Domains, Ranges and Strategy-Proofness: The Case of Single-dipped Preferences

Dolors Berga, Bernardo Moreno () and Salvador Barberà ()

No 418, Working Papers from Barcelona School of Economics

Abstract: We 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.

Keywords: Strategy-proof; group strategy-proof; binary range rules; single-dipped (search for similar items in EconPapers)
JEL-codes: D71 (search for similar items in EconPapers)
Date: 2015-09
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Related works:
Journal Article: Domains, ranges and strategy-proofness: the case of single-dipped preferences (2012)
Working Paper: Single-dipped preferences (2009)
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Persistent link: https://EconPapers.repec.org/RePEc:bge:wpaper:418

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