The division problem with voluntary participation
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.
Unable to display preview. Download preview PDF.
- Barberà S (1996) Notes on strategy-proof social choice functions. In: Arrow K, Sen AA, Suzumura K (eds) Social choice re-examinated. MacMillan, London (1996). French version: Sur les fonctions de choix non manipulables. Revue d’Économie Politique 106:61–81 (1996)Google Scholar
- Barberà S (2010) Strategy-proof Social Choice. In: Arrow K, Suzumura K (eds) Handbook of social choice and welfare, vol 2. Kluwer, DordrechtGoogle Scholar
- Thomson W (1994b) Resource-monotonic solutions to the problem of fair division when preferences are single-peaked. Soc Choice Welf 11: 205–223Google Scholar
- Weymark J (1999) Sprumont’s characterization of the uniform rule when all single-peaked preferences are admissible. Rev Econ Des 4: 389–393Google Scholar