Heller, Yuval (2009): Justifiable choice.
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Abstract
Abstract In many situations a decision maker has incomplete psychological preferences, and the weak axiom of revealed preference (WARP) is often violated. In this paper we relax WARP, and replace it with another axiom, the convex axiom of revealed noninferiority (CARNI). An alternative x is revealed inferior to y if x is never chosen when y is in the convex hull of the choice set. CARNI requires that an alternative is chosen if it is not inferior to all other alternatives in the convex hull of the choice set. We apply CARNI in two models and axiomatize nonbinary choice correspondences. In the first model we impose the standard axioms of expected utility model, except that WARP is replaced by CARNI. We prove that this axiomatization has a multipleutility representation: There is a unique convex set of vNM utilities, such that an alternative is chosen if and only if it is best with respect to one of the utilities in this set. In the second model we impose the axioms of subjective expected utility, relax WARP in a similar way, and obtain multipleprior representation: There is a unique convex set of priors over the states of nature, such that an alternative is chosen if and only if it is best with respect to one of these priors. Both representations are closelyrelated to psychological insights of justifiable choices: The decision maker has several ways to evaluate acts, each with a different justification. Observable payoffirrelevant information during the choice process triggers her to use a specific “anchoring” justification for the evaluation of the alternatives.
Item Type:  MPRA Paper 

Original Title:  Justifiable choice 
Language:  English 
Keywords:  uncertainty, multiple priors, multiple utilities, incomplete preferences, anchoring, framing, nonbinary choice. 
Subjects:  D  Microeconomics > D8  Information, Knowledge, and Uncertainty > D81  Criteria for DecisionMaking under Risk and Uncertainty 
Item ID:  17018 
Depositing User:  Yuval Heller 
Date Deposited:  01 Sep 2009 07:52 
Last Modified:  02 Oct 2019 04:32 
References:  F. J. Anscombe, and R. J. Aumann, 1963. A definition of subjective probability, Annals of Mathematical Statistics 34, 199295. Armstrong W.E., 1939. The determinateness of the utility function. Economic Journal 49. Batra R.N., Pattanaik P.K., 1972. On some suggestions for having nonbinary social choice functions. Theory and Decision 3, 111. Battigalli P., 1987. Comportanmento rezionale ed equilibrio nei glochi e nelle situazioni sociali, unpublished dissertation, Milano, Bocconi University. Bewley T.F., 2002. Knightian decision theory  part 1. Decisions in economics and finance 25, 79110. Cherepanov V., Feddersen T., Sandroni A., 2008. Rationalization. mimeo. Deb R, 1983. Binariness and rational choice. Mathematical Social Sciences 5(1), 97105. Ellsberg D., 1961. Risk, ambiguity and the Savage axioms. Quarterly Journal of Economics 75, 643669. Fishburn, P. C. 1970a, Intransitive individual indifference and transitive majorities, Econometrica, 38. Fishburn, P. C. 1970, Utility Theory for Decision Making. Wiley, NewYork. Fishburn, 1991. Nontransitive preferences in decision theory. Journal of risk and uncertainty 4, 113134. Fudenberg D., Levine D.K., 1993. Selfconfirming equilibrium, Econometrica 61, 523545. GeorgescuRoegen N., 1958. Threshold in choice and the theory of demand, Econometrica 26. Ghirardato P., Maccheroni F., Marinacci M., 2004. Differentiating ambiguity and ambiguity attitude, Journal of Economic Theory 118, 133173. Gilboa I., Schmeidler D., 1989. Maxmin expected utility with a nonunique prior, Journal of Mathematical Economics 18, 141153. Gilboa I., Schmeidler D., 2001. A Theory of CaseBased Decisions. Cambridge: Cambridge University press. Gilboa I., Maccheroni F., Marinacci M., Schmeidler D., 2008. Objective and Subjective rationality in a multiple prior model, manuscript. Heath C, Tversky A, Preference and belief: ambiguity and competence in choice under uncertainty, Journal of Risk and Uncertainty, 1991. Inada K, Majority rule and rationality, Journal of Economic Theory, 2. Kalai E., Lehrer E., 1993. Subjective equilibrium in repeated games, Econometrica 61 (1993), 12311240. Kalai G., Rubinstein A., Spiegler R., 2002. Rationalizing choice functions by multiple rationals. Econometrica 70 (6), 24812488. Kilbanoff P., Marinacci M., Mukerji S., 2005. A smooth model of decision making under ambiguity, Econometrica 73, 18491892. Kim T., Richter M., 1985. Nontransitive nontotal consumer theory, Journal of Economic Theory 38, 324363. Lehrer E., Teper R., 2009. Justifiable preferences. manuscript. http://www.math.tau.ac.il/~teperroe/Papers/just.pdf Loomes G., Sugden R., 1982. Regret theory: an alternative theory of rational choice under uncertainty, The Economic Journal 92, 805824. Luce R.D., Raiffa H., 1957. Games and Decisions. Wiley, New York. Luce R D, von Winterfeldt D, 1994. What common grounds exists for descriptive, perspective, and normative utility theories. Management Science, 40 (2), 263279. MacCrimmon K.R., Larsson S., 1979. Utility theory: axioms versus 'paradoxes'. In M. Allais and O. Hagen (eds.), Expected Utility Hypotheses and the Allais Paradox. Dordrecht, Holland: Reidal, 333409. Maccheroni F., Marinacci M., Rustchini A., 2006. Ambiguity aversion, robustness, and the variational representation of preferences, Econometrica 74, 14471498. Machina MJ, 1982. "Expected Utility" Analysis without the Independence Axiom. Econometrica 50(2), 277323. Majumdar T., 1962. The Measurement of Utility, London: Macmillan, 2nd ed. Mandler M., 2005. Incomplete preferences and rational intransitivity of choice. Games and Economic Behavior, 255277. Manzini P., Mariotti M., 2007. Sequantually rationalizable choice. American Economic Review 97 (5), 18241839. May K.O., 1951. Intransitivity, utility and the aggregation of preference patterns, Econometrica 22, 113. Nehring, K, 1997. Rational choice and revealed preference without binariness. Social Choice and Welfare 14, 403425 Raiffa H, 1961. Risk ambiguity, and the Savage axioms: comment. The Quarterly Journal of Economics. 75 (4), 690694. Rubinstein A. and Salant Y., 2006. Two comments on the principle of revealed preference. Mimeo. http://arielrubinstein.tau.ac.il/papers/frames.pdf Rubinstein A., Salant Y., 2008. Choice with frames. Review of Economic Studies 75, 12871296. Rubinstein A. ,Wolinsky A., 1994. Rationalizable conjectural equilibrium: between Nash and rationalizabilty, Games and Economic Behavior 6, 299311. Savage L.J., 1954. The Foundations of Statistics, Wiley, NewYork. Schwartz T., Rationality and the Myth of Maximum, Nous 6 (2), 97117. Schmeidler D., 1989. Subjective probability and expected utility without additivity, Econometrica 57, 571587. Sen A.K., 1971. Choice functions and revealed preferences, Review of Economic Studies 38, 307317. Shafir E, Simonson I, Tversky A, 1993. Reasonbased choice. Cognition 49, 1136. Sion M., 1958. On general Minimax theorems, Pac. J. Math. 8, 171176 Tversky A., 1969. Intransitivity of preferences, Psychological Review 76, 3148. Tversky, A, Kahneman, D, 1974. Judgments under uncertainty: Heuristics and biases. Science, 185, 11241131 Tversky A, Kahneman D, 1981. The framing of decisions and the psychology of choice, Science (211), 453458. 
URI:  https://mpra.ub.unimuenchen.de/id/eprint/17018 
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