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The Division Problem with Voluntary Participation

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  • Gustavo Bergantiños

    ()

  • Jordi Massó

    ()

  • Alejandro Neme

    ()

Abstract

The division problem consists of allocating a given amount of an homogeneous and perfectly divisible good among a group of agents with single-peaked preferences on the set of their potential shares. A rule proposes a vector of shares for each division problem. The literature has implicitly assumed that agents will find acceptable any share they are assigned to. In this paper we consider the division problem when agents' participation is voluntary. Each agent has an idiosyncratic interval of acceptable shares where his preferences are single-peaked. A rule has to propose to each agent either to not participate or an acceptable share because otherwise he would opt out and this would require to reassign some of the remaining agents' shares. We study a subclass of efficient and consistent rules and characterize extensions of the uniform rule that deal explicitly with agents' voluntary participation.

Suggested Citation

  • Gustavo Bergantiños & Jordi Massó & Alejandro Neme, 2010. "The Division Problem with Voluntary Participation," UFAE and IAE Working Papers 807.10, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
  • Handle: RePEc:aub:autbar:807.10
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    References listed on IDEAS

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    1. Thomson, William, 1997. "The Replacement Principle in Economies with Single-Peaked Preferences," Journal of Economic Theory, Elsevier, vol. 76(1), pages 145-168, September.
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    6. Sprumont, Yves, 1991. "The Division Problem with Single-Peaked Preferences: A Characterization of the Uniform Allocation Rule," Econometrica, Econometric Society, vol. 59(2), pages 509-519, March.
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    Citations

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    Cited by:

    1. Bergantiños, Gustavo & Massó, Jordi & Neme, Alejandro, 2015. "The division problem under constraints," Games and Economic Behavior, Elsevier, vol. 89(C), pages 56-77.
    2. Kim, Sunyoung & Bergantiños, Gustavo & Chun, Youngsub, 2015. "The separability principle in single-peaked economies with participation constraints," Mathematical Social Sciences, Elsevier, vol. 78(C), pages 69-75.
    3. Billette de Villemeur, Etienne & Leroux, Justin, 2016. "Accounting for Needs in Cost Sharing," MPRA Paper 73434, University Library of Munich, Germany.

    More about this item

    Keywords

    Division Problem; Single-peaked Preferences; Uniform Rule; Voluntary Participation;

    JEL classification:

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

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