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Single-basined choice

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  • Bossert, Walter
  • Peters, Hans

Abstract

Single-basined preferences generalize single-dipped preferences by allowing for multiple worst elements. Single-dipped and single-basined preferences have played an important role in areas such as voting, strategy-proofness and matching problems. We examine the notion of single-basinedness in a choice-theoretic setting, with the set of all compact convex subsets of Rn as the domain of choice sets. In conjunction with independence of irrelevant alternatives, single-basined choice implies a structure that conforms to the motivation underlying our definition. We establish the consequences of requiring single-basined choice correspondences to be upper semicontinuous. Moreover, we extend our results to larger domains of non-convex sets.

Suggested Citation

  • Bossert, Walter & Peters, Hans, 2014. "Single-basined choice," Journal of Mathematical Economics, Elsevier, vol. 52(C), pages 162-168.
    • Handle: RePEc:eee:mateco:v:52:y:2014:i:c:p:162-168
    DOI: 10.1016/j.jmateco.2013.12.010
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    as
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    Cited by:

    1. Bossert, Walter & Peters, Hans, 2014. "Single-basined choice," Journal of Mathematical Economics, Elsevier, vol. 52(C), pages 162-168.
    2. Doghmi, Ahmed & Ziad, Abderrahmane, 2015. "Nash implementation in private good economies with single-plateaued preferences and in matching problems," Mathematical Social Sciences, Elsevier, vol. 73(C), pages 32-39.
    3. Diss, Mostapha & Doghmi, Ahmed & Tlidi, Abdelmonaim, 2015. "Strategy proofness and unanimity in private good economies with single-peaked preferences," MPRA Paper 75469, University Library of Munich, Germany, revised 06 Dec 2016.
    4. Gong, Doudou & Dietzenbacher, Bas & Peters, Hans, 2022. "Mechanisms for division problems with single-dipped preferences," Research Memorandum 007, Maastricht University, Graduate School of Business and Economics (GSBE).

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    More about this item

    Keywords

    Single-basinedness; Choice correspondences; Independence of irrelevant alternatives; The weak axiom of revealed preference; Upper semicontinuity;
    All these keywords.

    JEL classification:

    • D11 - Microeconomics - - Household Behavior - - - Consumer Economics: Theory
    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations

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