Strategic requirements with indifference: single-peaked versus single-plateaued preferences

We concentrate on the problem of the provision of one pure public good whenever agents that form the society have either single-plateaued preferences or single-peaked preferences over the set of alternatives. We are interested in comparing the relationships between di¤erent nonmanipulability notions under these two domains. On the single-peaked domain, under strategy-proofness, non-bossiness is equivalent to convexity of the range. Thus, minmax rules are the only strategy-proof non-bossy rules. On the single-plateaued domain, only constant rules are non-bossy or Maskin monotonic; but strategy-proofness and weak non-bossiness are equivalent to weak Maskin monotonicity. Moreover, strategy-proofness and plateau-invariance guarantee convexity of the range. JEL Classi…cation Number: D71. Keywords: Strategy-proof, Single-plateaued preferences, Single-peaked preferences, Maskin monotonicity, Non-bossiness, Plateau-invariance. 1We thank Salvador Barberà, Matthew Jackson, Bettina Klaus, Jordi Massó, John Weymark, and two anonymous referees and the Associate Editor for helpful comments and suggestions. We also thank the participants in the 3rd Workshop on Social Decisions that took place in Málaga in November 2007. Dolors Berga acknowledges the …nantial support by the Spanish Ministry of Education and Science through Research Grants SEJ2004-03276 and SEJ200760671 and also by the Generalitat de Catalunya through Research Grant 2005SGR-213 and the Barcelona Economics Program (CREA). Bernardo Moreno gratefully acknowledges …nancial support from Junta de Andalucía through grant SEJ522 and the Spanish Ministry of Science and Technology through grant SEC2005-04805. yDepartament d’Economia, Campus de Montilivi, Universitat de Girona, 17071 Girona, Spain. E-mail: [email protected]. zDepartamento de Teoría e Historia Económica, Facultad de Ciencias Económicas y Empresariales, Campus de El Ejido, 29071 Málaga, Spain. E-mail: [email protected]