Domains, ranges and strategy-proofness: the case of single-dipped preferences
AbstractWe characterize the set of all individual and group strategy-proof rules on the domain of all single-dipped preferences on a line. For rules defined on this domain, and on several of its subdomains, we explore the implications of these strategy-proofness requirements on the maximum size of the rules' range. We show that when all single-dipped preferences are admissible, the range must contain two alternatives at most. But this bound changes as we consider different subclasses of single-dipped preferences: we provide examples of subdomains admitting strategy-proof rules with larger ranges. We establish exact bounds on the maximal size of strategy-proof functions on each of these domains, and prove that the relationship between the sizes of the subdomains and those of the ranges of strategy-proof functions on them need not be monotonic. Our results exhibit a sharp contrast between the structure of strategy-proof rules defined on subdomains of single-dipped preferences and those defined on subsets of single-peaked ones.
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Bibliographic InfoArticle provided by Springer in its journal Social Choice and Welfare.
Volume (Year): 39 (2012)
Issue (Month): 2 (July)
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Web page: http://link.springer.de/link/service/journals/00355/index.htm
Other versions of this item:
- Salvador Barberà & Dolors Berga & and Bernardo Moreno, 2009. "Domains, Ranges and Strategy-Proofness: The Case of Single-dipped Preferences," Working Papers 418, Barcelona Graduate School of Economics.
- Salvador Barberà & Dolors Berga & Bernardo Moreno, 2009. "Single-dipped preferences," UFAE and IAE Working Papers 801.09, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
- D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
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