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Weakened WARP and top-cycle choice rules. (English) Zbl 1141.91358
Summary: We propose the following weakened version of WARP: if the decision maker selects an alternative \(x\) and rejects another alternative \(y\) in some context, he cannot select y and reject x in another context. This axiom is consistent with cyclic choices. It is necessary and sufficient for the choice from every subset \(A\) of a (finite) universal set \(X\) to coincide with the weak upper-contour set of the transitive closure of some fixed complete relation at some alternative in \(A\). Adding further simple axioms forces the choice from each subset to coincide with the top cycle (in that subset) of some fixed tournament over the universal set.

91B06 Decision theory
91B14 Social choice
Full Text: DOI
[1] Aleskerov, F.; Monjardet, B., Utility maximization, choice and preference, (2002), Springer Verlag Heidelberg · Zbl 1010.91022
[2] Arrow, K., Rational choice functions and orderings, Economica, 26, 121-127, (1959)
[3] Bordes, G., Consistency, rationality, and collective choice, Review of economic studies, 43, 451-457, (1976) · Zbl 0361.90003
[4] Camerer, C., Individual decision making, (), 587-704
[5] Chernoff, H., Rational selection of decision functions, Econometrica, 22, 423-443, (1954) · Zbl 0059.12602
[6] Deb, R., On schwartz’s rule, Journal of economic theory, 16, 103-110, (1977) · Zbl 0369.90003
[7] Duggan, J., 1997. Pseudo-Rationalizability and Tournament Solutions, Working Paper, University of Rochester.
[8] Dutta, B., Covering sets and a new Condorcet choice correspondence, Journal of economic theory, 44, 63-80, (1988) · Zbl 0652.90013
[9] Fishburn, P., Condorcet social choice functions, SIAM journal on applied mathematics, 33, 469-489, (1977) · Zbl 0369.90002
[10] Kalai, E.; Pazner, E.; Schmeidler, D., Collective choice correspondences as admissible outcomes of social bargaining processes, Econometrica, 44, 233-240, (1976) · Zbl 0342.90001
[11] Kalai, E.; Schmeidler, D., An admissible set occurring in various bargaining situations, Journal of economic theory, 14, 402-411, (1977) · Zbl 0364.90146
[12] Kalai, G.; Rubinstein, A.; Spiegler, R., Rationalizing choice functions by multiple rationales, Econometrica, 70, 2481-2488, (2002) · Zbl 1130.91326
[13] Lahiri, S., The top cycle and uncovered solutions for weak tournaments, Control and cybernetics, 30, 439-450, (2001) · Zbl 1028.91018
[14] Laslier, J.-F., Tournament solutions and majority voting, volume 7 in the series “studies in economic theory”, (1997), Springer Verlag Heidelberg
[15] Lombardi, M., 2006. Uncovered Set Choice Rules, Working Paper, Queen Mary, University of London.
[16] Loomes, G.; Starmer, C.; Sugden, R., Observing violations of transitivity by experimental methods, Econometrica, 59, 425-440, (1991)
[17] Manzini, P., Mariotti, M., in press. Rationalizing boundedly rational choice: sequential rationalizability and rational shortlist methods. American Economic Review.
[18] Miller, N., A new solution set for tournaments and majority: further graph-theoretical approaches to the theory of voting, American journal of political science, 24, 68-96, (1980)
[19] Moon, J., Topics on tournaments, (1968), Holt, Rinehart and Winston New York · Zbl 0191.22701
[20] Moulin, H., Choice functions over a finite set: a summary, Social choice and welfare, 2, 147-160, (1984) · Zbl 0576.90004
[21] Moulin, H., Choosing from a tournament, Social choice and welfare, 3, 271-291, (1986) · Zbl 0618.90004
[22] Ray, I.; Zhou, L., Game theory via revealed preferenes, Games and economic behavior, 37, 415-424, (2001) · Zbl 1022.91008
[23] Schwartz, T., Rationality and the myth of the maximum, Noûs, 6, 97-117, (1972)
[24] Schwartz, T., 1986. The Logic of Collective Action. Columbia, New York.
[25] Xu, Y.; Zhou, L., Rationalizability of choice functions by game trees, Journal of economic theory, 134, 548-556, (2007) · Zbl 1157.91329
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