Abstract
A detailed theoretical analysis is presented of what five utility representations – subjective expected utility (SEU), rank-dependent (cumulative or Choquet) utility (RDU), gains decomposition utility (GDU), rank weighted utility (RWU), and a configural-weight model (TAX) that we show to be equivalent to RWU – say about a series of independence properties, many of which were suggested by M. H. Birnbaum and his coauthors. The goal is to clarify what implications to draw about the descriptive aspects of the representations from data concerning these properties. The upshot is a sharp rejection of SEU and RDU and no clear choice between GDU and TAX, but a list of 8 properties is given that should receive more attention to discriminate between the latter two models.
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J. Aczél M. Kuczma (1991) ArticleTitleGeneralizations of a ‘folk-theorem’ on simple functional equations in a single variable Results in Mathematics 19 5–21
M.H. Birnbaum (1997) Violations of monotonicity in judgment and decision making A.A.J. Marley (Eds) Choice, Decision, and Measurement: Essays in Honor of R. Duncan Luce Erlbaum Mahwah, NJ 73–100
M.H. Birnbaum (1999) The paradoxes of Allais, stochastic dominance, and decision weights J. Shanteau B.A. Mellers D.A. Schum (Eds) Decision Science and Technology: Reflections on the Contributions of Ward Edwards Kluwer Academic Publishers Boston, MA 49–78
M.H. Birnbaum (2000) Decision making in the lab and on the web M.H. Birnbaum (Eds) Psychological Experiments on the Internet Academic Press San Diego, CA 3–34
M.H. Birnbaum (2001) A Web-based program of research on decision making U.-D. Reips M. Bosnjak (Eds) Dimensions of Internet Science Pabst Science Lengerich, Germany 23–55
Birnbaum, M.H. (2005), Three new tasks of independence that differentiate models of risky decision making. Management Science, in press.
M.H. Birnbaum D. Beeghley (1997) ArticleTitleViolations of branch independence in judgments of the value of gambles Psychological Science 8 87–94
M.H. Birnbaum A. Chavez (1997) ArticleTitleTests of theories of decision making: Violations of branch independence and distribution independence Organizational Behavior and Human Decision Processes 71 161–194 Occurrence Handle10.1006/obhd.1997.2721
M.H. Birnbaum G. Coffey B.A. Mellers R. Weiss (1992) ArticleTitleUtility measurement: Configural-weight theory and the judge’s point of view Journal of Experimental Psychology: Human Perception and Performance 18 331–346 Occurrence Handle10.1037/0096-1523.18.2.331
M.H. Birnbaum W.R. McIntosh (1996) ArticleTitleViolations of branch independence in choices between gambles Organizational Behavior and Human Decision Processes 67 91–110 Occurrence Handle10.1006/obhd.1996.0067
M.H. Birnbaum J.B. Navarrete (1998) ArticleTitleTesting descriptive utility theories: Violations of stochastic dominance and cumulative independence Journal of Risk and Uncertainty 17 49–78 Occurrence Handle10.1023/A:1007739200913
M.H. Birnbaum J.N. Patton M.K. Lott (1999) ArticleTitleEvidence against rank-dependent utility theories: Tests of cumulative independence, interval independence, stochastic dominance, and transitivity Organizational Behavior and Human Decision Processes 77 44–83 Occurrence Handle10.1006/obhd.1998.2816 Occurrence Handle9924141
M.H. Birnbaum R. Veira (1998) ArticleTitleConfigural weighting in judgments of two-and four-outcome gambles Journal of Experimental Psychology; Human Perception and Performances 24 216–226
S.H. Chew (1983) ArticleTitleA generalization of the quasilinear mean and applications to the measurement of income inequality and decision theory resolving the Allais paradox Econometrica 51 1065–1092
Y.-H. Cho R.D. Luce L. Truong (2002) ArticleTitleDuplex decomposition and general segregation of lotteries of a gain and a loss: An empirical evaluation Organizational Behavior and Human Decision Processes 89 1176–1193 Occurrence Handle10.1016/S0749-5978(02)00026-2
Green J.R. and Jullien B. (1988), Ordinal independence in non-linear utility theory, Journal of Risk and Uncertainty, 1, 355–381. Erratum: (1989) Journal of Risk and Uncertainty, 2, 119.
M.-H. Ho M. Regenwetter R. Niederée D. Heyer (2005) ArticleTitleAn alternative perspective on von Winterfeldt et al.’s (1997) Test of Consequence monotonicity Journal of Experimental Psychology: Learning, Memory, and Cognitions 31 365–372
U.S. Karmarkar (1978) ArticleTitleSubjectively weighted utility: A descriptive extension of the expected utility model Organizational Behaviour and Human Performance 21 61–72 Occurrence Handle10.1016/0030-5073(78)90039-9
U.S. Karmarkar (1979) ArticleTitleSubjectively weighted utility and the Allais paradox Organizational Behavior and Human Performance 24 67–72 Occurrence Handle10.1016/0030-5073(79)90016-3
P.K. Lattimore J.R. Baker A.D. Witt (1992) ArticleTitleThe influence of probability on risky choice Journal of Economic Behavior and Organization 17 377–400 Occurrence Handle10.1016/S0167-2681(95)90015-2
Liu, L. (1995), A Theory of Coarse Utility and its Application to Portfolio Analysis, University of Kansas, Ph.D. dissertation.
R.D. Luce (1959) Individual Choice Behavior: A Theoretical Analysis Wiley New York
Luce, R.D. (2000), Utility of Gains and Losses: Measurement-Theoretical and Experimental Approaches. Erlbaum, Mahwah, NJ. Errata: see Luce web page at http://www.social.science.uci.edu.
R.D. Luce A.A.J. Marley (2005) ArticleTitleAdditive utility representations of gambles: Old and new axiomatizations Journal of Risk and Uncertainty 30 21–62 Occurrence Handle10.1007/s11166-005-5832-9
A.A.J. Marley R.D. Luce (2001) ArticleTitleRanked-weighted utility and qualitative convolution Journal of Risk and Uncertainty 23 135–163 Occurrence Handle10.1023/A:1011132102314
Meginniss, J.R. (1976), A new class of symmetric utility rules for gambles, subjective marginal probability functions, and a generalized Bayes’ rule, Proceedings American Statistical Association, Business and Economic Statistics Section, 471–476.
A. Tversky D. Kabneman (1992) ArticleTitleAdvances in prospect theory: Cumulative representation of uncertainty Journal of Risk and Uncertainty 5 297–323 Occurrence Handle10.1007/BF00122574
K.W. Viscussi (1989) ArticleTitleProspective reference theory: Toward an explanation of the paradoxes Journal of Risk and Uncertainty 2 235–264
D. Winterfeldt Particlevon N.-K. Chung R.D. Luce Y. Cho (1997) ArticleTitleTests of consequence monotonicity in decision making under uncertainty Journal of Experimental Psychology: Learning, Memory, and Cognition 23 406–426
P. Wakker I. Erev E.U. Weber (1994) ArticleTitleComonotonic independence: The critical test between classical and rank-dependent theories Journal of Risk and Uncertainty 9 195–230 Occurrence Handle10.1007/BF01064200
E. Weber B. Kirsner (1997) ArticleTitleReasons for rank-dependent evaluation Journal of Risk and Uncertainty 14 41–61 Occurrence Handle10.1023/A:1007769703493
G. Wu (1994) ArticleTitleAn empirical test of ordinal independence Journal of Risk and Uncertainty 9 39–60 Occurrence Handle10.1007/BF01073402
G. Wu R. Gonzalez (1996) ArticleTitleCurvature of the probability weighting function Management Science 42 1676–1690
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Economics Classification. D46, D81
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Marley, A.A.J., Luce, R.D. Independence Properties Vis-À-Vis Several Utility Representations. Theor Decis 58, 77–143 (2005). https://doi.org/10.1007/s11238-005-2460-4
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DOI: https://doi.org/10.1007/s11238-005-2460-4