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The division problem with voluntary participation


  • Gustavo Bergantiños


  • Jordi Massó


  • Alejandro Neme



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.
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Suggested Citation

  • Gustavo Bergantiños & Jordi Massó & Alejandro Neme, 2012. "The division problem with voluntary participation," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 38(3), pages 371-406, March.
  • Handle: RePEc:spr:sochwe:v:38:y:2012:i:3:p:371-406
    DOI: 10.1007/s00355-011-0530-9

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    References listed on IDEAS

    1. Thomson, William, 1995. "Population-Monotonic Solutions to the Problem of Fair Division When Preferences Are Single-Peaked," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 5(2), pages 229-246, March.
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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

    JEL classification:

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


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