On Top-connected Single-peaked and Partially Single-peaked Domains

Gopakumar Achuthankutty () and Souvik Roy ()

MPRA Paper from University Library of Munich, Germany

Abstract: We characterize all domains for which the set of unanimous and strategy-proof social choice functions coincides with the set of min-max rules. As an application of our result, we obtain a characterization of unanimous and strategy-proof social choice functions on maximal single-peaked domains (Moulin (1980), Weymark (2011)), minimally rich single-peaked domains (Peters et al. (2014)), maximal regular single-crossing domain (Saporiti (2009)), and distance based single-peaked domains. We further consider domains that exhibit single-peaked property only over a subset of alternatives. We call such domains top-connected partially single-peaked domains. We characterize the unanimous and strategy-proof social choice function on such domains. As an application of this result, we obtain a characterization of the unanimous and strategy-proof social choice functions on multiple single-peaked domains (Reffgen (2015)), single-peaked domains on graphs, and several other domains of practical significance.

Keywords: Strategy-proofness; min-max rules; min-max domains; single-peaked preferences; top-connectedness property; partially single-peaked preferences; partly dictatorial generalized median voter schemes. (search for similar items in EconPapers)
JEL-codes: D71 D82 (search for similar items in EconPapers)
Date: 2017-04-04
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https://mpra.ub.uni-muenchen.de/79048/1/MPRA_paper_79048.pdf revised version (application/pdf)

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