On single-peaked domains and min–max rules

Article Type

Research Article

Publication Title

Social Choice and Welfare

Abstract

We consider social choice problems where the admissible set of preferences of each agent is single-peaked. First, we show that if all the agents have the same admissible set of preferences, then every unanimous and strategy-proof social choice function (SCF) is tops-only. Next, we consider situations where different agents have different admissible sets of single-peaked preferences. We show by means of an example that unanimous and strategy-proof SCFs need not be tops-only in this situation, and consequently provide a sufficient condition on the admissible sets of preferences of the agents so that unanimity and strategy-proofness guarantee tops-onlyness. Finally, we characterize all domains on which (i) every unanimous and strategy-proof SCF is a min–max rule, and (ii) every min–max rule is strategy-proof. As an application of our result, we obtain a characterization of the unanimous and strategy-proof social choice functions on maximal single-peaked domains (Moulin in Public Choice 35(4):437–455. https://doi.org/10.1007/BF00128122, 1980; Weymark in SERIEs 2(4):529–550. https://doi.org/10.1007/s13209-011-0064-5, 2011), minimally rich single-peaked domains (Peters et al. in J Math Econ 52:123–127. https://doi.org/10.1016/j.jmateco.2014.03.008. http://www.sciencedirect.com/science/article/pii/S0304406814000470, 2014), maximal regular single-crossing domains (Saporiti in Theor Econ 4(2):127–163, 2009, J Econ Theory 154:216–228. https://doi.org/10.1016/j.jet.2014.09.006. http://www.sciencedirect.com/science/article/pii/S0022053114001276, 2009), and distance based single-peaked domains.

First Page

753

Last Page

772

DOI

10.1007/s00355-018-1137-1

Publication Date

12-1-2018

Comments

All Open Access, Green

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