Social Choice and Welfare

, Volume 38, Issue 3, pp 371–406 | Cite as

The division problem with voluntary participation

  • Gustavo Bergantiños
  • Jordi Massó
  • Alejandro Neme
Original Paper


The division problem consists of allocating a given amount of a 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 article 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.


Voluntary Participation Order Priority Equal Division Division Problem Uniform Rule 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  • Gustavo Bergantiños
    • 1
  • Jordi Massó
    • 2
  • Alejandro Neme
    • 3
  1. 1.Research Group in Economic Analysis, Facultade de EconómicasUniversidade de VigoVigo (Pontevedra)Spain
  2. 2.Departament d’Economia i d’Història Econòmica and CODEUniversitat Autònoma de BarcelonaBellaterra (Barcelona)Spain
  3. 3.Instituto de Matemática Aplicada de San LuisUniversidad Nacional de San Luis and CONICETSan LuisArgentina

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