The division problem with maximal capacity constraints
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. Most of the literature has implicitly assumed that all divisions are feasible. In this paper we consider the division problem when each agent has a maximal capacity due to an objective and verifiable feasibility constraint which imposes an upper bound on his share. Then each agent has a feasible interval of shares where his preferences are single-peaked. A rule has to propose to each agent a feasible share. We focus mainly on strategy-proof, efficient and consistent rules and provide alternative characterizations of the extension of the uniform rule that deals explicitly with agents’ maximal capacity constraints.
KeywordsDivision problem Single-peaked preferences Uniform rule Capacity constraints
- Barberà S (1996) Notes on strategy-proof social choice functions. In: Arrow K, Sen A, Suzumura K (eds) Social choice re-examinated. MacMillan, London. 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
- Bergantiños G, Massó J, Neme A (2011) The division problem with voluntary participation. Soc Choice Welf. doi:10.1007/s00355-011-0530-9
- Kim S (2010) The separability principle for the division problem with participation constraints. MimeoGoogle Scholar
- Manjunath V (2010) When too little is as good as nothing at all: rationing a disposable good among satiable people with acceptance thresholds. MimeoGoogle 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
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