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 InfoPaper provided by Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC) in its series UFAE and IAE Working Papers with number 801.09.
Date of creation: 31 Dec 2009
Date of revision:
strategy-proof; group strategy-proof; binary range rules; single-dipped;
Other versions of this item:
- Salvador Barberà & Dolors Berga & Bernardo Moreno, 2012. "Domains, ranges and strategy-proofness: the case of single-dipped preferences," Social Choice and Welfare, Springer, vol. 39(2), pages 335-352, July.
- 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.
- D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
This paper has been announced in the following NEP Reports:
- NEP-ALL-2010-06-04 (All new papers)
- NEP-CDM-2010-06-04 (Collective Decision-Making)
- NEP-POL-2010-06-04 (Positive Political Economics)
- NEP-PUB-2010-06-04 (Public Finance)
- NEP-UPT-2010-06-04 (Utility Models & Prospect Theory)
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