# zbMATH — the first resource for mathematics

Uncovered set choice rules. (English) Zbl 1163.91348
Summary: I study necessary and sufficient conditions for a choice function to be rationalized in the following sense: there exists a total asymmetric relation $$T$$ (a tournament) such that, for each feasible (finite) set, the choice set coincides with the uncovered set of $$T$$ restricted to that feasible set. This notion of ‘maximization’ offers testable restrictions on observable choice behavior.

##### MSC:
 91B14 Social choice 05C90 Applications of graph theory 91B68 Matching models
Full Text:
##### References:
 [1] Bar-Hillel M and Margalit A (1988). How vicious are cycles of intransitive choice? Theory Decis 24(2): 119–145 · doi:10.1007/BF00132458 [2] Dutta B (1988). Covering sets and a new condorcet choice correspondence. J Econ Theory 44(1): 63–80 · Zbl 0652.90013 · doi:10.1016/0022-0531(88)90096-8 [3] Ehlers L, Sprumont Y (2007) Weakened WARP and top-cycle choice rules. J Math Econ (forthcoming) · Zbl 1141.91358 [4] Fishburn PC and LaValle IH (1988). Context-dependent choice with nonlinear and nontransitive preferences. Econometrica 56(5): 1221–1239 · Zbl 0657.90004 · doi:10.2307/1911365 [5] Fishburn PC (1991). Nontransitive preferences in decision theory. J Risk Uncertainty 4(2): 113–134 · Zbl 0723.90004 · doi:10.1007/BF00056121 [6] Laslier J-F (1997). Tournament solutions and majority voting. Vol 7 in the series studies in economic theory. Springer, Heidelberg · Zbl 0948.91504 [7] Manzini P, Mariotti M (2007) Sequentially rationalizable choice. Am Econ Rev (forthcoming) [8] May OK (1954). Intransitivity, utility and the aggregation of preference patterns. Econometrica 22(1): 1–13 · doi:10.2307/1909827 [9] Miller NR (1977). Graph-theoretical approaches to the theory of voting. Am J Polit Sci 21(4): 769–803 · doi:10.2307/2110736 [10] Miller NR (1980). A new solution set for tournaments and majority: further graph-theoretical approaches to the theory of voting. Am J Polit Sci 24(1): 68–96 · doi:10.2307/2110925 [11] Moulin H (1986). Choosing from a Tournament. Soc Choice Welf 3(4): 271–291 · Zbl 0618.90004 · doi:10.1007/BF00292732 [12] Russo JE and Dosher BA (1983). Strategies for multiattribute binary choice. J Exp Psychol Learn, Memory Cogni 9(4): 676–696 · doi:10.1037/0278-7393.9.4.676 [13] Sen AK (1970) Collective choice and social welfare. Oliver and Boyd Edinburg · Zbl 0227.90011 [14] Suzumura K (1983). Rational choice, collective decisions, and social welfare. Cambridge University Press, Cambridge · Zbl 0541.90003 [15] Zhang J, Hsee CK and Xiao Z (2006). The majority rule in individual decision making. Organ Behav Hum Decis Process 99(1): 102–111 · doi:10.1016/j.obhdp.2005.06.004
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.