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
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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.
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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
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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.
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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.
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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.
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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.
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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
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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
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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
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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.
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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.
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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.
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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
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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
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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
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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
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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.
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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
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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.
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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
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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
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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.
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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.
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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
I 19. Security Class (This Report)
unclassified
i 20. Security Class (This Page)
1 unclassified
21. No. of Pages
58
22. Price
(See ANSI-Z39.18)
See Instructions on Reverse
OPTIONAL FORM 272 (4-77)
(Formerly NTIS-35)
Department of Commerce
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