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King-chicken choice correspondences

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  • Costa, Matheus
  • Riella, Gil

Abstract

Given a complete, though not necessarily transitive, preference relation, we propose a family of choice representations inspired by the king-chicken procedure, according to which an alternative x is chosen among a set of alternatives A if, for every other alternative y in A, either x is preferred to y or there is another alternative z in A such that x is preferred to z, and z is preferred to y. We generalize this process by allowing the path from x to y to include more than one alternative z and fully characterize the choice correspondences that can be achieved through it. Two of the most relevant tournament solutions, the uncovered set and the top-cycle, are special cases of this generalized king-chicken choice procedure, so this work improves previous results that have appeared in the choice theory literature by delivering axiomatizations for those models in generic (not necessarily finite) choice spaces.

Suggested Citation

  • Costa, Matheus & Riella, Gil, 2022. "King-chicken choice correspondences," Mathematical Social Sciences, Elsevier, vol. 120(C), pages 113-118.
    • Handle: RePEc:eee:matsoc:v:120:y:2022:i:c:p:113-118
    DOI: 10.1016/j.mathsocsci.2022.10.001
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    References listed on IDEAS

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    1. Michele Lombardi, 2008. "Uncovered set choice rules," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 31(2), pages 271-279, August.
    2. Felix Brandt & Christian Geist & Paul Harrenstein, 2016. "A note on the McKelvey uncovered set and Pareto optimality," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 46(1), pages 81-91, January.
    3. Fuad Aleskerov & Denis Bouyssou & Bernard Monjardet, 2007. "Utility Maximization, Choice and Preference," Springer Books, Springer, edition 0, number 978-3-540-34183-3, September.
    4. Elizabeth Penn, 2006. "Alternate Definitions of the Uncovered Set and Their Implications," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 27(1), pages 83-87, August.
    5. Nishimura, Hiroki, 2018. "The transitive core: inference of welfare from nontransitive preference relations," Theoretical Economics, Econometric Society, vol. 13(2), May.
    6. Amartya K. Sen, 1971. "Choice Functions and Revealed Preference," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 38(3), pages 307-317.
    7. Ehlers, Lars & Sprumont, Yves, 2008. "Weakened WARP and top-cycle choice rules," Journal of Mathematical Economics, Elsevier, vol. 44(1), pages 87-94, January.
    8. Herzberger, Hans G, 1973. "Ordinal Preference and Rational Choice," Econometrica, Econometric Society, vol. 41(2), pages 187-237, March.
    9. Georges Bordes, 1976. "Consistency, Rationality and Collective Choice," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 43(3), pages 451-457.
    10. Christian Saile & Warut Suksompong, 2020. "Robust bounds on choosing from large tournaments," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 54(1), pages 87-110, January.
    11. Smith, John H, 1973. "Aggregation of Preferences with Variable Electorate," Econometrica, Econometric Society, vol. 41(6), pages 1027-1041, November.
    12. I. Good, 1971. "A note on condorcet sets," Public Choice, Springer, vol. 10(1), pages 97-101, March.
    13. Eliaz, Kfir & Ok, Efe A., 2006. "Indifference or indecisiveness? Choice-theoretic foundations of incomplete preferences," Games and Economic Behavior, Elsevier, vol. 56(1), pages 61-86, July.
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