The division problem under constraints

The division problem under constraints consists of allocating a given amount of an homogeneous and perfectly divisible good among a subset of agents with singlepeaked preferences on an exogenously given interval of feasible allotments. We characterize axiomatically the family of extended uniform rules proposed to solve the division problem under constraints. Rules in this family extend the uniform rule used to solve the classical division problem without constraints. We show that the family of all extended uniform rules coincides with the set of rules satisfying e¢ ciency, strategy-proofness, equal treatment of equals, bound monotonicity, consistency, and independence of irrelevant coalitions. Journal of Economic Literature Classi…cation Number: D71. Keywords: Division Problem, Single-peaked Preferences. We thank two anonymous referees for their extremely valuable comments. The work of G. Bergantiños is partially supported by research grants ECO2008-03484-C02-01 and ECO2011-23460 from the Spanish Ministry of Science and Innovation and FEDER. J. Massó acknowledges …nancial support from the Spanish Ministry of Economy and Competitiveness, through the Severo Ochoa Programme for Centres of Excellence in R&D (SEV-2011-0075) and through grant ECO2008-0475-FEDER (Grupo Consolidado-C), and from the Generalitat de Catalunya, through the prize “ICREA Academia”for excellence in research and grant SGR2009-419. The work of A. Neme is partially supported by the Universidad Nacional de San Luis, through grant 319502, and by the Consejo Nacional de Investigaciones Cientí…cas y Técnicas (CONICET), through grant PIP 112-200801-00655. yResearch Group in Economic Analysis. Facultade de Económicas, Universidade de Vigo. 36310, Vigo (Pontevedra), Spain. E-mail: [email protected] zUniversitat Autònoma de Barcelona and Barcelona Graduate School of Economics. Departament d’Economia i d’Història Econòmica, Campus UAB, Edi…ci B. 08193, Bellaterra (Barcelona), Spain. Email: [email protected] xInstituto de Matemática Aplicada de San Luis. Universidad Nacional de San Luis and CONICET. Ejército de los Andes 950. 5700, San Luis, Argentina. E-mail: [email protected]