-attribute  utility theory (MAUT), a decision
making tool based on describing  the utility function of  a person or group when
several factors  (attributes, criteria,  variables)  are important in determining
that  function.   Selection  of advertising campaigns,  nuclear power plant sites,
and vacation resojrts are  examples of  decisions  which  have been  subjects  of
MAUT  research.

Utility   functions   are   generally   discussed   in   terms  of   mathematical
expressions,  although  it  is   not clear  that  an   appropriate  and  accurate
description of a utility function is always possible  in mathematical terms.

The utility  function  is  of the  form:   U = f(a,  b,  c,  . .   .).   The  number of
variables depends on the decision to be made.

Most  work  in this  area addresses  discovery  of the  appropriate variables, and
discovery  of. the form of  the  utility function,  u.   Appropriate  variables are
usually identified through interviews and/or questionnaires involving actual

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or  surrogate  decision-makers.   Selecting  the  form of  the function  is more
difficult.   The papers  addressing this  problem vary  from highly  theoretical
treatments    to    specific   applications.     Many    demonstrate    considerable
mathematical  complexity.

Most theorists  seem to have  focused  on  a simple  linear  form for u:

                                U =  X  w .   s  .
                                     *•*    i     i

In  such cases,  the  s.  are the values  (scores)  for  the  i criteria  and  the
w^  are  weighting factors which  are  used to adjust  for the varying  importance
of  the  different  criteria.   Appropriate  weighting  factors  are  also   often
discovered by interviews and/or questionnaires.

The  primary  appeal   of  the linear   form for u is its  simplicity.  Complex
formulations  have rarely been shown  to predict  or  describe human  behavior  any
more accurately.  The success  of  the  linear  formulation  seems  to derive from
the  fact that  the  decisions generally studied  are  amenable  to  the necessary
assumptions   of  the  linear  model.    These  assumptions,  however,  limit  the
applicability of the  linear formulations.  The most  important weakness is that
it  requires   the  variables  (criteria)  to  be  independent  of   one another.
Unfortunately,   many  problems   do   not   meet   this   somewhat   artificial
requirement.   More complex forms of u  are  tested in several of the  papers  but
the  results  are often disappointing.

An  apparent  goal of  MADT  and  other  multiple  criteria  decision-making research
is  to  reduce  the  entire  decision   context   to  a   single  expression  such   as
"utility",  "go/no-go",  or  "alternative A is  preferable  to alternative B".  A
desire  to  avoid complexity seems to permeate much of the  literature.  Perhaps,
greater progress  could be  made  by employing  partial utility  functions  and
                                                                 •?*
partial results, describing only  those  interactions of  criteria  which can be
readily discerned.   Chipman in his  article The  Foundations of Utility writes
of utility not as a number,  but as a vector, the components of which cannot be
combined arbitrarily.  This  may well  be a step in the right direction.
                                       ii

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Priority-Setting

Many  large  organizations  such  as  government  agencies  need   to  establish
priorities for  investment  of limited resources.  The Environmental Protection
Agency  - Office of Pesticides  and  Toxic  Substances (OPTS),  for  example, has
oversight  responsibility for  more than  fifty  thousand  chemicals manufactured,
processed, or distributed  in  the  United States.  Screening these chemicals and
selecting  small subsets for closer scrutiny is  a difficult task, easily involv-
ing enough  data to overwhelm  human abilities  to store,  sort, and comprehend.
This  and similar problems have  sometimes  been addressed by use  of  so called
"scoring methods or systems".  In such  a system,  a  set  of relevant criteria is
estab-  lished,  and  each member of the  set of  alternatives  (chemicals,  in the
OPTS  example) is scored  for  each  criterion.  An overall  score for each member
is derived from its scores  for  the various criteria,  usually by  adding them
together.  The members can then be ranked according to their overall scores.

Theoretically,  scoring systems  are very  closely  related   to MADT  and   other
multiple-criteria decision making  models.  The  main  differences arise  from
practical  considerations in priority-setting;  the cost  of the priority-setting
step  should  not exceed  the  savings  that  it   will  provide.  This  constraint
leads to use  of "soft" data and  approximate  or partial utility  functions for
deriving overall scores.  Scoring systems  frequently use  a weighted sum of the
scores as an overall score, thus making the comparison  to classic  MAUT all the
more  striking.

Scoring  systems  are an  obvious  approach  to  problems such  as those at  OPTS.
However,   they  have   often   been  designed  and  used   without   an  adequate
understanding of  their  limitations.   The  fundamental  difficulty  in  applying
classical  MADT  or  scoring methods  to  priority-setting  in chemical regulatory
agencies is  that independence of the  criteria may  not  be  assumed; in   fact,
synergistic  relationships  between  the  criteria  is  the  rule  rather than the
exception.  Therefore, the linear formulations cannot be made to work.
                                      111

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Development  of  scoring  systems  is becoming  widespread in  Federal regulatory"
agencies.   Some  large conmitments  of  resources are being made for long-range
study of  how scoring may be more  widely used.  An important  first step  is to
study and appreciate  what has  already been done  in the closely related fields
covered by  these  papers. This annotated'bibliography was initiated to provide
the literature groundwork for  what promises to be  an  exciting effort over the
next few  years.   It  was  completed by Tracer Jitco  Inc.,  for the U.S. Environ-
mental Protection Agency - Office  of Pesticides and Toxic Substances.

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Annotated Bibliography

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Aschenbrenner KM.   1977.   Influence  of attribute formulation on the  evaluation
of  apartments  by  multiattribute utility  procedures.   In:   Jungermann  H,  de
Zeeuw  G  eds.    Decision  making  and  change  in  human affairs.    Dordrecht,
Holland: Reidell, p. 81.
    The robustness  of  multiattribute utility (MAU)  measures against attribute
variations  was  investigated  within  the  framework  of  students   evaluating
off-campus  apartment   facilities.    Two   groups  of  students  developed   two
attribute  sets  against  which  descriptions  of   lodgings were  evaluated.   The
students  first  intuitively  rank-ordered  the   lodgings  according  to   their
impressions  of  suitability for student  housing.   They  then used  two  MAU
methods for the decomposed  evaluations:  a  riskless simple rating procedure  and
the risky  basic reference  lottery  ticket.   Initial results  suggest that  the
MAU evaluations are not  robust  against differences in attribute sets; both  MAU
methods  reveal  less   agreement  between  groups  than   the  groups'  intuitive
evaluations.   It  is   noted,  however,  that  elimination  of   two  attributes,
monthly and investment  costs, yields a much  better convergence between the  MAU
evaluations based on the otherwise different attribute sets.

Aumann RJ.  1962.  Utility theory without the completeness axiom.
Econometrica 30:445.
    A utility  theory  is  developed  that parallels  the   von-Neumann-Morgenstern
utility  theory,  but  makes  no   use   of  the  assumption  that   preferences   are
complete,   i.e.,   that   any  two   alternatives   are   comparable.   The   von
Neumaim-Morgenstern utility theory  with the completeness  axiom  is  reviewed,
and  reasons  for   dropping  the  completeness   axiom   are   offered.   Proofs
demonstrating the similarity of the  two theories  are presented.

Aumann RJ.  1964.  Utility theory without the completeness axiom: A correction.
Econometrica 32:210.
    A correction is presented for two theorems  published in another article by
this author.  The correction is explained  for Theorem B  and  it is  noted that a
corresponding correction must be made  for Theorem C.

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Bacharach M.  1975.  Group  differences  in the  face  of differences  of opinion.
Manage. Sci. 22:182.
    The problems  of ranking individual  opinions  in a group decision situation
is  addressed.   The  problem  is  posed  mathematically  in  an  abstract  form
encompassing  a  wide  range  of hypothetical  cases,  allowing  small  and  big
differences  over objectives  as well  as  over probability  assessments  of  the
facts.  General rules  are then derived  for  generating a group ranking  for  the
acts  which  simultaneously  satisfy  axioms referring  to  varying extreme  cases.
On  certain  assumptions,  the  group ranking  of  acts  implies  an  underlying
consensus  about  the  facts.    Different  axioms  of  group  choice  leading  to
different formulas  for consensus are demonstrated.  Both positive  and negative
results  are achieved.   Under  two  alternative sets  of  appealing axioms,  the
group's  implicit  consensus  is given as a  linear  opinion pool;  that  is,  the
consensual probabilities are  weighted averages of the individual1  ones.   On  the
other  hand,  under a third  set of  reasonable  axioms,  the group ranking  cannot
be  determined by any  rules  for  combining  the  probabilities  separately  and
combining the  utilities.  It  is concluded that  this impossible result  depends
on  wanting  the rule to  work  for cases  of extreme  differences over  ranking  of
acts.

Bajgier  SM  et  al.   1978.   Multiattribute  risk/benefit  analysis  of  citizen
attitudes  towards societal  issues  involving  technology.   In:  Zionts  S,  ed.
Multiple criteria problem solving.   Berlin:   Springer-Verlag,  p. 424.
    Factors  determining  public attitudes  and  responses  to  societal   issues
involving   technology   are   examined.    Ten  politically  sensitive   issues,
including  genetic research,  nuclear energy,  and  the use  of saccharin, were
presented  to  85   college  students.   Data  collected  included  the perceived
economic,  environmental,  physical,   and  psychological  risks   and benefits
associated  with  each  of these  issues.  Multiattribute  utility  models were
developed  to predict  and represent aggregated perceived  risks,  benefits,  and
attitudes  regarding  these issues.   It  is  felt  that  results  should  provide
policy makers  and researchers with  a better  understanding  of the factors  the
public considers  important and the cognitive processes employed in formulating
an  overall social attitude  or  preference regarding  these issues.

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Bauer  V  et  al.   1977.   Applications  of  multi-attribute  utility   theory:
Comments.  In:  Jungermann  H,  de Zeeuw G, eds.   Decision  making and change  in
human affairs.  Dordrecht, Holland: Reidel, p.  209.
    Three papers  reviewing  the applicability of  multiattribute  utility  theory
(MAUT) are discussed.   The  problem of MAUT model validation is examined, with
the conclusion  that,  except in very  simple  laboratory experiments, validation
of  MAUT makes  no  sense at  all.   The  didactic potential of  MAUT  is then
considered with reference to  the problem of multigroup decision making.  Next,
the  absense  of  real-world applications  of  MAUT  is  discussed,   and   it   is
concluded that  a  misconception of MAUT  is  responsible for  its  limited  use by
analysts.   It  is argued  that  simple MAUT  models  are  capable   of  handling
complex decision-making problems in the real world.

Bell DE.   1978.   Interpolation Independence.   In:    Zionts S,   ed.  Multiple
criteria problem  solving.  Berlin:  Springer-Verlag, p. 1.
    The  decompositions  of  multiattribute  cardinal   utility  functions  which
result  from assumptions  based  on  interpolation  independence  are described.
The decompositions discussed  involve only  single attribute marginal  utility
functions, together with constants, and  are  stronger than other decompositions
of  this  type.   Complete proofs are  not  given, but may  be obtained  from the
references.

Blin JM et al.  1978.   A multiple criteria decision model for  repeated choice
situations.  In:   Zionts S, ed.  Multiple  criteria decision making.   Berlin:
Springer-Verlag, p. 8.
    Explanations  of  observed   consumer  brand  switching  are  reviewed   and  a
multiattribute choice model is  proposed  which relies  on weaker  input data than
that required  by  similar models.   It is demonstrated  that  the origin  of the
brand-switching   phenomenon  can  be   explained  by   the   interaction  of  two
factors:  (1)  multiplicity of evaluative dimensions  for  the brands;  and (2)
consumer uncertainty  over salient attributes and  product  performance  on these
attributes.  The  analysis  also  integrates  two  apparently  divergent views  of
consumer  choice:   the  deterministic  view  which  has  evolved around  multiple
attribute choice  models and  the stochastic view which has been  proposed  to

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explain  brand  switching.    It  is  concluded  that,  far  from  being  a random
element superimposed  over  an intrinsically multiattributed evaluation  process,
brand  switching appears in  the  model as  a  perfectly  rational  strategy for a.
consumer  faced with  imperfect  knowledge about  multiattributed  brands.   The
applicability  of  the  methodology  to  other  existing  multiattribute choice
models is briefly discussed.

Bolinger JJ  et  al.   1978.   Decision analysis utilizing multi-attribute  utility
theory in engineering evaluation.
IEEE Trans.  Power Appar. Sys. PAS-97:1245.
    The  application of decision  analysis using  multiattribute utility theory
to  a  power  system  engineering evaluation  is demonstrated  through  an  example
problem  involving  the  evaluation   of   streetlight  expansion options in  a
regulated  utility.   The  streetlight  example  problem  is   defined  and  then
presented in terms  of a decision  tree.   The methodologies of  establishing the
main  and subobjectives,  determining  the single  attribute  utility  functions,
quantifying  the preference  trade-offs,  and-  calculating  the scaling  constants
are  illustrated.    A  detailed problem analysis  is  also  performed,  including
expected value  and  sensitivity  analyses.  The multiattribute decision  analysis
is  compared  with evaluations that consider  only a  single decision  criterion,
and  the  advantages  of  the  multiattribute  analysis  are  documented.   It   is
concluded that  this theory  allows a  decision maker to  account for  impacts  on
all  relevant  areas  when making a   decision,   and  results  in  a   completely
documented,  sound  decision.   Examples where  multiattribute  utility  theory can
be used are  cited.

Bowman EH.   1963.   Consistency and optimality in  managerial  decision making.
Manage. Sci. 9:310.
    Some  research,  ideas,  and  theory  about managerial  decision  making  are
reported.  Aggregate production  and  employment  scheduling  are discussed with
specific  reference to  the Holt,  Modigliani, Muth,  and  Simon (HMMS)  decision
rules.  The  idea  that management's own  past decision  can be incorporated into
a  system  of  improving  present  decisions  is proposed.   Decision  rules  are
developed, with the  coefficients  in the rules derived  from management's past

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decision  rather than  from a cost  or value  model.  Half  a  dozen test  cases
illustrate  and  test  these  ideas.   Some  rationale  about  decision  making  in
organizations  and  criteria  surfaces  is supplied  to help  interpret  the  major
ideas presented.

Charnetski  JR  et al.   1978.  Multiple-attribute decision  making with  partial
information:  The comparative hypervolume criterion.
Naval Res. Log. Quart.  25:279.
    An  approach   is   presented  for   analyzing  multiple-attribute  decision
problems  in which  the  set  of  actions  is  finite,  the  utility  function  is
additive,  and  the decision  maker is  operating with only  partial information
about the situation.  The  construction of a set of feasible weight vectors  for
the  various  criteria   from  an  ordinal  rating  by  the  decision  maker   is
discussed.   The Comparative  Hypervolume  Criterion  (CHC)   is  introduced  for
choosing  an action when  the  set of  feasible weight vectors  is  not  a unique
point,  and  the Monte Carlo  method  developed for  accurately approximating  the
numerical quantities  used by the  CHC is described.   The  numerical  method  is
summarized  and  a simple  example  is  provided to  evaluate the efficiency  of  a
computer code developed  to implement the method.

Charnetski  JR  et al.   1979.  Multiple-attribute decision making with  partial
information:  The expected-value criterion.
Naval Res. Log. Quart.  26:249.
    The  multiple-attribute  decision  problem   with  finite  action  set   and
additive  utility function  is  considered.   It  is  assumed  that  the  decision
maker  cannot specify  nonnegative weights  for  the  various  attributes which
would  resolve   the  problem, but  that  he   supplies  ordinal information about
these  weights   which  can be  translated  into  a  set  of   linear constraints
restricting  their  values.  A bounded polytope  of feasible weight vectors  is
then  determined.  It  is  further  assumed  that each  element  of  the   bounded
polytope  has  the same  chance  of being  the  "appropriate one."   The  expected
utility value of each action is  computed on that supposition.   The computation
method used  a  combination of numerical integration  and Monte  Carlo simulation
and  is  deemed  equivalent to  finding  the  center  of   mass  of  the   bounded
polytope.   Comparisions  are made  with  the comparative  hypervolume  criterion
and two numerical examples are presented.
                                       5

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Chipman JS.  1960.  The foundations of utility.
Econometrica 28:193.
    The  mathematical  foundations of  rational  behavior,   in the  sense  of a
transitive   ordering   of   alternatives,   are  developed   without  making   any
assumptions about  the  special character of the  set  of alternatives from which
choices  are made.   It  is  shown that  the  ordering  of  alternatives  may  be
characterized by a utility function,  where utility  is  represented by a vector
with real-valued components,  such vectors  being  ordered lexicographically.  It
is stated  that  if  an axiom permitting comparison  of intensities is permitted,
such  a   utility   index  must   be  unique  up  to   transformation  (such  as
proportionality  transformations)  preserving   group   operations.    A  purely
topological  axiom,  called the  axiom  of substitution,  is  shown  to imply that
utility is real-valued, i.e., that the above vector has only  one  component.

Churchman  CW et al.  1954.  An  approximate measure of value.
J. Ops. Res. Soc. Am. 2:172.
    A method for estimating  importance on  a scale  of value is presented, based
on actual  or verbal choices  of decision makers.   It  is  felt  that the method
can be  applied  to  any number of objectives or  outcomes,  and  to  any number of
decision  makers.    It  is  observed that  measures  of  the  reliability  of   the
estimates  can be obtained, but  that the  method  does not  provide any estimate
of the accuracy or bias of the  judgments.

Dalkey  NC.  1976.   Group  decision  analysis.   In:    Zeleny  M,  ed.  Multiple
criteria decision making.  Kyoto 1975.  New York:  Springer-Verlag,  p. 45.
    Group  decision making is investigated.  It  is  shown that consistent group
preference  functions  can be  formulated  by the  use  of  anchored  scales, i.e.,
individual  preference  scales  with fixed  reference objects.   It  is  observed
that  no  general  resolution  of  the   aggregation   problem  for  probabilities
appears  feasible,  but that  a justification  for the use  of  group  probability
judgments  can  be made based on a family  of theorems  to  the  effect  that  the
accuracy  of  a  group judgment is  always  greater  than (or,   at  worst, equal  to)
the  average accuracy  of  the  individual judgments.   Some empirical  data  and
analytical results  are  felt to indicate that these  aggregation rules are more
generally  applicable and more powerful than has  been assumed  in the  past.

                                       6

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Daves RM.   1971.   A case-study  of graduate  admissions:   Application of  three
principles of human decision making.
Am. Psyehol. 26:180.
    Three  major  principles  are  discussed  that have  been  determined  to  be
applied  to  the   decision  making  problems  of  evaluating  graduate  school
applicants.  As a case  study of  the admission  decision of  one university's
psychology department,  the  work is concerned with  the  decision making process
rather than  with  the validity  of the criteria  on  which  decisions  are based.
The three  principles  examined are:   (1)  that a simple  linear  combination of
the criteria considered by the  admissions  committee will  predict performance
in  graduate  school better  than the  committee;  (2) that  the behavior  of the
committee  can  be  simulated   by  a  linear   combination   of  the  criteria  it
considers;  and (3)  that the paramorphic  representation  of  the  committee's
judgements  should be  more  valid  than  the  judgments   themselves.   Multiple
regression  analysis  was  performed  using  four  variables  commonly  used for
evaluating applicants.   It  was found that a  paramorphic  representation of the
admissions  committee's   judgments  predicts  the   first-year  evaluation  better
than  does  the  judgment  itself.   A  cost-benefit analysis  of  the  method  is
presented, and the ethics of using a  regression  analysis  in this situation are
considered.

Diamond PA.  1965.  The evaluation of infinite utility streams.
Iconometrica 33:170.
    Impatience implications of several axiom sets assumed for preferences over
an infinite  future are explored.   Sufficient  conditions  for  the existence of a
continuous utility function are presented.   This  analysis  is  done both for the
product  topology  and the metric  function  equating the  distance between two
infinite streams to the maximal one-period difference between them.

Dyer  JS.   1973.   A time-sharing  computer  program for  the  solution of the
multiple criteria problem.
Manage. Sci. 19:1379.
    A description  is  presented of a  time-sharing computer program written to
implement a man-machine  interactive algorithm for the  solution of the multiple
criteria problem.  It  is stated that a unique  feature  of this  program is the

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man-machine dialog  which obtains information from the decision maker through a
series  of simple,  ordinal  comparisons.   This procedure  requires  the decision
maker  to  specify his local marginal rates of substitution  among criteria and
to  solve  a  step-size  problem at  each  of several  interations.   The computer
program was  written in  APL and  implemented on an  IBM  360-91  time-sharing
system.   It  may  be  used  successfully  by  untrained   individuals  to   solve
problems  involving  multiple criteria.

Edwards W.    1977.   How to use  multiattribute utility  measurement  for  social
decision making.
IEEE Trans. Syst. Man Cybern. SMC-7:326.
    Multiattribute  utility measurement  is  proposed  for determining  individual
or  group  values, showing  how  and how much they differ and how the  extent of
such   differences   can   be  reduced.    Ten   steps   concerning   the  use  of
multiattribute  utility  measurements are  explained.   Data  are  then presented
illustrating  the application of this technique  to  three  situations: land use
regulation  by  the  California  Coastal  Commission,  selection  of   government
research  programs,  and development  of  a water  quality index.   A different
approach  was  used  in each  case.  It is  felt  that face-to-face  discussion was
most  successful in producing agreement,  while procedures  depending on written
or  verbal feedback of  other  expert's judgments  were  less  so.  The  importance
of  simplicity in any elicitation procedure is discussed.  It  is concluded that
exploitation  of multiattribute  utility  measurement permits  a decision  making
agency to  shift  attention from the specific actions  being  regulated  to the
values these actions serve  and  the  decision  making mechanisms  that implement
these  values.

Einhorn HJ.  1971.   Use of nonlinear, noncompensatory models  as a function of
task and  amount of  information.
Org. Beh. Human Perform. 6:1.
    The effect of  the  two variables  of  type of decision  task  and  amount of
information was  assessed  as  the  two variables  affect  the use  of  nonlinear,
noncompensatory models   in  decision  making.  The  former variable  was found to
have  a marked  effect  on the kind  of combination model used  by the subjects,

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while the  latter  variable  had a significant effect  on  the accuracy with which
the various models  could adequately represent  the decision process.  The major
findings are deemed  to  show considerable use of the nonlinear, noncompensatory
models with differential use  in the two decision tasks used.   It is felt that
results  for   amount  of   information   suggest  that  subjects   use  complex
combinations  of  models   (or  compound  models)   to  simplify  the  situation
cognitively.  In  addition,  it is felt  that  the claim that  decision makers do
not use additive models in  their strategies is given support by these data.

Einhorn HJ.  1972.  Expert measurement and mechanical combination.
Org. Beh. Human Perform 7:86.
    The  superiority  of  mechanically combining  components  as opposed  to  using
the global  judgment  for predicting some external criterion  is  discussed.  The
use of  components  is  extended  to  deal  with  multiple  judges  since  specific
judges may  be  differentially valid with  respect  to subsets of  components for
predicting  the  criterion.   These  ideas  are  illustrated  using  results  of  a
study dealing  with  the prediction  of  survival  on the  basis  of  information
contained  in  biopsies   taken  from patients having  a certain  type  of  cancer.
Judgments  were  made by  three highly trained  pathologists.  Implications  and
extensions  for  using  expert  measurement  and  mechanical  combination  are
discussed.

Einhorn  HJ et  al.   1978.   A  simple  multiattribute  utility  proceedure  for
evaluation.  In:   Zionts  S,  ed.  Multiple  criteria problem solving.   Berlin:
Springer-Verlag, p. 87.
    A simple multiattribute utility procedure  (SMAUP) is  developed  within the
context of  the  evaluation  of overall  performance  of players  in  the  National
Basketball Association  (NBA).   The  specific simplifications assume  that:   (1)
utility functions  for the  attributes are linear; (2) the  total utility  of  an
object is an additive function of the utility of  the attributes making  up that
object; (-3) the variables  are scaled so that they are monotonically increasing
in  utility;  (4)   the   relative  importance  of   the  attributes  is  correctly
identified  and  no  important  attributes  have  been  omitted;  and  (5)  the
attributes are essentially  uncorrelated with each other.   Results are  compared

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with  an  independent measure  of overall performance  (viz.,  the players picked
for  the  NBA all-star  team),  and  the advantages  of  SMAUP  versus  clinical
judgement  are  discussed.   Generally,  it  is  felt  that  SMAUP  is   a  useful
procedure  in   any  situation  where  the  above  assumptions  are  considered
reasonable.              ~

Farquhar  PH.   1974.  Fractional  hypercube  decompositions  of multiattribute
utility  functions.   Tech.  Rep.  222,  Dept.  of  Oper.  Res.,  Cornell  Univ.,
Ithaca, N.Y.
    Some  new results in  multiattribute utility theory .are  presented,  showing
how  fractional  hypercubes  induce  the multiple  element conditional preference
orders  used  to  specify  attribute  independence conditions  and how  they also
provide a  system of equations used to produce the corresponding multiattribute
utility decomposition.   Fractional hypercube  decompositions  incorporating  the
additive,    quasi-additive,   and    diagonal   forms   are   reviewed;    then,
decompositions   with  nonseparable   attribute  interactions   are  discussed.
Several special  cases  examined in detail give decompositions with  nonseparable
lower order  interactions  and  separable  higher   order   interactions.    Other
examples  illustrate hybrid decompositions which combine different  independence
conditions in  one form.  A thorough  discussion is given  of  the various  types
of  nonseparable and separable interactions appearing  in fractional  hypercube
decompositions.   Several examples  and  potential applications  to real decision
problems  are provided.

Farquhar   PH.    1975.    A   fractional   hypercube   decomposition   theorem   for
multiattribute utility  functions.
Oper. Res. 23:941.
    A general  method  is  presented  for producing  independence conditions  for
nonadditive  utility  decompositions  based  on  geometric  structures  called
fractional   hypercubes.    A   fractional   hypercube   is   defined   and    the
corresponding  multiple  element  conditional preference  order  is  introduced.
The main  theorem is produced  from the solution of  equations  that are  derived
from  transformation of   linear  functions  that  preserve  these  conditional
preference orders.   The computations  and  scaling  required in  implementing  the
                                       10

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main result  are  demonstrated  by obtaining four utility decompositions  on  three
attributes:  apex,  diagonal, quasi-pyramid,  and semicube.   The methodology  is
illustrated  with  geometric  structures  that  correspond   to  the   fractional
hypercubes.  Because  this method  is  so general and since fractional  hypercubes
illustrate the  interactions they ultimately produce  in  a decomposition,  it  is
argued that  an  analyst  will be able to tailor  his independence conditions and
utility  decomposition   to  a   particular  decision  problem  rather   than   be
restricted to a  few nonadditive decompositions.

Farquhar  PH.   1976.   Pyramid  and  semicube  decomposition  of multiattribute
utility functions.
Oper. Res. 24:256.
    The fractional hypercube  decomposition  theorem  for  multiattribute utility
functions  is applied  to  the  quasi-pyramid,   the pyramid,  and   the  semicube
fractions.   The  resulting  nonadditive  utility  models   illustrate   the  broad
range of  decompositions that  can be  obtained  with  this  fractional hypercube
methodology.  The pyramid  decompositions  have nonseparable  interaction  terms
for  each   pair  of  attributes,  whereas   the   semicube   decomposition  has
nonseparable interaction terms  for each proper subset of attributes.   Although
the   semicube    decomposition   is   much   more   general   than   the  pyramid
decomposition,  it is  suggested that  the latter  is simpler to   implement   in
practical problems.   It  is  noted  that  the illustrated computations and scaling
can be  performed with other  fractional  hypercubes to produce  various results
between these  two extremes.  A condensed version of the  fractional hypercube
methodology  is presented.

Farquhar  PH.    1977.   A   survey  of   multiattribute   utility   theory   and
applications.
TIMS Studies in  the Management  Sciences 6:59.
    An extensive  survey  is  presented of  the  state-of-the-art in multiattribute
theory and applications.   Particular attention is given  to recently developed
utility models  for evaluating risky decision alternatives  when the  attributes
describing  the   outcomes  of these  possible  decisions may  be  interdependent.
Nonrisky  and  risky  additive  utility   models  are  discussed,   as  well   as
                                      11

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multiplicative  and  quasi-additive  utility models and extensions, bilateral and
multilateral utility models,  fractional hypercubes, interdependent additivity,
parametric  utility  models,  approximation  methods,   and  trade-off  analysis.
Some practical  applications of multiattribute utility models  are reviewed and
directions  for  future  research  are  suggested.   A  brief  overview   of  the
terminology and results of  expected utility  theory  also  is  offered.

Farquhar PH.   1978.   Interdependent criteria in utility analysis.  In:  Zionts
s, ed.  Multiple criteria problem  solving.   Berlin:   Springer-Verlag, p. 131.
    Decision   problems  are   examined   where   the   evaluative  criteria  are
interdependent.  After a brief study of interaction effects in the statistical
analysis  of  multifactor  experiments,   a  classification  of   interactions '  is
developed   for  multiple   criteria   decision  problems.   The   classification
includes' artificial,  ordinal,  configural,  and  holistic interactions.   It  is
shown  that  some interactions are  removable  by transforming the response scale
or  restructuring  the  factors,  while  other  interactions  are not removable and
must be  considered  explicitly.  The interaction effects in various nonadditive
utility models  are  discussed, and the  method of fractional hypercubes  is used
to interpret the structrual forms  of  these models.

Fisher  GW.   1972.   Four methods for assessing  multi-attribute utilities:   An
experimental validation.  Tech.  Rep.  037230-6-T. Ann Arbor, Mich:  Engineering
Psych. Lab., Univ. Mich.
    Decomposition  evaluation  procedures  are  investigated   to  determine their
superiority  over holistic  intuitive  judgements.  The  theoretical  basis  for
multiattribute  value  assessment  is  first described  and it is concluded  that
while  additive evaluation  models  are appropriate  for most  riskless decisions,
nonadditive   models   are   frequently  required  for   decision  making  under
uncertainty.   The  sensitivity of  evaluation models  to assessment  errors   is
then  discussed.   Next,  four  procedures  are  described  for  constructing  a
                                                             '*£
decomposed  evaluation model  and  the  general problem  of validating evaluation
procedures   is  considered.    Finally,  two  experiments   are  presented    to
demonstrate  that  the  four  decomposition procedures  described  can  provide  an
appropriate measure of subjective  value.
                                       12

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Fischer GW.  1975.  Experimental applications of multi-attribute utility models
utility probability and human  decision  making.  In:  Wendt D, Vlek CAJ,  eds.
Dordrect, Holland:  Reidel, p. 7.
    Experimental  studies  attempting to model the  subjective trade-off  process
involved  in  decision  making are reviewed.   Literature devoted to  the goal  of
developing procedures which can be used to improve  the  subjective evaluation
process also is reviewed.  Formal  models for  both riskless and  risky choice
are  discussed.   Some practical  scaling procedures  are briefly  outlined, and
results from experimental attempts to validate  these scaling  techniques are
presented.   The superiority of non-additive evaluation procedures  to additive
evaluation methods  is also considered.

Fischer   GW.    1977.    Convergent   validation   of  decomposed  multi-attribute
utility assessment  procedures for risky and riskless decisions.
Org. Beh. Human Peform. 18:295.
    The relative  merits of holistic  and decomposed assessment  procedures are
considered,  and  decomposition  procedures for both  risky  and riskless decision
making  are  described.  Next,  the  validity  of  evaluation   functions  for both
procedures is assessed.   Conjoint  and function measurement  are  considered for
the  holistic  evaluation  method,   and  convergent  or  conjoint  validity   is
examined  for the  decomposition approach.   Finally,  an  experiment  comparing
holistic  and decomposed assessment procedures  is  discussed in which  the two
approaches   to  scaling  were   found   to  assign  very  similar  utilities   to
three-dimensional job descriptions  for both risky and riskless decisions.

Fishburn PC.  1965.  Independence in utility theory with whole product sets.
Oper. Res. 13:28.
    Because it  is felt  that a  satisfactory definition  of  independence based on
multidimensional  consequences  and  hypothetical   gambles   composed  of  such
consequences is  lacking,  a definition  of independence is  presented  for cases
where  the set  of  consequences  X  is  a product  set  (X..) (X. )...(X  ),  each
element  in  X  being   an   ordered   n-tuple   (x.,  x.,...,x  ).   The  definition
is  stated in terms of indifference  between special  forms of gambles  formed
from the  set of consequences.   It  is  then shown that if the condition  of the
                                      13

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definition  holds,  the  utility   of  each  (x. ,   x«,...,  x )  in  X  can  be
                                               12        n
written  in  the  additive   form u(x, ,  x,, , . . . ,  x )  =  u(x.)  +  u(x_)   +   ...
                                     12        n         l         L
+  u(*n)»  where  u is  a real-valued function defined  on  the  X.,  i =  1,  2,
. .., n.   Uniqueness  properties  for the individual  utility functions are also
offered.   The  development  is  carried  out  for  two   factors  and  then   for
n-f actors.   It  is  noted   that the development  is  free  from  any  specific
assumptions about  the utility  function (e.g., continuity,  differentiability),
except  that it  be a  von  Neumann -Morgens tern utility  function,  and  that  it
places no  restrictions on  the  natures  of  the individual factors.  An example
is  offered to  illustrate  one  type of  situation  with which the  theory  is
concerned,  and  some  comments are  given about experimentation  and extension to
the  case   where  the  set  of   consequences  X   is   a   proper  subset  of
Fishburn  PC.   1965.   Independence,  trade-offs,  and  transformation bivariate
utility functions.
Manage. Sci. 11:792.
    Interrelationships between independence in the utility sense, trade-off  or
indifference  curves,  and  transformation curves -are  examined  with  respect  to
bivariate  utility functions,  i.e.,  those  defined  on  rectangular  regions  in
the  xy-plane   and  on  50-50  gambles  formed  from  points  in  such   regions.
Following  the  form  in which  a  set  of  basis  axioms  of  utility  are   stated,
independence is defined  in terms of indifference between 50-50 gambles.   It  is
shown  that,  if  the condition  of  the  definition holds,  the bivariate  utility
function  of (x,  y)   can  be written  in  the additive  form.   The  concepts  of
trade-off  curve and  transformation curve are also  defined  on the basis of the
indifference  relation  but  are  seen  as  not  concerned with  gambles.   After
exploring  relationships  among the  three  notions,  it  is  shown how the  utility
curves  for  the two  variables under  independence  can  be   constructed  on the
basis of two trade-off curves.
                                       14

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Fishburn PC.   1965.   Markovian dependence in utility theory with whole  product
sets.
Oper. Res. 13:238.
    The  notion  of  Markovian dependence   in  utility   theory   is   developed,
considering an entire  product  set as the basic set of consequences.  Markovian
•dependence  in  the utility  sense  is  defined  on  the  basis   of indifference
between  special  types of  gambles for several  sequential processes.  Theorems
stating  how  the basic utility function may be broken up  into  additive  forms
under  Markovian   dependence   are  presented.    In  addition,   the  notion   of
stationary  transition  value   mechanisms  is  explored   in   the  context   of
completely homogeneous sequential processes.

Fishburn  PC.   1966.   Additivity  in  utility theory  with  denumerable   product
sets.
Econometrica 34:500.
    The  expression  of  utility  in  the  additive  form  is   extended   to   the
denumerable-set  context.  The extension  is   accomplished  by  a gross  axiom
containing three basic parts:  monotonicity, additivity,  and  convergence.   The
axiom is then  interpreted  in  three  settings for utility: gambles or  lotteries,
utility differences, and binary-choice probabilities.

Fishburn  PC.   1966.   A  note  on  recent   developments   in   additive   utility
theories for multiple-factor situations.
Oper. Res. 14:1143.
Developments in  additive utility theories  are  summarized for  research  workers
interested in  the  subjective  evaluation of multiple-factor  alternatives.   In
particular,  assumptions  (axioms)  that  permit  the  use  of an  additive-value
formula  are presented.   It is  felt that these may enable  the  user  to test  the
warrantability  of   an additive  procedure  in  specific  situations   where   the
theory might be applied.
                                      15

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Fishburn   PC.    1967.    Interdependence   and   additivity   in   multivariate
unidimensional expect utility theory.
Int. Econ. Rev. 8:335.
    Additivity in expected  utility  theory  is investigated in the presence of
interdependencies  among  different coordinates when the set  of pure prospects
is in  the  Cartesian product of n-other sets.  A special case of  the theory is
mentioned  which  deals with additivity  in the  expected utility  context when
there  are  no interdependencies among  the coordinates.   The additivity theorem
is  developed and  its  proofs are  given.   Admissible  transformations  also are
specified  for the  expected  utility function.

Fishburn PC.  1967.  Methods of estimating additive utilites.
Mange. Sci.  13:435.
    Additive  utility  formulations  for  risky  and  nonrisky multiple-factor
decision  situations are  reviewed.  Twenty-four methods  of estimating additive
utilities  are listed and classified.   References  to the  theory  and technique
of  each method  are given along with a short discussion of each.   A number of
examples are used  to illustrate the methods.

Fishburn PC.  1968.  Utility theory.
Manage. Sci.  14:335.
    The concept  of utility is discussed, explaining  why people are interested
in  it and  how  it  is  interpreted and used  in  the management and behavioral
sciences.   Several utility  theories  are summarized and a semi-technical  survey
of  particular theories  is  presented for readers  interested  in greater  depth.
A prescriptive interpretation of  utility theory is  emphasized.

Fishburn  PC.  1970.  Utility  theory  with  inexact preferences and degrees of
preference.
Synthese  21:204.
    Various  properties   of  the strength-of-preference  comparison  relation are
examined   along   with  properties  of  simple  preferences  defined  from  the
relation.   The  investigation  recognizes  an  individual's  limited  ability to
make  precise judgments.  The  relationship between the concept  of comparable
preference  differences  and ordinal,  cardinal,  and measurable  utility  also is
considered.
                                       16

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Fishburn  PC.   1973.   A mixture-set  axiomatization of  conditional  subjective
expected utility.
Econometrica 41:1.
    An axiomatization  is  presented for  a states-of-the-world-type conditional
subjective  expected  utility  model.    The  axioms   consist   of  extensions   of
previously  derived  axioms   for  measurable  utility,  a  generalization  of   an
averaging  condition,   and   several   structural  conditions.   The   structural
conditions are  examined in  some  detail, and  examples  are  given  showing what
happens to the numerical model when the  conditions  do  not hold.   The numerical
model is found to express the utility of an  act,  given  an event, as a weighted
sum of the utilities of the  act given events that partition the initial  event,
the weights being personal  probabilities for  the partition  events conditioned
on  the  initial  event.   The  theory   is  compared  to  other  theories  for
conditional expected utility.

Fishburn  PC.    1973.   Bernoullian utilities   for  multiple-factor-situations.
In:   Cochrane  JL,  Zeleney M,   eds.    Multiple  criteria  decision  making.
Columbia, S.C. Univ. of S.C. Press, p. 47.
    Under the  assumption  that an  individual has a  von  Neumann-Mor gen stern  or
Bernoullian utility function  u  on a  product  set  X,  x  X- x  ...x X  (with
gambles defined on  this set on n-tuples), preference conditions are discussed
which are  necessary and  sufficient  for  a special  form  for u  which involves
sums and  products of functions on the   several X.  factors.   It is  noted that
the preference conditions for  this form specify a  certain type  of consistency
among the  preference orders  over gambles defined  on one factor  for  various
pairs of fixed n  - 1 tuples of values  from  other n - 1  factors.   The special
form  is   presented  in the  three-factor  case.   A two-period  income-stream
example then  illustrates  the  potential  applicability of the two-factor case
when simpler forms  cannot be used  for u.  The  general theory for  the n-factor
case and a sufficiency proof are given  and  aspects of scaling  procedures  for
the functions and constants of the theorem are discussed.
                                      17

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Fishburn  PC.   1976.  Conjoint  measurement in  utility theory  with incomplete
product sets.
J. Math. Psychol. 4:104.
    A set of  axioms  is  introduced for additive conjoint measurement in utility
theory when the set  of consequences is a  subset of  the  Cartesian product of
two sets.   Axioms  for preference, patterned  after the von Neumann-Morgenstern
axioms,  are presented  first.   These axioms  imply the existence  of a utility
function on the set  of  consequences  and on gambles formed from the elements in
that  set  that is unique  up to  a positive linear  transformation,  but they do
not imply the additive  form of  conjoint measurement.   It is  then shown that
the addivite  form  results  when  one of the  basic axioms is  strengthened,  so
that  the  utility of  each  consequence equals  the sum of  the  utilities  of its
two factors.  Uniqueness properties  of  the  factor utilities are also discussed.

Fishburn PC.  1977.   Approximations  of  two-attribute utility functions.
Math Oper. Res. 2:30.
    Von Neumann-Morgenstern utility functions are  assessed  from the viewpoint
of mathematical  approximation  theory since  it  is felt  that  the  independence
conditions  that  characterize two-attribute and other  special  forms of utility
functions  may be  inapplicable  because  of evaluative  interdependences among
the  attributes.   The assessment  focuses  on  approximations  v of  the utility
function   u  that   can  be   written   as   v(x,y)  =   f,(x)g,(y)  +   ...   +
f (x)g (y)    where   f,    and/or    g,    are    based    on    single-attribute
 mm                 1              1
conditional utility  functions.   It is observed that the paper does not rely on
independence  axioms  that  enable  u(x,y)  to  be  expressed in  simplified forms
when  they are valid.

Fishburn  PC.   1977.  Multiattribute  utilities in expected utility  theory.  In:
Keeny RL, Raiffa H,  eds.  Conflicting objectives.  New York:  Wiley, p. 172.
    The  problem of assessing multiattribute  utilities  within  the context of a
von Neumaim-Morgenstern utility  function on  a multiattribute  utility space is
examined.   Possibilities  for simplifying multiattribute utility assessment are
investigated, with  emphasis on  the  idea of expressing the n-attribute utility
function   as  some   combination   of   conditional   single-attribute  utility
                                       18

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functions.   To  this end a sequence  of increasingly sophisticated  independence
conditions  is considered,  beginning  with  the  concept  of  value  independence
among  attributes.   Also  examined  are  aspects  of  the  concepts  of utility
independence  and   generalized  utility  independence,  which,   in  appropriate
conditions,   are   observed   to    lead    to    additive,   multiplicative,    or
quasi-additive   forms  for  the  utility  function.   This   is   followed  by   a
discussion  of the  concept of  bilateral independence,  which  can  accommodate
more interdependencies  among  attributes  but still -allows  the utility  function
to be written in terms  of conditional single-attribute utility  functions.  The
discussion  of   independence  concludes  with  a  general  view   of   fractional
independence   that  involves   numerous   special   cases,   including  utility
independence  and bilateral independence.  The  final section, which is viewed
as  not  predicated  on  any  independence  conditions,  considers  the  use   of
conditional  single-attribute  utility  functions  in  constructing  approximations
of arbitary n-attribute utility functions.

Fishburn  PC.   1978.  A  survey   of  multiattribute/multicriterion  evaluation
theories.   In:   Zionts  S,  ed.   Multiple  criteria  problem  solving.   Berlin:
Springer-Verlag, p. 181.
    Multiattribute/multicriterion  evaluation   theories  are   reviewed.    The
general  formulation  for  the  survey  is  presented   first,  followed  by  a
discussion of classificatory  attributes of the  theories.   Later sections  are
organized  around  a three-valued  attribute  whose  values   correspond  to  the
familiar  categories of  decision   under  certainty,  decision  under risk,  and
decision under uncertainty.   Reference is  occasionally made to  various choice
models,  but  the emphasis is  on  evaluation  theories  rather than assessment
methodologies in the main body of  the  paper.   The  final   section  presents  a
brief review of  assessment literature.

Fishburn PC  et   al.   1967.   Additive  utilities  with incomplete  product  sets:
Application to priorities and assignments.
Oper. Res. 15:537-
    Additive  utilities   are    investigated   for  cases  where   the   set   of
consequences  is  a  subset of the product of n-other sets, i.e.,  an incomplete
product set.  It was found that, under a finiteness restriction, an additivity

                                       19

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axiom leads  to  an additive utility representation  for  the elements in the  set
of  consequences.   The  potential  usefulness of  the theory  in connection with
incomplete   product  sets   is  demonstrated   with  priority  orderings   and
assignments.

Fishburn  PC.  1974.  Lexicographic  orders, utilities  and  decision  rules:   A
survey.
Manage. Sci. 20:1442.
    Recent   developments   in  lexicographic  orders,  preferences,  utilities,
probabilities,  and  decision  rules   are   reviewed  and  some  new  results   are
presented.   Two   trends   in  the  literature   on   lexicographic  orders   are
identified:  the   pragmatic  and  the  mathematical.    For   the  former,   two
axiomatizations  for lexicographic preferences  that avoid direct reference to
the  importance  ordering  of  criteria are  offered,  along  with  comments  on
additive  utilities, dictators  in  social  choice  theory, and  an example which
illustrates  the  failure of the axiomatizations when  the number of criteria is
infinite.   Modifications  on  the  basic lexicographic  idea  are  discussed that
are designed to make the  lexicographic approach more palatable in studies of
normative  decision making and choice  behavior.   Focus  is then  shifted to  the
mathematical question of whether  a  preference order  can be  represented  by a
real-valued  function and,  if not, what  sort of  lexicographic  representation
might  apply.  Necessary and  sufficient conditions  for  unidimensional utility
are considered.   Examples,  including several in  consumer  choice  theory,   are
presented,  as  well as  some  related material for mapping  into real intervals.
The idea  of lexicographic  representations in structures that  possess some type
of  additive operation  is  examined.   Examples  of  lexicographic  probability
                                                      b
representations which cannot be characterized by a single probability measure
are presented.  Finally, lexicographic  expected utility  is discussed.

Fishburn   PC.    1974.   von  Neumann-Morgenstern   utility  functions   on   two
attributes.
                                                             r-
Oper. Res.  22:35.
    Five  special  forms for  a  von Neumann-Morgenstern  utility  function  on a
product  set  (A  times  X)   are  examined.   Each  form  expresses  the  utility
function  as  a  combination  of functions defined on  the  separate factors of  the

                                       20

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product set.  The  five  forms  include the additive and the multiplicative  forms
and  the additive  form  with   independent  product.   Necessary  and  sufficient
preference  conditions  are  indentified  for  each  form,  along  with  admissible
transformations on the  single-argument functions.

Fishburn PC.  1975.  Unbounded expected utility.
Annals. Stat. 3:884.
    Axioms  are  presented  for a  preference  relation on  P,  a convex  set  of
finitely additive probability measures defined on a Boolean algebra of subsets
of a  set X of consequences.  The  axioms are necessary and  sufficient for the
existence of  a  real-valued utility function  u  on X for which  p is preferable
to q  if and only if E(u,p) is  greater than E(u,q),  for  all p and q  in  P.  A
slightly simpler  set  of  axioms  is  found  to yield  the  same  results  when the
algebra is  a  Borel algebra and  every measure in  P  is countably additive.  The
axioms  allow  P  to contain nonsimple probability measures  without necessarily
implying that the utility  function is bounded.

Fishburn  PC  et  al.    1974.    Seven  independence  concepts  and  continuous
multiattribute utility  functions.
J. Math. Psychol. 11:294.
    Seven independence  concepts are  examined  based  on a preference relation on
the  set of  simple  probability measures defined  on a  set  of multiattribute
consequences.   Three  of  the  independence  relations involve  gambles  and the
other  four  are  based   on riskless preferences  over  the  n-tuples  in  the
consequence set.  The main theorems  state  conditions under which  one or more
of  the  risky   independence  relations   can  be  derived   from   a  riskless
independence  relation   in conjunction  with  other  conditions.    The  other
conditions  include a  risky independence condition which differs from the ones
derived, the  assumption  that  the  consequence  set is  a convex  subset  of  a
finite-dimensional Euclidean  space,  and the  assumption that  the  individual's
von Neumann-Morgenstern utility function on the consequences set is continuous.
                                      21

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Fishburn  PC   et   al.   1975.   Generalized   utility   independence  and  some
implications.
Oper. Res. 23:928.
    The  concept of  generalized  utility  independence  is introduced  and three
functional forms  for a multiattribute von Neumann-Morgenstern utility function
are derived,  subject to various generalized  utility independence  assumptions.
The three  forms are the additive,  the multiplicative,  and the quasi-additive,
each  of which expresses  the multiattribute  von  Neumann-Morgenstern   utility
function  as  a  combination  of  utility  functions defined   on   the  separate
attributes.  It is  demonstrated  that if the utility function is unbounded from
above  and  below,  then given the  three  forms,  either  reversal  of preference
over some attributes occurs or else  the additive  form must hold.

Giauque  WC et  al.   1976.  Application of multidimensional  utility  theory  in
determining  optimal  test  treatment  strategies  for streptococcal  sore  throat
and rheumatic  fever.
Oper. Res. 24:933.
    A model  is presented for determining optimal test and treatment strategies
for  streptococcal  sore  throat  and  rheumatic  fever, in  which the formulation
and  assessment of a  multidimensional  utility  function  are a  central part.
Unanimity  of opinion  regarding  the proper course  of  medical  care implied by
the   utility  theory  is  explained   by  the  overriding  importance   of   the
catastrophic   possibilities   of   either  severe  antibiotic  reaction   or   the
long-term  effects  of  rheumatic  fever.   As  the probability  of experiencing a
catastrophic  antibiotic  reaction  was  the  lesser  of  the  two,  the  option of
using  penicillin  fairly liberally was  dominant.  Model  results also confirmed
the  propriety of  continued  prophylactic penicillin treatment and of  routine
community-wide streptococcal screenings.  Finally,  the  relative  effectiveness
of  a  physician was  compared  to  that of  a  nurse-practitioner in the diagnosis
and care of  streptococcal  infections, with the result that the nurse was shown
to  be  at  least  as  effective  as  the  physician.   It  is  concluded  that   the
complexity    and    time   demands    of   the   analysis   probably   preclude
patient-by-patient   analysis,  but  the  methods  could  assist  in determining
practices  for dealing with entire  groups of  patients with  specific  groups of
symptoms.

                                       22

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Goldberg  LR.   1968.   Simple  models or  simple  processes?   Some  research  on
clinical judgements.
Am. Psychol. 23:483.
    Because  the validity  of  clinical judgments  has been  questioned,  results
are  presented  of investigations  which  focused  on the  process  of  clinical
inference,   the  aim  of   the  investigations  being  to  simulate  the hidden
cognitive  processes  of   the  clinician  as  he  makes  judgmental   decisions.
Multiple-regression analysis  of  simple  linear models and  fixed-model  analysis
of variance  are examined and  it  is  concluded  that, although judges can process
information  in  a  configural way, the general linear model  is  powerful enough
to reproduce most of  these judgments with very  small error.   Results  are then
discussed  of attempts  to  improve  the   accuracy  of  judgments  of   practicing
clinicians.  The  hypothesis that  receiving  immediate feedback would increase a
clinician's judgmental accuracy was  not verified.   It is  felt that a good deal
more than outcome feedback is necessary to accomplish this goal.

Goldberg  LR.   1971.   Five  models of  clinical  judgement:    An  empricial
comparison between linear  and  nonlinear representations  of the  human inference
process.
Org. Beh. Human Perform. 6:458.
    Two  nonlinear models  which  had been  proposed  in previous research  as
approximations  of the  conjunctive  and  disjunctive  strategies  were   compared
with   the   linear,   logarithmic    and   exponential   models    as   potential
representations of  the  judgments made  by 29 clinical  psychologists,  each  of
whom attempted  to differentiate  neurotic  from psychotic patients on  the basis
of their MMPI profiles.   For this task the linear  model  was  found to provide a
better representation of the  judgments made  by all  clinicians  than did either
of the  nonlinear  models,   and  only  the logarithmic  model  provided  the linear
model with  any real  competition.   In addition,  it is  felt  that  the   serious
problems  endemic  to  all   of  the  nonlinear  models  call  into  question their
utility as potential judgmental representations.
                                      23

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Gorman  WM.   1968.   Symposium  on  aggregation:   The   structure  of  utility
functions.
Rev. Econ. Stud. 35:367.
    A  continuous  utility  function  is  defined  and  a  theorem  stating   the
separability  and  essentiality of  two  sets  is  proved.  A  decision  tree  is
developed  and  results are applied to  the theory of decision  over  time and  to
the  aggregation of production relations.  An alternative  approach is briefly
discussed  that  is  felt  to be easier to  apply  in the  case of complete  additive
separability.   The results  of relaxing  the  condition  of  strict  essentiality
are sketched.

Green PE et al.  1972.   Subjective evaluation models  and conjoint measurement.
Behav. Sci. 17:228.
    The  predicted  effectiveness  of  self-explicated  models   and  empirically
derived  evaluation functions  is compared.  Several  types of  measurement  and
scaling models  are applied to empirical data involving  a sample  of housewives'
preferences  for  profile descriptions   on 27   hypothetical   retail   discount
cards.   Additive conjoint measurement  is used  to  obtain part-worth  functions
for  the  various component descriptors.  In addition, subjects'  self-explicated
models  are  compared  with  actual   ranking of  the  discount  cards.   Results
indicate  that  additive  conjoint models provide good descriptions  of  the  data
and  that  self-explicated models also  show reasonable  accuracy  in predicting
actual  ranking.  No  significant  association was found  between differences  in
evaluative  behavior   and   a  battery   of   attitudinal   and  socioeconomic
measurements  obtained   from   the  same  subjects.   The  compensatory   type  of
subjective evaluation  model  used  in  this study  is described,  and  con-joint
measurement  is  briefly  explained.

Green  PE et al.   1973.   Consumer evaluation of discount cards:   A conceptual
model  and  experimental  test.
J. Retailing 49:10.
     The  application of  conjoint measurement to  a study of consumer evaluation
of  discount card  characteristics  is illustrated.  The  principles  of  conjoint
measurement  and its uses in  consumer  attitude research are briefly described;
then,  a  particular case of conjoint measurement, namely the additive model,  is

                                       24

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applied  to measure  consumer  evaluations  of the benefit-cost profiles of  retail
discount cards.  Findings  indicate  that  simple main-effects conjoint model  can
provide  a  good account of the data and  that  a more  complex interactive-type
model  is not  required  in this  type of  experiment.   Subjects'  tendencies  to
exhibit  more  uniform  self-explicated   weights  than  the  part-worth  weights
developed from overall preference responses are also analyzed.

Hauser  JR et  al.    1979.   Assessment  of attribute  importances  and consumer
utility  functions:  von Neumann-Morgenstern theory appled to consumer behavior.
J. Consumer Res. 5:251.
    The  applicability of  von  Neumann-Morgenstern utility  theory  to modeling
consumer choice behavior  is  assessed.  Key concepts  of utility theory that  are
important  to  consumer behavior  are reviewed  and  the differences  between von
Neumann-Morgenstern  utility theory and  other methods   of modeling  consumer
preferences  are  emphasized.   The  appropriateness  of von  Neumann-Morgenstern
utility theory to consumer choice  is discussed and  an empirical application  of
modeling a consumer utility function for new health services is presented.

Hausner  M.   1954.    Multidimensional utilities.  In:   Thrall  RM,  Coombs  CH,
Davis RL, eds.  Decision processes.  New York:   Wiley, p. 167.
    The  von  Neumann and  Morgenstern  theory  of  utility  is  generalized  by
omitting  the  Archimedean  postulate.   Refined  methods  are   introduced   to
simplify  the  work   and  extend  it  to   the  infinite  dimensional  case.   Two
distinct  concepts  are  considered:   the  set  of prospects,  called  the  mixture
space, and the ordering or utility  on  this set.  Axioms  for  both concepts are
discussed.   It  is   felt   that   the  two  set  of   axioms,   taken  together,
characterize a utility  space.   A weak utility space is  also  considered.  The
weakened  axioms  are   deemed   strong   enough  to  permit  identification  of
indifferent elements  and   still preserve  the  operations  of mixture  and  order.
Results  indicate that a mixture  space  may be embedded  in  a vector  space and
that  a utility  space  may be  embedded  in an  ordered  vector  space.   Ordered
vector spaces are examined.
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Hoepfl RT et al.  1970.  A  study of  self-explicated utility models.
Behav. Sci. 15:408.
    Two types of utility models were compared on the basis of their ability  to
predict the  subjects'  evaluations of  hypothetical  university faculty members.
The models  obtained using  mutiple regression were better predictors  than the
models  obtained using  a parameter-eliciting questionnaire,  as  expected, but
the differences were  small.  An analysis of variance suggested that increasing
the number  of factors included in the descriptions caused the  subjects  to  be
less  able  to  make consistent evaluations  even in the  small  range included  in
the  study,  and also  suggested  that subjects  who  were required  to  respond  to
fewer  factors in  early  trials  and  more  factors  in  later  trials made  less
consistent  evaluations  overall than subjects who were  required  to  respond  to
more  factors  in early trials  and  fewer factors in later trials.  The data also
suggested that the  subjects thought that the factors had a more uniform impact
on  the  evaluations  than  was  actually   the  case.   It  is  concluded   that
self-explicated  utility models  have  predictive validity in situations  where
the  important variables have no important  interactions and can be categorized
into  mutually  exclusive   levels   within   mutually  exclusive  factors.   More
information  is  deemed necessary  to determine the  superiority  of these models
over  pure regression  or hybrid  rating-regression models.

Howell WC et  al.   1971.  On  the allocation of inference functions in decision
systems.
Org.  Beh. Human Perform. 6:132.
    Information processing  and  decision performance by a hierarchal system was
studied  under  the   realistic  circumstance  in which  some input  data are
processed  intuitively and  some are processed by a  man-machine  (PIP) combine,
the objective being to determine  how much  use  the  system is able  to  make  of
information  that  must be added to the PIP  aggregate, "by hand".   Three ranges
of  such unanticipated  data were  introduced with two  procedures  for handling
it:   before and after  PIP  arrived  at its opinion (i.e., as an adjustment  in
the priors  for PIP, and as  a  revision in the PIP posteriors).  From a total  of
1,722  problems,  it  is  concluded  that  performance  improves  with  manually
aggregated  data,  but  that  it asymptotes after four to six such  items.    It  is
felt  that  this  implies  a limited  human  capacity.    Order  of  processing  is
deemed  to have  little or no effect.
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Huber GP.   1968.  Multiplicative utility models  in cost  effectiveness analysis.
J. Ind. Eng.  1-9:17.
    The  improvement  of  cost  effectiveness  analysis  as  an  aid  in  decision
making  is  demonstrated  by   regarding  a  key   step,   the development   of  a
quantitative  measure   of effectiveness,   as  the  development   of   a general
multiplicative utility  model.  An example problem illustrates  this proposal.

Huber GP.   1974.   Methods for quantifying  subjective probabilities  and multi-
attribute utilities.
Decision Sci. 5:430.
    Methods   are   described   for   eliciting   subjective   probabilities    and
multiattribute  utilities whose  usefulness has   been  empirically studied  and
reported in the  research literature.  The  variable interval method,  the  fixed
interval method,  the equivalent prior  sample  method, the  hypothetical future
sample method,  and  betting and wagering are analyzed for eliciting subjective
probabilities.  Client-explicated and observer-derived models  are examined  for
eliciting multiattribute  utilities.  Guidelines  for the  elicitation  and use of
such judgements are also  included.

Huber  GP.   1974.   Multi-attribute  utility models:  A review  of   field and
field-like  studies.
Manage. Sci. 20:1393.
    Published  field  and  field-like  research   studies  concerned   with  the
development and  use of multi-attribute  utility  models  are reviewed  with the
particular  needs  of the  management scientist in mind.   The  studies reviewed
include only  those  conducted  under conditions where uncertainties were not of
practical   importance.    In  addition,  the experimental  subjects   were   all
occupationally experienced in  making the utility judgments required  of   them.
The findings  from the research dealing with additive and multiplicative models
are discussed and methods for  estimating the parameters  of each are  presented,
along with  the advantages and  disadvantages of these methods.   It is  concluded
that behavioral  science  research  validated the   relatively recent  management
science practice of using subjective values  as   parameters  in multi-attribute
utility functions.  It  is also observed  that,  using as  a choice  criterion the
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ability  of  the  model  to  predict  actual  decisions  and  evaluations,   simple
additive models  usually do as well  as  more complex  additive  models, about as
well as  the conjunctive multiplicative model,  and better that the disjunctive
multiplicative models.   Although individual studies  sometimes  resulted  in the
finding  that a  particular  model form  is more   predictive  for  a  particular
client-problem  combination,  the differences  in  performance are  deemed  small
from a practical point  of view.

Huber GP et al.  1969.  A study  of subjective evaluation models.
Behav. Sci.  14:483.
    To  identify  the difficulties  that  arise  when staff groups must obtain a
quantitative  representation of  an individual's  or an organization's  evaluation
scheme,  the ability of professional hospital  personnel  to develop  and use a
subjective  evaluation model  in a reliable manner was  studied.   The assigned
task was to  evaluate  twelve hypothetical hospital wards, described in terms of
seven quantitive factors;  linear, addilog,  and  multiplicative models were used
to  approximate  the resulting evaluation models.   Results  indicate that while
professionals can  develop  and use a reliable  subjective evaluation model, they
are  not   very   effective  in   perceiving  and/or  using  the  organizational
evaluation  scheme.  A  lack  of  similarity among  their evaluation  models was
observed.   It is  also  noted  that  earlier  arguments  supporting  the  use  of
addilog  or multiplicative  model forms  are not particularly  relevant  in this
experimental  situation,  based  on  a  comparison  of  the   magnitudes   of  the
multiple correlations and  other significant  values.  Reasons  are  offered for
this finding.

Humphreys  P.   1977.   Application  of  multi-attribute utility   theory.   In:
Jungennaim  H, de Zeeuw 6,  eds.   Decision making  and change  in human affairs.
Dordrecht, Holland: Reidel: p.  165.
    Multiattribute utility  theory (MADT) is evaluated in terms of its claim to
success  in providing an axiomatization of decomposition and, recomposition of
complex  phenomena  which  is  both coherent and didactic.   MAUT  is  placed  in
context as  part  of a multilevel axiomatic system which affords a decomposition
of  processes  underlying  choice  behavior through  a   theoretically infinite
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                                                                   0TS-TIC REPORT FILE
number of levels; however,  only  the  three levels of acts, choice  alternatives,
and  multiattributed outcomes  for riskless choice  are  descibed,  along with
various   solutions  which   can  be  adopted  in   applications   of  MAUT  when
assumptions  underlying  the  axiomatizations  are  found  to  be  violated   in
practice.   The  mapping of  raw data obtained  in  applications  of MAUT  into a
form  suitable  for  input  to a MAUT  composition  algorithm is  considered,  and
mapping-plus-composition    algorithms    commonly   proposed    for    use    in
MAUT-appropriate situations are evaluated.   Three approaches  to the validation
of MAUT are discussed.  Problems  involved in the future development of dynamic
multiattribute utility theory are presented.

Humphreys P et  al.  1975.   An  investigation of subjective preference orderings
for  multi-attributed   alternatives.   In:   Wendt  D,   Vlek C,  eds.   Utility,
probability, and human decision making.  Dordrecht, Holland: Reidel: p. 119.
    Development  is  presented of  a meaningful set of descriptors  linking  the
Raiffa analysis  of  preference  for multi-attributed alternatives with the Kelly
"repertory  grid"   technique  for  the  elicitation  of  attribute  dimensions.
Providing  the  assumptions  underlying  the  repertory  grid  were  reasonably
upheld, it  was  found  that  people's actual preference orderings  were closely
replicated  by  preference orderings  predicted by a  technique developed from
Raiffa's model.  The basis  for such  replication was examined  by comparing  the
accuracy  of predictions  based  on the  Raiffa  analysis  with  those based   on
several  other   analyses  which   did   not  incorporate  the  complete  set   of
operations  described by  the Raiffa model.   These comparisons  indicated that:
(1)   models    for   deriving    unidimensional    preference   orderings   from
multidimensional  data which   do  not   take   utilities  into   account  were
unsuccessful;  (2)   techniques  for converting multidimensional  representations
of  utility  into   preference   orderings  based   on   additive   rules  yielded
considerably better results  than did  a  selection rule;  and  (3)   given   the
adoption of an additive model,  the  use of  a  lottery technique  for assessing
the  relative  value-wise   importance   of  the   various   attribute  dimensions
resulted, in most cases, in an improvement  of  the predictive  efficiency of  the
model  over  models which   assign equal  weights  to  all  dimensions.    Two
limitations on the  generality of  these conclusions are also noted.
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Johnsen  E.   1976.   Experiences in  multiobjective management  processes.   In:
Zeleney  M,  ed.   Multiple  criteria decision  making,  Kyoto  1975.   New York:
Springer-Verlag, p.  135.
    Conclusions  are   reported   from  experiences  in  multiobjective  problem
solving  at  the   individual,   group,   organizational,  and  national  levels.
Solution  approaches  combined  managerial   and  problem   solving  roles   to
facilitate  a  mutual  search  and  learning  process.   Different  problems   are
analyzed with  respect  to an individual's or a  group's reaction to them; group
interactions  in  pursuit  of a collective  goal  also  are  examined.    It   is
concluded that:   (1)  people  are  normally unaware  of  their  objectives  but  do
need them in the managerial process;  (2)  people are willing and  able to cope
with objective problems  as a  link  in a  normal problem solving  process;   (3)
objectives  change  all the time;  (4)  objectives become  meaningful  only in  a
process  in  which   they  interact  with  means;   and  (5)  the objective-setting
process  never  stops.

Johnson  EM et al.   1977.   The technology of utility assessment.
IEEE Trans, on Sys. Man Cyber.  SMC-7:311.
    Utility assessment is defined, the utility assessment process  is reviewed,
and selected  issues and problems  are  discussed.   The focus is  on  applications
in  field and field-like  settings  where it  is  necessary, in order to solve  a
problem,  to  assess the utility of items or alternatives having more than  one
valued property.  Although some aspects of the paper are new, it is  noted that
much of  the work  is  tutorial  in  nature.  Assessment techniques are discussed
with   particular  emphasis  on  the   factors   which   determine  the  relative
effectiveness  of  the  various  techniques  in  specific situations.   Assessment
models  also are discussed,  along  with a  description of the  areas where they
have been  applied.  Guidelines are  developed  for improving the probability  of
success  in  applying  utility  assessment,  and  suggestions  are made  for   the
research necessary  to  improve  further  the  technology  of utility  assessment.
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Kasubek  W  et  al.   1978.   Optinierung  subjektiver  urteile:    anwendung der
multiattributen nutzentheorie bei medizinischen therapieentscheidungen.
Zeitschrift fur experimentslie und angewandte Psychlogie 25:594.
    The  usefulness  of  multiattribute  utility   theory  in   improving  medical
therapy  decisions  is  demonstrated  with respect  to the use of  cortisone for
treatment  of  certain  respiratory illnesses.   The  seven  most  used cortisone
drugs were evaluated.  Five  experienced physicians estimated utility functions
and  importance  weights   for   the   six  side  effects  which   were  used  as
attributes.  An  indifference curve method  and  a  conditional  rating procedure
were used.  Results show  that  the  physician's multiattribute  judgments  agree
nearly perfectly and much  more  than their  intuitive global  evaluations of the
alternatives.

Keeley  SM  et  al.    1972.   Bayesian  and  regression  modeling  of  graduate
admission policy.
Org. Beh. Human Perform. 8:297.
    Bayes1  theorem   and  multiple   regression   analysis   are   compared  as
descriptive models of four  faculty  judgments  of  528  hypothetical  graduate
school  applicants.  Both  approaches   are  conceptualized  within   lens  model
terminology.  All  four  judges  weighted grade point  average very  heavily and
showed relatively  similar  weighting strategies.   Number  of  cues did not have a
major effect on cue utilization,  but  cue  inconsistency did.   Both the Bayesian
model and  the multiple regression model were found  to provide  reasonably good
descriptions of  the overall jugdments, with  the regression model  accounting
for  more  of  the  judgment  variance  in  all  cases.   Assuming  conditional
independence,   aggregation  was  observed   to  be  non-optimal,  the  judgments
generally  being  conservative.    The  simple  linear model  proved an excellent
descriptive model of three of the judges,  and  a  configural  model described the
fourth   judge  very well.   Some  fruitful  hypotheses  for  explaining  the
discrepancy between man's  policy  and  Bayesian  policy were  provided by captured
policies.  It is  argued  that comparing Bayesian  and regression  models  on the
same  data may  prove  fruitful,  especially in  understanding  deviations  from
optimality.
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Keeney  RL.   1971.   Utility  independence  and  preference  for multiattributed
consequences.
Oper. Res. 19:875.
    The concept  of  utility independence is defined and general expressions are
derived  for  simplifying  the assessment  of multiattribute  utility  functions,
given that certain utility  independence assumptions  hold.   These expressions
are presented as representation  theorems;  the proofs for them  are  given and
the additive  utility function is  shown  to  be a  special  case.  The  usefulness
of certainty  equivalents in evaluating multiattributed  utility preferences  in
uncertain  situations  is  discussed.  The relevance of  the work is considered  as
an approximation technique when requisite assumptions  are  not  satisfied.

Keeney RL.  1968.   Quasi-separable utility  functions.
Naval Res. Log.  Quart.  15:551.
    A   method   of    assessment   of  utility   functions   of  multi-numeraire
consequences   is presented.   Emphasis   is restricted   to   the  case  of  two
numeraires,   where   utility   is   non-decreasing   in   one  numeraire   and
non-increasing  in the other.  Based  on von Neumann and  Morgenstern axioms  of
rational behavior and two additional assumptions, an  equation is derived for a
quasi-separable  utility function  of  two-numeraire  consequences.    Implications
and ramifications of  such a utility function and its  requisite assumptions are
discussed.  A technique  for  practical  application of this  work  is  presented.
It  is   felt   that   quasi-separable  utility   functions   are  more  generally
applicable  and  less  restrictive  than  separable utility functions,  and only
slightly more difficult  to use.

Keeney  RL.   1973.  A decision  analysis with multiple objectives:   The Mexico
City airport.
Bell J. Econ. Manage.  Sci. 4:101.
    Results are  reported of a study  done for the Ministry  of Public Works  of
Mexico  to  help  select the  most  effective  strategy for  developing the airport
facilities  of the Mexico City metropolitan area  to  insure quality air service
for  the  remainder  of  the   century.   The decision  analytic model used   to
evaluate strategies is described.  The attributes of  cost, safety, capacity  of
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airport  facilities,  noise  levels,  social  disruption,  and access  times  were
adapted  to account  for  impacts over  time,  and  probability density  functions
and  a utility  function were  assessed over  the  six attributes.   Details  of
these  assessments are  given.   Results  and  implications  of  the  analyses  are
discussed.   It  is   noted  that  a   unique  aspect  of  the  study  involved  the
assessment  of  a  multiattribute  utility  function  and  its   use  to  aid  an
important policy decision.  -

Keeney RL.  1973.  Risk independence and multiattributed utility functions.
Econometrica 41:27.
    Conditional  risk   aversion,   the  conditional   risk   premium,   and   risk
independence pertaining to multiattributed utility functions are defined.   The
functional  form  of   the   two-attribute  utility  function   satisfying  certain
reasonable  assumptions  concerning  an individual's  conditional risk aversion
attitudes is derived.  The notion  of risk  independence is then generalized  and
renamed  utility independence.   Two representation  theorems are  stated which
simplify  the  assessment  of  multiattributed utility functions, provided  that
specified risk independence and utility independence assumptions hold.

Keeney RL.  1974.  Multiplicative utility functions.
Oper. Res. 22:22.
    Sufficient  conditions  for  a multiattribute  utility  function  to  be  either
multiplicative  or  additive are  presented.   It  is stated  that the  number of
requisite  assumptions  to  imply the  main result  is  equal to  the  number of
attributes.   Because the assumptions involve  only  trade-offs  between   two
attributes at a  time or lotteries  over one attribute, it  is deemed reasonable
to expect that  decision  makers can ascertain  whether  these  assumptions   are
appropriate for  their  specific problems.  Procedures are given for verifying
the assumptions and  assessing  the  resulting utility functions.   Application of
the results to  a six-attribute problem relating to the development  of  Mexico
City's airport facilities is sketched.
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Keeney RL.  1976.  A group preference, axiomatization with cardinal utility.
Manage. Sci. 23:140.
    The group  decision problem is  formulated  whereby  the group preference and
the  individual  preferences  are   utilities  of  the  alternatives  in  the  von
Neumann-Morgenstern  sense.   Two  models  are   investigated:  (1)   the   certain
alternative  model,   where   it   is  assumed  that  alternatives   have  known
consequences;  and  (2) the  uncertain  alternative  model,  where there  may be
uncertainties  associated with the  consequences of  the  decision.  For both
models, five  reasonable assumptions  are  postulated,  and it  is  shown that the
group cardinal  utility function which  is  implied must  be a  linear combination
of  the  individual  cardinal  utility functions.  It  is  noted  that  the rules
explicitly  require interpersonal  comparison of preferences.   Suggestions for
obtaining  the  necessary  assessments to  utilize these aggregation  rules are
given.

Keeney RL.  1972.  Multiplicative  utility functions.
Tech. Rep.  70,  Cambridge, Mass:  Mass.  Inst. Tech.
    Necessary  and  sufficient conditions for a multiattributed utility  function
to  be  either multiplicative  or additive  are presented.  It  is  shown that the
additive  form  is  a   limiting case  of  the multiplicative   form,  and  it  is
observed  that  the number of  requisite  assumptions  to  imply the main result is
equal  to  the  number   of  attributes.   Because the  assumptions  involve only
trade-offs  between two attributes  at a time  or  lotteries  over one  attribute,
it  is  deemed reasonable  to expect  that  decision  makers can ascertain if the
assumptions are appropriate  for their  specific  problem.  Procedures are given
for verifying  the  assumptions and assessing  the resulting utility  functions.
The application  of the  results   to  a  six-attribute  problem relating  to the
development of  Mexico  City's airport facilities  is  briefly  discussed.

Keeney RL.  1972.   Utility  functions for  multiattributed consequences.
Manage. Sci.  18:276.                                         *
    The  restrictiveness  of  existing techniques for  systematically assessing
multiattributed utility functions  valid  for decision  making  under uncertainty
is  addressed.   Utility  independence  and  conditional  utility  functions  are
defined,  and operational  assumptions  about the decision  maker's preferences

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for multiattributed  consequences  are postulated.   General functional forms  are
then  derived  which  the  two-attribute and  n-attribute utility  functions must
satisfy subject  to  the  attributes being mutually utility independent.   In both
cases,  the assessment  of  the  multiattributed  utility  function  is   greatly
simplified.   The resulting functional  forms  are  deemed more  general than  the
additive  and  log-additive utility  functions  discussed in the brief survey  of
previous  work on multiattributed utility functions.   A procedure  is suggested
for verifying whether  an attribute  is utility  independent  of the  others in a
particular situation.

Keeney RL.  1977.  The art of assessing multiattribute utility functions.
Org. Beh. Human Perform. 19:267.
    The appropriateness of multiattribute utility theory (MADT)  for developing
preference models to address  value trade-offs among multiple  objectives  and
uncertainty in complex problems is  demonstrated by applying  MADT to a specific
problem  involving  energy  policy.   An  11-attribute  utility  function  over
attributes  including  deaths,   sulfur  dioxide  pollution,  radioactive  waste,
health  effects,  and  electrical  energy  generated   is  assessed.   A  dialog
indicating the procedure  used,  with  comments  on  why various  questions were
asked,  is presented in  detail.    It  is  noted   that the  resulting  utility
function  is being used  to examine energy policies differing in terms  of main
fuel (fossil or nuclear) and degree  of conservation.

Keeney RL  et  al.  1975.  Group decision making using  cardinal  social  welfare
functions.
Manage. Sci.  22:430.
    A  formal  method for  group  decision making  is suggested  which  explicitly
addresses  two  complexities  often  present  in group  decision  problems:  (1)
uncertainty exists  concerning the  exact impact  of each of  the alternatives;
and (2) the individuals have different- preference attitudes  toward risks.  The
group  Bayesian  position  is   accepted  for   analyzing two  extreme  types  of
decision  problems.   In  the first,  a single person or a small  subgroup makes
the  decision;  in  the  second,  the  entire  group  is  responsible  for  the
decision.  Representation  theorems  are  then  developed which  provide  for  the
                                      35

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functional  form  of   a   social   welfare  function  whose  arguments  are  the
individual utility  functions  of the group members.   The results are discussed
for different types of group decisions.  Related work  is briefly reviewed.

Keeney RL et al.   1977.   An illustrative^ example  of  the use of multiattribute
utility theory for water  resource planning.
Water Resour. Res. 13:705.
    Five  alternative  plans  for developing  the water  resources of  the Tisza
River  basin in  Hungary,  involving  consideration of  economic,  environmental,
social,  and  technical   objectives,  are  evaluated.   Twelve  attributes  are
defined  to  indicate the  degree  to which the  objectives are  achieved  in this
project.  A preliminary multiattribute  utility function is assessed over these
attributes.   This  is combined  with   existing  information  describing  the
possible  consequences of the  five  plans to yield an overall rating  of their
desirability.   The utility  function   was  found  explicitly  to indicate  the
preference  trade-offs  among the attributes.   Discussion  suggests  further uses
of the utility function in  the planning and evaluation processes.

Kirkwood  GW.   1976.   Parametrically dependent preferences for multiattributed
consequences.
Oper. Res. 24:92.
    The  concept  of  parametric  dependence  of  preferences  is  introduced  to
assist  in  assessing   multiattributed   consequences.    The usefulness   of  the
concept  for the  assessment of  multiattribute utility  functions  is  shown  by
proving  several  representation  theorems that  simplify  the  assessment  problem
when  parametric  dependence   holds.    Operational  problems  related   to  the
application of the theorems in practical situations are also discussed.

Kirkwood  CW.   1978.   Social  decision   analysis  using  multiattribute   utility
theory.   In:   Zionts S,  ed.   Multiple  criteria  problem  solving.    Berlin:
Springer-Verlag, p.335.
    Incorporation  of  the  preferences   of  different  groups  into   a  decision
analysis  for  public  sector decision making  is examined.  A conflict  between
Pareto  optimality and certain  equity  considerations  is  identified.   It  is
                                       36

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shown  that there  is no  way  to  incorporate preferences  in such  a  situation
which  is  guaranteed  to  be both efficient, in the  sense  that no other  solution
will  make  some  group  better  off  without making  another   worse   off,   and
equitable,  in  the  sense of  considering  the  different  impacts   on various
groups.    In   addition,   practical  difficulties  in   applications  work   are
discussed, and areas for  future research are indicated.

Klahr  D.   1969.  Decision  making  in  a  complex  environment:    The  use  of
similarity judgements to predict preferences.
Manage. Sci. 15:595.
    Judgments of the relative  similarity of pairs of  alternatives  are used to
construct  a  model  of  the  decision  space  of  a  group  of  college admissions
officers.  The model  is  then used to  predict  the preferences  of  the officers
for a  set  of hypothetical college  applicants.   The accuracy of the predictions
supports  the hypothesis  that  preference  judgements  are made  on the  basis  of
the  similarity  of  given alternatives  to an ideal  alternative.   A nonmetric
multidimensional  scaling  procedure  is  used  to  construct the  space.   This
procedure  yields a dimensional representation based upon  very  few assumptions
about the nature of the similarity measures.

Klee AJ.   1971.   The role of  decision models  in  the evaluation of competing
environmental health alternatives.
Manage. Sci. 18:B-52.
    Problems  faced  by   the   Solid  Waste   Management  Office   in  evaluating
competing  environmental health alternatives, given a set of decision criteria,
are  discussed.   The concepts  of scoring models  are  reviewed,  and techniques
for  implementing a linear scoring  model  or  pairwise  comparisons are critically
examined.  The  Decision  Alternative  Ratio  Evaluation  (DARE)  method  is  then
introduced.  Using a  sample  problem  of dismantling  retired   wooden  railroad
cars,  it  is  shown that  the  DARE  method is based upon a  pairwise comparison
concept  but  that  it  drastically  restricts  the  total  number  of  comparisons
involved.  Use of  DARE in conjunction with  other rating  methods  is suggested
for further simplifying the decision making process.
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Kornbluth  JSH.   1978.  Ranking  with multiple objectives.   In:   Zionts S,  ed.
Multiple criteria problem  solving.   Berlin:   Springer-Verlag,  p.  345.
    An   interactive  method  for   ranking  items  subject   to   an   initially
unspecified  linear  utility function is presented.  The method is economical  on
the  number of paired  judgments that  must be made  by the  decision maker  and
leads  to the identification  of the desired  ranking  and the  space of weights
for  the  corresponding  linear  utility  functions  which  would  lead  to   this
ranking.   Simulation  results  suggest  that  in  cases  where  the  number  of
attributes  is  six or less, a maximum of  20  to  30  items  must be considered  in
order  to obtain  a reasonable estimate of  the appropriate weight space.  It  is
felt that  the method  is useful  in  any situation where either the rank  order  or
the associated utility weights  (or both) are of interest.  The method  can  also
be  used as  an  aid  in the  analysis  of decision making,  finding  appropriate
weights  or weight  intervals  for further  multi-criterion  optimization, and  as
an  alternative   approach   to  interrogative  techniques  for  evaluating   the
preferences  of a decision  maker.

Kunreuther   H.    1969.    Extensions    of  Bowman's   theory   on    managerial
d ec i sion-making.
Manage.  Sci. 15:B-415.
    The  validity  of  Bowman's   theory  concerning  the  quality  of  managerial
decision   making  is  evaluated   against  the  three   general   criterial   of
consistency  over time,  economic  significance,  and  statistical significance.
These  criteria are then used to evaluate a production planning model for  an
electronics  firm where  the  rules  are  based on  average past  behavior.   The
production plans based on an average  rule are  compared  with  the actual plans
for  the company.   It was found  that when  a manager  has  limited  information
regarding  future sales,  as when he develops his initial production  estimates,
then  a plan based on  average behavior performs  better than  actual initial
plans.   However,  when  environmental  cues  provide   reliable  information  on
future  sales  of specific  items  (as  when  revisions  are  made),  then actual
decisions  are  clearly superior  to  those suggested  by  an  average rule.  It  is
felt that  this case study  offers insight  into the potential usefulness as  well
as  the limitations  of Bowman's hypothesis.   Suggestions for future  research
are offered.
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Lincoln  DR  et  al.   1979.   Cross-media  environmental  impacts  of  coal-fired
power plants:  An approach using multi-attribute utility theory.
IEEE Trans. Sys. Man Cybern. SMC-9:285.
    A human  preference model,  developed  using multiattribute  utility  theory,
was linked to an  environmental  emission model for a  coal-fired power plant  to
develop  a methodology  for  identifying  optimal  control  strategies  reflecting
specific  pollutant  trade-off  decisions by environmental  decision makers.  Six
emissions  to air,  water,  and  land  were  evaluated.   It was  found  that the
pollutant most desired  to be  reduced  was  either  sulfur dioxide or particulates
to  the   air.   For  solid  wastes,  most individuals  tested  preferred reducing
sludge  rather  than ash  to  minimum levels;  heat emitted  to air  received the
lowest  rating  from all individuals.   It  is stressed  that the results  do not
represent  a  comprehensive analysis because individuals  were asked  for  their
environmental preferences only,  and other important  factors  such as cost were
not considered

Luce BD.  1956.  Semiorders and a theory of utility discrimination.
Econometrica 24:178.
    Imperfect response  sensitivity  to small changes  in utility is examined in
relationship   to   intransitivities   of   the   indifference   relation.    A
comparatively simple  theory  of utility  is  constructed in which  an  individual
is not sensitive  to all changes  in  utility;  the  theory yields a nonstatistical
analog  of the  "just noticeable difference" concept of psychophysics.  Next,  a
set of  preference axioms which  allow for intransitive  indifference relations
is introduced, and  relations  satisfying  these  axioms  are  termed "semiorders."
The set of intransitive  indifference relations  is  shown to  be  substantially
equivalent to a utility theory in  which  there are just  noticeable difference
functions which state  the  change in  utility for  any  value of  utility  so that
the change is  just noticeable.   The  precise form of  the  function is examined
in detail in the  case  of  risk represented by a linear utility  function over a
mixture  space.
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Luce RD.  1958.  A probabilistic theory of utility.
Econometrics 26:193.
    A  model for  choices among  uncertain alternatives  is developed  in which
preferences between  pure alternatives and likelihood judgements between events
are assumed to  be independent probabilistic processes.   It is noted that this
model  is, in  some respects, a probabilistic version of von Neumann-Morgenstern
utility  models.  Certain plausible  notions  about  subjective  probability are
shown  to imply  a very  simple discrimination function between events in which
the  probability  of  choice  depends  only  upon  differences  of   subjective
probabilities.   Similarly,  the expected  utility hypothesis is  shown to imply
that preference discrimination depends upon utility differences,  and the form
of  that discrimination  function  is  determined.   Questions  of  empirical
verification are  discussed.

MacCrimmon  KR.   1968.  Decision making  among multiple-attribute alternatives:
A survey and consolidation  approach.
Memorandum RM-4823-ARPA,  Rand Corporation, Santa Monica,  California.
    Several  methods  and techniques  for making quantitative  and qualitative
evaluations between  multiple attribute alternatives are examined.  The methods
discussed   include   dominance,   satisficing,  maximim,  maximax,  lexicography,
additive weighting,   effectiveness   index,  utility  theory,   trade-offs,  and
non-metric  scaling.   The assumptions underlying each  approach are  critically
reviewed,  as are the  .information requirements of  each.  In  addition,  each
method  is  described  in a  general  way  and  by  using  a   formal,  abstract
mathematical representation.   Two  examples,  the choice of  a weapons  system and
of  a  space  suit,  illustrate  the  discussion.   It  is  observed   that  most
theoretical  discussions  of  decision making  methods  assume  that  the  exact
values of  the  attributes are known when, in fact,  such  information is seldom
known  with  such precision.   It  is  then noted  that  this  survey  discusses
situations  where there   is  uncertainty  about  attribute   values,  presenting a
combination of  methods  which  may be used  as  a  more  reasonable  and  valid
approach than the choice of any  single method.
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MacCrimmon KR.   1973.  An  overview of multiple objective decision making.   In:
Cochrane  JL,  Zeleny  M,  eds.   Multiple criteria  decision  making.   Columbia,
S.C.:  Univ. S. C. Press, p. 18.
    The feasibility  of  combining methods when dealing  with  multiple objective
and multiple  attribute  decisions  is  investigated.   A meta-model  is developed
to  relate  the'  multiple  objectives  of  a  decision maker  and  the  multiple
attributes characterizing his  alternatives to the models  an analyst builds of
these  processes and  choices.    This  serves  as  a  framework  for examining a
variety of  prescriptive  and descriptive models  grouped under  the  headings of
weighting methods,   sequential  elimination  methods, mathematical  programming
methods,  and  spatial proximity methods.   Each method  is  briefly described by
its   most  prominent   features   and  by   its    underlying   assumptions;   a
representative example of each model's  use is also presented.  As  a basis  for
developing effective  combinations of methods,  the conditions  appropriate  for
using each model are indicated through an extended example.

Madden JM.  An  application to job  evaluation  of a  policy-capturing  model  for
analyzing individual and group judgement.
Tech. Rep. PRL-TDR-63-15,  Lackland Air Force Base,  Texas:   Personnel Research
Lab.
    A multiple regression model  combined with  a  mathematical grouping model is
presented as a method of estimating individual rater consistency  and degree of
interrater agreement  in  developing a  job evaluation plan.   Officers  ranked 50
simulated Air Force  specialities, each  of  which  consisted   of  pre-assigned
scale values for 10  job requirement factors.   Thirty-eight officers  ranked  the
jobs on the basis of merited grade, and 36  officers  ranked the  jobs  on merited
pay.  Each rater's consistency was  evaluated by  a  multiple regression equation
predicting his  rank  ordering of the jobs from the  factor  values.  Consistency
of policy among  raters was  measured by the loss in  predictive  efficiency when
a  single  equation  represented  the joint  policy  of the  group.   Measures  of
rater  consistency   showed  that  all  but  two  of  the   raters  were  adequately
consistent.    Measures of   interrater  agreement  indicated  that  raters  were
applying  a homogeneous policy,  whether they ranked  on  merited pay  or  merited
grade.  The officer  raters  were found  to  be  capable of applying a  consistent
policy in evaluating  jobs  when their  only  information  was an  estimate  of  the
job requirements.
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May  KO.   1954.   Intransitivity, utility,  and  the aggregation  of preference
patterns.
Econometrica 22:1.
    Some  experimental   evidence  and   theoretical  arguments  are  presented
suggesting  that  neither cardinal nor  ordinal  utility  theory can reflect, even
to an  approximation, the existing preferences of individuals in many  economic
situations.   The  argument  is  based   on  the  necessity  of  transitivity  for
utility,  observed circularities  of preferences,  and  a  theoretical framework
that predicts  circularities in  the  presence  of  preferences  based on  numerous
criteria.

Miller JR.   1967.  A systematic  procedure  for assessing  the worth of complex
alternatives.
AD 662001, Defense Documentation  Center.
    An explicit,  logically consistent, and  replicable procedure for assessing
the  worth of complex alternative  is developed.  The  procedure  assumes that a
decision  context  has  been   specified and  that  a   fixed   set   of   discrete
alternatives has  been chosen.   It then assesses the worth of  each  alternative,
estimates   the   resource   drain  required   by   each,  and   combines   these
considerations,  along  with considerations  of  risk and  uncertainty,  to arrive
at a final  decision.  Results of an experiment de.signed  to measure the impact
of  this   procedure  upon professional  decision makers also  are  reported.  To
place  the procedure  in perspective,  it is compared with alternative procedures
discussed in the  literature and  practiced by decision  makers.

Newman JR.   1975.   Assessing  the reliability  and  validity of multi-attribute
utility procedures:  An application  of the  theory of generalizability.
SSRI Res. Rep. 75-7, Los Angeles:  Univ. Southern Calif.
    A  theoretical   rationale   is  presented  for  assessing   the   reliability,
validity,  and  dependability of  multiattribute utility models and  techniques.
A study  of  generalizability is conducted by taking measurements assumed  to be
randomly  representative of  the universe  to which the  investigator wishes to
generalize.   The ratio of an  estimate of  the universe  score variance  to an
estimate  of the  observed  score  variance   is  defined as  the  coefficient  of
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generalizability.    It    is   estimated   by   the   intra-class    correlation
coefficient.   Analysis  of variance  and an  expected mean  square  paradigm  are
used to obtain the appropriate variance estimates.   It  is felt that the  theory
dispenses  with  unnecessary  and  unwarranted  assumptions  and eliminates   the
distinction  between  reliability  and validity.   It is  further felt  that  any
generalizability  study  can  be   conducted   without reference to   a  parallel
measure  of  the  multiattribute   utility  (MAU)   instrument   or some  external
criterion of success.   If a MAU  technique  is  compared  to  a non-MAU technique
for  doing the  same  thing,  it  is  possible  to   calculate  the coefficient of
generalizability  for both models and  choose the method  best  suited  to one's
needs.  Three  examples  are given for this  theory.   Preliminary investigations
are believed to indicate  that MAU models,  and  techniques  based on such models,
may be better  than non-MAU models since the former have a  tendency to  reduce
the interation between  judges  and the  item being judged when such interation
represents inconsistency of judgement.

Pekelman D et al.  1974.  Mathematical programming models for  the determination
of attribute weights.
Manage. Sci. 20:127.
    Several  versions  of  a  mathematical  programming  model   which  determines
attribute weights for  each  consumer are empirically  evaluated using  data on
dry  cereals  and  automobiles.   The   model   uses  a  linear  compensatory  model
incorporating an  ideal  point concept and  is found  to  be a  good  predictor of
consumer preferences, particularly for  dry cereals.  The model also indicated
that most  consumers  use very  few attributes in  evaluating  brands,  suggesting
that it is feasible to  segment  the market in terms  of  determinant attributes.
Managerial  implications   for  product repositioning,  new product  design,  and
market segmentation are then discussed.

Polak  E.    1976.   On  the  approximation  of  solutions   to  multiple  criteria
decision  making   problems.   In:   Zeleny M,  ed.    Multiple   criteria  decision
making, Kyoto 1975.  New York:  Springer-Verlag,  p. 271.
    An adaptive precision method  is presented based  on  cubic  splines and a new
scalarization  procedure   which  constructs  approximations  to  the   surface  of
noninferior  points.   The  method  is  felt  to be  particularly  well-suited  for
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two-criteria and  three-criteria optimization  problems and applicable  to some
extent  to  high dimensional  problems.  The  technique is  considered efficient
since  it computes  no more points  than  necessary to  ensure  a prescribed level
of precision of approximation.

Pollak RA.  1967.  Additive von Neumann-Morgenstern utility functions.
Econometrics 35:485.
    A   necessary   and   sufficient  condition   for   the  additivity   of  von
Neumann-Morgenstern  utility  functions   is  presented.  A "strong  additivity
axiom" is introduced,  and  it  is shown that an individual's preferences satisfy
this  axiom if  and only  if his  von Neumann-Morgenstern  utility  function  is
additive.   Next,   a  "weak   additivity   axiom"  is  presented,   and   it  is
demonstrated that  an  individual's preferences  satisfy  it  if and  only  if his
von Neumann-Morgenstern  utility function  is either additive or  log additive.
Restrictions    resulting    from    these    assumptions   about    the    von
Neumann-Morgenstern  utility  function  are discussed.   The extension  of these
results to the continuous  consumption case is indicated.

Richard  SF.   1975.   Multivariate  risk   aversion,   utility  independence  and
separable utility  functions.
Manage. Sci. 22:12.
    The  concept of multivariate  risk  aversion is  introduced  as  a  pairwise
property which  a  decision maker may  evidence  when making decisions concerning
some pairs of  variables  but not when making decisions concerning other pairs.
Multivariate  risk-averse  behavior,   risk-neutral behavior,  and  risk-seeking
behavior  are  examined.    Next,  a multivariate  risk premium  is  defined  and
sufficient  conditions  are given  for  one  multivariate  risk  averse  utility
function to  have  larger multivariate  risk premiums  than  another.  Operations
preserving  multivariate risk aversion  are  proved,   and  all definitions  and
theorems  are  generalized   to utility  functions  for n-attributes.   Finally,
certain  assumptions   are  given  which  are   necessary  and rsufficient  for  a
multivariate utility function to  have  one of  three  possible separable forms.
It  is  shown  that  the  negative  multiplicative  form  has   multivariate  risk
aversion,  while the  positive multiplicative  form and  the  additive  form are
risk-seeking and risk-neutral,  repectively.

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Roy B.  1973.  How outranking relation helps multiple criteria decision making.
In:  Cochrane JL, Zeleny M, eds.  Multiple criteria decision making.  Columbia,
S.C.:  Univ. of S. C. Press, p. 179.
    The  concept  of  an  outranking  relation   SA  is  developed  as  a  binary
relation  defined  on a  set A of  feasible decisions.    Implications  of  the
definition  are  then  studied  with  regard  to  the  transitivity  of  the  binary
relation  S.  and  to the  stability  of  S.  when A  is  enriched  with  some  new
decisions.   Practical   ways   of   building   outranking   relations   also  are
considered.  The use of  outranking  relations is examined in different kinds of
decision problems  to:   (1) rough out a  problem by eliminating a  large  subset
of elements of A when one  and  only  one decision must be  selected;  (2)  build a
trichotomy of A including decisions  accepted,  rejected,  or those  requiring a
complement of information; and (3) obtain a weak order on A.

Shepard  RN.   1964.   On subjectively  optimum  selection  among  multiattribute
alternatives.  In:  Shelley MW, Bryan 6L, eds.   Human judgement and optimality.
New York:  Wiley, p-.257.  "
    Techniques  are  examined to  help  an individual  achieve his  subjectively
given subgoals and  to  reduce  the occurrence of subsequent judgements that the
wrong choice was made in some earlier decision.  Two  aspects of this situation
are  identified.   In   the  first,   the  failure   to  achieve  a   subgoal   is
attributable to  limitations on an individual's  power of rational  calculation.
In the  second,  the  conflict between  subgoals  is considered as  resulting from
the number of objectively  disparate attributes  that the  subgoals  possess.  The
suggestion  is then put forward  of  having individuals  and computers  share  in
the  decision making process.   Elementary  comparisons   with  respect  to  the
underlying  subjective  attributes would  be  performed by an individual,  while
the  purely  logical  or combinatorial   process  of  putting  these  elementary
judgements  together to  reach  an  overall decision would  be  entrusted  to  a
computer.   An  experiment  then  illustrates  that  the  relative weights   to  be
assigned  to  component  attributes are not  always determineable and  may  depend
on the adoption of  one  of  several incompatible but equally  tenable  systems  of
subjective goals.   It  is hypothesized that the tendency  to accept  a spurious
resolution of a problem  is caused by temporarily accepting  a  special state  of
                                      45

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mind  or  an unrealistic  goal  that has  the  advantage of entailing  a system of
weights  that  clearly favors  one  alternative over  its  competitors  and permits
the decision  to be consummated.

Slovic  P.   1969.   Analyzing the  expert  judge:   A  descriptive  study   of  a
stockbroker's decision processes.
J. Appl. Psychol. 53:255.
    An analysis-of variance  technique is illustrated for describing the use of
information  by  persons  making  complex  judgments.   The  subjects   were  two
stockbrokers  who rated  the  growth  potential of  stocks  on  the basis  of all
factors  taken from Standard  and Poor's  reports.   The  technique proved capable
of   providing   a   precise   quantitative   description   of   configural   and
nonconfigural   information  utilization.   It  was  found  that  each  broker
exhibited  a  substantial amount of  configural processing.  The method is felt
to have  promise for  providing  experts  with  insight into  their own  processes
and for  teaching and  evaluating student  judges.

Slovic P et al.   1971.   Comparison  of  bayesian and  regression approaches to
the study  of  information processing  in  judgement.
Org.  Beh.  Human Perform. 6:649.
    A review  and  comparative  analysis  is  presented  of  the Bayesian  and
regression approaches to the  study  of information utilization  in judgement and
decision making.  For  each  approach the  following  items are examined:   (1)
models  developed  for describing and prescribing  the  use of  information  in
decision making;  (2) major  experimental  paradigms,  including  the  types  of
judgement,  prediction,   and decision tasks and  the kinds  of information that
have  been  available  to  the decision maker  in these tasks; (3) key independent
variables  that have  been  manipulated  in experimental  studies;  and  (4)  major
empirical  results  and  conclusions.    The  two  approaches   are  compared  to
determine,  first,  if   the   specific models and  methods   characteristic  of
different  paradigms  direct the researcher's  attention  to  certain problems and
cause him to neglect  others  that may  be equally  important  and,  secondly,  to
learn if a researcher  studying  a particular substantive  problem can increase
his understanding by  employing diverse models and experimental  methods.
                                      46

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Slovic  P  et  al.    1972.   Analyzing  the  use  of  information  in   investment
decision making:  A methodological proposal.
J. Business 45:283.
    Techniques  for  analyzing  the  cognitive  processes  involved  in decision
making  are investigated.   Complex  computer  simulations,  linear models,  and
configural models  are briefly  reviewed  and  the analysis of  variance  (ANOVA)
technique  is  explained.   An experiment involving  broker's and student's stock
predictions is used  to illustrate  the  ANOVA model.  Results  suggest  that ANOVA
and multiple  regression analysis  show promise  as devices for describing the
use of  information  in investment decisions.   Factors  determining which method
would be more suitable in a given situation are also discussed.

Slovic P et al.  1977.  Behavioral decision theory.
Ann. Rev. Psycho1. 28:1.
    Normative  and  descriptive   facets  of  behavioral  decision  theory  are
reviewed.   Descriptive  studies  of   judgement,   inference,   and  choice  are
considered first,  and then  the  development  of  decision-aiding  techniques  is
discussed.  Several trends in the  literature  are noted.  First, it is observed
that  while  decision  making  is  being  studied  by  researchers  in  diverse
disciplines,   the  importance of  psychological concepts  in  decision  making  is
increasing in both  normative and descriptive work.  Second,  increasing effort
is  seen being devoted  to  the  development  of practical methods for  helping
people cope with uncertainty.  Third,  the  number of reviews  and bibliographies
appearing  in  recent  years   is  felt to  indicate  that the  field of decision
theory  is  growing  rapidly.   It  is then noted that the present review focuses
on psychological aspects of individual judgement and decision making.

Smith  CG.   1979.    Consultation  and  decision  processes in  a  research  and
development laboratory.
Admin. Sci. Quart. 15:203.
    A study of the relationship between consultation and decision processes in
an  industrial research  laboratory  showed  the   efficacy  of  multidirectional
consultation coupled with a  pattern of shared,  decentralized  decision making.
The   loose,    decentralized   pattern   is    closely   associated   with   more
                                      47

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science-oriented  activity,  while the  hierarchical pattern  is  associated with
more  practical  or organizationally  relevant  activities.   The  relationships
obtained between  either the loose  or  the  hierarchical pattern and performance
are  found  to be mediated by coordination, adequacy  of  work expectations, and
levels  of  member  involvement.  The  results also suggest  that  when decision
centers  are   consistent  with  consultation  centers,   implying  a   congruence
between  authority and  expertise,  the overall  structure of  the  laboratory  is
less important.

Stimson DH.   1977.  Utility  measurement  in public  health decision making.
Manage. Sci.  16:B-17.
    The utilities of objectives  of decision makers  in a  large  public health
agency  were  assessed  using  the  Churchman-Ackoff  approximation  measure   of
value.  The values obtained formed part  of  a  model of a resource  allocation
problem  faced by  the  agency in  allocating a  federal  grant  to  improve the
out-of-hospital  care  of the chronically  ill and  aged.   A  comparision  of the
normative  solution derived  from the model with  the solution already chosen  by
the  agency tended to  support the  hypothesis  that agency  members  chose  among
                             \
alternatives  as  if they were maximizing  expected utility.

Swezey  RW.   1979.  An application  of  a multi-attribute  utilites model   to
training analysis.
Hum. Factors  21:183.
    A  multiattribute  utilities  model  is applied to  the design  of improved
gunnery  ranges  for  a  military  anti-armor  training  system.  Results  of the
application are presented and the  model  is  then  compared to  a  second simple
judgement  analysis model using the  same  input data.  It was  found that the two
methods  agreed  on five  of  the six  top-ranked  attributes.   Aspects  of the
multiattribute utilities approach are  discussed.
                                       48

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Thrall  EM.   1954.    Applications   of  multidimensional  utility   theory.    In:
Thrall RM, Coombs CH, Davis RL, eds.   Decision processes.   New York:  Wiley,
p.181.
    Some  non-Archimedean  utility   space   axioms   are  presented   with  special
attention  given  to   the  consequences  of weakening  certain  of  them.   Next,
several applications  of  non-Archimedean  utilities are discussed.   It  is noted
that  non-Archimedean utilities  are perfectly  satisfactory  for  game  theory.
The  equivalence  of  game   theory   and   linear  programming  guarantees  that
non-Archimedean  utilities  will  be  satisfactory  also  for  linear programming
problems.

Turban  E  et  al.    1971.    Utility theory  applied  to  multivariable  system
effectiveness evaluation.
Mange. Sci. 17:B-817.
    Utility  and  decision theories   are applied  to determine  the  effectiveness
of  a  complex system  with  several   measures  of performance.   Systems  analysts
and operational personnel  in the  Naval  Air  Development  Center  and  related
organizations were asked  to rank the measurements of performance according to
their  importance  and  to   assign   utility  indices  to  each.   Churchman  and
Ackoff's method  for  checking the consistency of  the ranking  was  modified and
applied  to the  study.   The  evaluations  of  the   individual  judges were  then
adjusted and the estimates  of  all  the  judges were combined  to form an overall
utility index.  The  "coefficient of concordance"  test was used  to measure the
degree  of  agreement  among  the   judges.   The  weighted  overall  measure  of
performance  is  used  to evaluate proposed courses of  action  and  to establish
stopping rules for a  simulation study.

von Winterfeld  D.   1975.   An overview, integration, and evaluation of utility
theory for decision analysis.
SSRI Res. Rep. 75-9.  Los Angeles:   Univ. Southern Calif.
    Measurement  theoretic   literature  on utility models  and  assessment  is
         »
surveyed.  The  role  of utility  theory  as  a  part  of  the  general theory  of
measurement  is explained first, and a  classification scheme  for utility models
is  developed.   Models  are  classified   according  to  some   of   their  formal
                                      49

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properties and  to the type of  decision  situation to which  they apply.  Next,
the  main utility  models of  weak  order  measurement,  difference measurement,
bisynmetric   measurement,   conjoint   measurement,   and   expected   utility
measurement  are  described  through  their assumptions,  model  forms,   formally
justified   assessment   procedures,   and   common   approximation   methods.
Similarities  and  differences among models and assessment procedures  are then
discussed.  Topics include logical relationships  between models, similarities
in  the cognitive  processes  involved  in  the  different  assessment procedures,
and  model  convergence by  insensitivity.   Finally,  the  use of  utility theory
for  decision  analysis  is evaluated as a  tool  in  formal  treatments of  decision
problems.  It is  concluded  that  utility  theory  can be  useful  in structuring
evaluation problems and  in eliciting appropriate model  forms, but  that  the
theoretically   feasible  assessment  procedures  are  often   too  clumsy  and
complicated  to  be applicable in  real world preference  assessment.   A general
critique of current  trends to mathematize utility theory  concludes the  report.

von  Winterfeldt D et  al.   1973.   Evaluation  of  complex  stimuli using multi-
attribute utility  procedures.
Tech.  Rep^  011313-2-T.  Ann-Arbor, Mich.:  Engineering  Psych.  Lab.,  Univ.  of
Mich.
     The  validity  and  the  usefulness  of  multiattribute   utility  theory (MAUT)
models  and  procedures for evaluating complex stimuli were  investigated  in  an
apartment evaluation problem.   After  the  construction of utility functions and
importance weights,  the  subjects  were trained to  apply the evaluation  strategy
with  which  they  felt  most comfortable  and  which reflected  their preferences
best.   The correlation between model predictions  and  complex judgements after
training  constituted  a general  measure  of  the  usefulness  of MAUT.  Three
procedures to assess utility functions and  importance  weights were tested for
their   differential  validity   beyond differences  in  the  correlation  with
post-training  judgements.   Descriptions  of  apartments  were  constructed  from
weights  and  utility functions  such  that the three procedures  would predict
different  preferences  in  simple  choices.   The   three   methods  of  assessing
importance weights  and  utility  functions were  a probabilistic  procedure,  a
direct   rating   procedure   with   importance   weights   derived   from   the
                                      50

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unstandardized utility  functions,  and a direct  rating  procedure with directly
assessed  importance weights.   Results are  deemed to  indicate that  MAUT  can
improve   upon  a  decision  maker's   unaided   intuition.    The  probabilistic
procedure was  found to be  the superior method  for predicting simple  choices
between stimuli.

von  Winterfelt D  et  al.   1973.   Multi-attribute  utility  theory:   Models  and
assessment procedures.
Tech. Rep. 011313-7-T.  Ann Arbor, Mich:  Engineering Psych. Lab.
    Multiattribute  utility theory  is  reviewed  from  a measurement  theoretic
perspective.   Decision  situations  are described  and  classified  according to
three   salient   aspects   of   choice:  uncertainty,    time-variability,    and
multi-dimensionality.   For   each   choice   situation   the   main  mathematical
representations,   their  interrelations,   and   differences   are   discussed.
Measurement   theoretic   tests   are   described    which   separate   between
multiattribute utility  models  in  riskless  and  risky  time  invariant  choice
situations.  Assessment procedures  are outlined  to  encode utility functions
for   the    representations   developed,   and  experimental   applications   of
multiattribute utility theory are briefly reviewed.

von  Winterfeldt  D et al.   1975.   Multi-attribute utility  theory:   Models  and
assessment procedures.  In:   Wendt D, Vlek CAJ, eds.   Utility, probabilty  and
human decision making.  Dordrecht, Holland: Reidel, p. 47.
    This  article   is   an  exact   duplicate   of   Technical   Report  011313-7-T
summarized above.

Wilkie WL et al.   1973.  Issues  in marketing's use of multi-attribute attitude
models.
J. Market. Res. 10:428.
    Results and  conclusions  of marketing  research on the  linear  compensatory
multiattribute attitude model  are  discussed.   The  basic compositional model is
defined  and  a  chart  is  constructed indentifying  specific  researches   and
issues.   The  issues  are  seen  to   include  attributes,  importance  weight,
beliefs, model structure,  and model testing.  Salient  aspects of  these issues
                                      51

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are then analyzed.   It  is  felt that the  review demonstrates the rapid advance
from uncritical  model application  to  a present atmosphere  of controversy and
cumulative analyses  on specific  issues.   The  review  is also  seen  as showing
the  significance and  difficulty  of model  formulations.   Models  that  yield
understanding  and   suggest  feasible  procedures  for   favorable  control  are
recommended for  future research.

Woods DH.  1966.  Improving estimates that involve uncertainty.
Har. Bus. Rev. Vol.  ?, p.  91.
    The   problems   of  bias   and   distortion   which    occur   in   the  upward
communication   of   judgements   about  crucial  company  sales   and  capital
investments  are  examined.  Specific reasons are  cited for  the  occurrence of
these problems and  positive  steps are offered  to  eliminate  or reduce them.  A
capital  budget   format  is   proposed   for   incorporating  information  about
uncertainty  in   a   visible   and  precise   manner.    Relevant  judgments  are
quantified at various  points  in the organization  as they  are passed upward so
that a  top-level manager  has  a better idea of what his  operational managers
and  information  specialists  actually are thinking.  In addition,  the proposal
to  let  individuals  report the complete  probability distribution  of outcomes
instead  of  forcing  them  to  commit  to  a single  estimate  is  seen  as reducing
bias because  it  allows operating  managers  to  hedge their  estimates and still
communicate  comprehensive  information to  the  final approval level.  Finally,
it  is suggested  that top management communicate its actual preferences down to
the expert who has  to make the  forecast.

Yilmaz MR.  1978.  Multiattribute  utility theory:  A survey.
Theory and Decision  9:317.
    Axiomatic  developments in multiattribute  utility  theory,  i.e.,  sets of
preferential  conditions that  lead  to multiattribute  utility  representations,
are  surveyed.   Decomposition  of multiattribute  utilities  is considered in
situations  involving  riskless choice  and  decomposition  under  risk.   It is
noted  that,   in  contrast  with  the  former  situation,  decomposition involves
preferences  among probability  distributions  over  a set of  sure alternatives.
Lexicographic utilities  under certainty or  risk  are  also  covered, and results
                                       52

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are presented  pertaining to the existence  of  group preferences and utilities.
Some definitions  and  notation are  included,  as well as  some standard results
in  unidimensional utility  theory.   Various  empirical  studies  are  excluded,
such  as  experimental  applications,   assessment  of utilities,   or  tests   of
preference axioms.

Yntema DB  et  al.   1965.  Telling  a computer how  to evaluate multidimensional
situations.
IEEE Trans. Hum. Factors Electron. HFE-6:3.
    The  feasibility  of  the  "interpolation between corners"  procedure  as  a
psychophysical  method for  telling a machine  how  to  compute  the worths   of
multidimensional  alternatives  is demonstrated.  A  statistic  called fractional
disagreement  is  proposed as  the proper  measure of  the  machine's  success   in
mimicking  the  man's decisions.  The  subjects  were  military  officers  who were
asked  to  make  decisions  to  which  they  could  bring  a  large  amount   of
experience.  The  fractional  disagreement between a  subject and  the machine he
had instructed  was found to  be, on  the average,  four  percent,  and  the data
suggest that  the  disagreement between subjects  was of roughly  the same  size.
The concept  of conflict  between the  dimensions of  two  alternatives  is also
explained.  The  size  of the  conflict and the  size of the difference  between
the worths  that the machine  ascribed to the alternatives  were found  to help
predict  the   correctness  of  the machine's  decision.   It is  concluded that
conflict and difference  in  computed worth would be  useful  in defining regions
where the machine would give the decision back  to  the man  and tell him to make
the choice.   Some statistics and  terminology  that  may  be used  in describing
the performance of an evaluative decision maker are presented.

Zeleny M.   1975.   MCDM  Bibliography-(1975).    In:   Zeleny  M,  ed.   Multiple
criteria decision making, Kyoto 1975.  New York:  Springer-Verlag, p. 291.
    A bibliography  is presented which  includes only published  works  directly
related  to  multiple  criteria  decision  making.   Works  excluded  from  the
bibliography  are  those   dealing with  multidmensional  scaling   and  conjoint
measurement, multiple cues modeling of human  judgment, multiattribute attitude
models of consumer behavior,  statistical decision  theory,  and similar topics.
                                      53

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It is  noted  that working papers and  research memoranda appearing in  regularly
maintained  institutional  series  are  considered published  materials  for  the
purposes of  this unofficial  compilation.

Zeleny  M.    1976.   The  theory of  the displaced  ideal.   In:   Zeleny  M,  ed.
Multiple  criteria decision  making, Kyoto  1975.  New  York:   Springer-Verlag,
p.153.
    An  operational model  is developed for  analyzing  the  phenomenon of  ideal
displacement in the  decision making process.  Preferences are  considered  fully
cardinal  in character,  though  in  a  fuzzy  and  adaptive  way.   No indifference
concept,  no  intransitivity  assumption,  and  no axiom  of  the  independence  of
irrelevent  alternative apply.  The paradigm is based on  the ideal alternative,
infeasible  in  general,  providing  the  highest score with  the  respect  to  all
individual  attributes considered.   The infeasibility of the ideal is observed
to create a pre-decision conflict  and generate the impulse to move as close as
possible  toward  it,   thus  initiating  adaptive information  gathering  and  an
evaluation  process.   Partial decisions  are  then made,  inferior alternatives
are  removed, and post-decision dissonance  is seen to  ensue.   Included in  the
decision making process are readjustment of  attribute  weights,- displacement of
the  ideal,  and  new  pre-decision conflict   formation.   The  entire man-made
interactive procedure  is viewed  as   capable of  leading to  a decision  in  a
finite  number of iterations.
                                       54

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 50277-101
 REPORT DOCUMENTATION , i-_ REPORT NO.
        PAGE          j  EPA 560/7-81-005
                                                 ! 2.
                                                                 3. Recipient's Accession No.
4. rr.., .nd subtme  The  Relevance of  Multiple Criteria
       Decision  Making  to Priorities for  Chemical
       Regulation: An Annotated Bibliography
                                                                 5. Report Date
                                                                  July  6,1981
 7. Author(s)
 Steve Wilhelm (EPA)
                                               (Tracor  Jitco)
                         Doug Sellers(EPA) Patricia  Foreman
                                                                 8. Performing Organization Rept. No.
 9. Performing Organization Name and Address
        Tracor Jitco, Inc.
        1776 East Jefferson Street
        Rockville,  Maryland  20852
                                                                10. Project/Task/Work Unit No.

                                                                  Tech. Dir.  9
                                                                11. Contract(C) or Grant(G) No.

                                                                (o 68-01-6021

                                                                (G)
 12. Sponsoring Organization Name and Address
        U.S.  Environmental Protection  Agency
        Office of  Pesticides and  Toxic Substances
        401 M Street S.W.
        Washington D.C.  20460	
                                                                13. Type of Report & Period Covered

                                                                   Final
                                                                14.
 15. Supplementary Notes
 16. Abstract (Limit: 200 words)
        This  bibliography  contains one  hundred  and  thirteen references
        and original  abstracts on  multiple criteria  decision making and
        multi-attribute utility  theory.  It is a selection of representative
        articles and  reviews rather than an exhaustive review of  the
        literature. This report  was prepared in cooperation with
        the Office of Toxics Integration within the  Office  of Toxic
        Substances.
 17. Document Analysis  ». Descriptors
   b. Identifiers/Open-ended Terms

     Decision  Making,  Multi-attribute Utility Theory,  Ranking,

        Priority Setting


   c. COSATI Field/Group
 IS. Availability Statement

       unlimited
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21. No. of Pages
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