Heller, Yuval (2009): Justifiable choice.
Download (234Kb) | Preview
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 non-inferiority (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 non-binary 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 multiple-utility representation: There is a unique convex set of vN-M 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 multiple-prior 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 closely-related to psychological insights of justifiable choices: The decision maker has several ways to evaluate acts, each with a different justification. Observable payoff-irrelevant 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|
|Keywords:||uncertainty, multiple priors, multiple utilities, incomplete preferences, anchoring, framing, non-binary choice.|
|Subjects:||D - Microeconomics > D8 - Information, Knowledge, and Uncertainty > D81 - Criteria for Decision-Making under Risk and Uncertainty|
|Depositing User:||Yuval Heller|
|Date Deposited:||01. Sep 2009 07:52|
|Last Modified:||19. Feb 2013 08:22|
F. J. Anscombe, and R. J. Aumann, 1963. A definition of subjective probability, Annals of Mathematical Statistics 34, 199-295.
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 non-binary social choice functions. Theory and Decision 3, 1-11.
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, 79-110.
Cherepanov V., Feddersen T., Sandroni A., 2008. Rationalization. mimeo.
Deb R, 1983. Binariness and rational choice. Mathematical Social Sciences 5(1), 97-105.
Ellsberg D., 1961. Risk, ambiguity and the Savage axioms. Quarterly Journal of Economics 75, 643-669.
Fishburn, P. C. 1970a, Intransitive individual indifference and transitive majorities, Econometrica, 38.
Fishburn, P. C. 1970, Utility Theory for Decision Making. Wiley, New-York.
Fishburn, 1991. Nontransitive preferences in decision theory. Journal of risk and uncertainty 4, 113-134.
Fudenberg D., Levine D.K., 1993. Self-confirming equilibrium, Econometrica 61, 523-545.
Georgescu-Roegen 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, 133-173.
Gilboa I., Schmeidler D., 1989. Maxmin expected utility with a non-unique prior, Journal of Mathematical Economics 18, 141-153.
Gilboa I., Schmeidler D., 2001. A Theory of Case-Based 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), 1231-1240.
Kalai G., Rubinstein A., Spiegler R., 2002. Rationalizing choice functions by multiple rationals. Econometrica 70 (6), 2481-2488.
Kilbanoff P., Marinacci M., Mukerji S., 2005. A smooth model of decision making under ambiguity, Econometrica 73, 1849-1892.
Kim T., Richter M., 1985. Nontransitive nontotal consumer theory, Journal of Economic Theory 38, 324-363.
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, 805-824.
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), 263-279.
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, 333-409.
Maccheroni F., Marinacci M., Rustchini A., 2006. Ambiguity aversion, robustness, and the variational representation of preferences, Econometrica 74, 1447-1498.
Machina MJ, 1982. "Expected Utility" Analysis without the Independence Axiom. Econometrica 50(2), 277-323.
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, 255-277.
Manzini P., Mariotti M., 2007. Sequantually rationalizable choice. American Economic Review 97 (5), 1824-1839.
May K.O., 1951. Intransitivity, utility and the aggregation of preference patterns, Econometrica 22, 1-13.
Nehring, K, 1997. Rational choice and revealed preference without binariness. Social Choice and Welfare 14, 403-425
Raiffa H, 1961. Risk ambiguity, and the Savage axioms: comment. The Quarterly Journal of Economics. 75 (4), 690-694.
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, 1287-1296.
Rubinstein A. ,Wolinsky A., 1994. Rationalizable conjectural equilibrium: between Nash and rationalizabilty, Games and Economic Behavior 6, 299-311.
Savage L.J., 1954. The Foundations of Statistics, Wiley, New-York.
Schwartz T., Rationality and the Myth of Maximum, Nous 6 (2), 97-117.
Schmeidler D., 1989. Subjective probability and expected utility without additivity, Econometrica 57, 571-587.
Sen A.K., 1971. Choice functions and revealed preferences, Review of Economic Studies 38, 307-317.
Shafir E, Simonson I, Tversky A, 1993. Reason-based choice. Cognition 49, 11-36.
Sion M., 1958. On general Minimax theorems, Pac. J. Math. 8, 171-176
Tversky A., 1969. Intransitivity of preferences, Psychological Review 76, 31-48.
Tversky, A, Kahneman, D, 1974. Judgments under uncertainty: Heuristics and biases. Science, 185, 1124-1131
Tversky A, Kahneman D, 1981. The framing of decisions and the psychology of choice, Science (211), 453-458.
Available Versions of this Item
Justifiable choice. (deposited 11. Aug 2009 05:42)
- Justifiable choice. (deposited 01. Sep 2009 07:52) [Currently Displayed]