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Individually Rational Rules for the Division Problem when the Number of Units to be Allotted is Endogenous

Author

Listed:
  • Gustavo Bergantiños

    (Universidade de Vigo)

  • Jordi Massó

    (Universitat Autónoma de Barcelona. Barcelona Graduate School of Economics)

  • Alejandro Neme

    (Instituto de Matemática Aplicada San Luis. Universidad Nacional de San Luis . CONICET.)

Abstract

We study individually rational rules to be used to allot, among a group of agents, a perfectly divisible good that is freely available only in whole units. A rule is individually rational if, at each preference profile, each agent finds that her allotment is at least as good as any whole unit of the good. We study and characterize two individually rational and eficient families of rules, whenever agents' preferences are symmetric single-peaked on the set of possible allotments. Rules in the two families are in addition envy-free, but they differ on wether envy-freeness is considered on losses or on awards. Our main result states that (i) the family of constrained equal losses rules coincides with the class of all individually rational and eficient rules that satisfy justified envy-freeness on losses and (ii) the family of constrained equal awards rules coincides with the class of all individually rational and eficient rules that satisfy envy-freeness on awards.

Suggested Citation

  • Gustavo Bergantiños & Jordi Massó & Alejandro Neme, 2020. "Individually Rational Rules for the Division Problem when the Number of Units to be Allotted is Endogenous," Working Papers 6, Red Nacional de Investigadores en Economía (RedNIE).
    • Handle: RePEc:aoz:wpaper:6
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    JEL classification:

    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations

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