Domains, Ranges and Strategy-Proofness: The Case of Single-dipped Preferences
Salvador Barberà (),
Dolors Berga and
Bernardo Moreno ()
No 418, Working Papers from Barcelona Graduate School of Economics
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)
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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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