On strategy-proofness and symmetric single-peakedness

We characterize the class of strategy-proof social choice functions on the domain of symmetric single-peaked preferences. This class is strictly larger than the set of generalized median voter schemes (the class of strategy-proof and tops-only social choice functions on the domain of single-peaked preferences characterized by Moulin (1980)) since, under the domain of symmetric single-peaked preferences, generalized median voter schemes can be disturbed by discontinuity points and remain strategy-proof on the smaller domain. Our result identi…es the speci…c nature of these discontinuities which allow to design non-onto social choice functions to deal with feasibility constraints. JEL Classi…cation: D7. Keywords: Strategy-proofness, Single-peaked Preferences, Median Voter, Feasibility Constraints. We thank Gilat Levy for her helpful comments as well as the participants of the Bag Lunch Workshop on Game Theory and Social Choice at the UAB and the participants of the Theory Work in Progress Seminar at LSE. Support for the research of Jordi Massó was received through the prize “ICREA Acadèmia” for excellence in research, funded by the Generalitat de Catalunya. He also acknowledges the support of MOVE, where he is an a¢ liated researcher, and of the Barcelona Graduate School of Economics (through its Research Recognition Programme), where he is an a¢ liated professor. His work is also supported by the Spanish Ministry of Science and Innovation through grants ECO2008-04756 (Grupo Consolidado-C) and CONSOLIDER-INGENIO 2010 (CDS2006-00016), and by the Generalitat de Catalunya through grant SGR2009-419. Inés Moreno de Barreda acknowledges …nancial support from the Fundación Ramón Areces. yDepartament d’Economia i d’Història Econòmica and CODE, Universitat Autònoma de Barcelona, 08193 Bellaterra (Barcelona), Spain; e-mail: [email protected] zDepartment of Economics and STICERD, London School of Economics, Houghton Street, London WC2A 2AE, United Kingdom; e-mail: [email protected]