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The single-peaked domain revisited: A simple global characterization

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  • Puppe, Clemens

Abstract

It is proved that, among all restricted preference domains that guarantee consistency (i.e. transitivity) of pairwise majority voting, the single-peaked domain is the only minimally rich and connected domain that contains two completely reversed strict preference orders. It is argued that this result explains the predominant role of single-peakedness as a domain restriction in models of political economy and elsewhere. The main result has a number of corollaries, among them a dual characterization of the single-dipped do- main; it also implies that a single-crossing ('order-restricted') domain can be minimally rich only if it is a subdomain of a single-peaked domain. The conclusions are robust as the results apply both to domains of strict and of weak preference orders, respectively.

Suggested Citation

  • Puppe, Clemens, 2016. "The single-peaked domain revisited: A simple global characterization," Working Paper Series in Economics 97, Karlsruhe Institute of Technology (KIT), Department of Economics and Business Engineering.
  • Handle: RePEc:zbw:kitwps:97
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    References listed on IDEAS

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    Cited by:

    1. Stefano Vannucci, 2017. "Tree-Wise Single Peaked Domains," Department of Economics University of Siena 770, Department of Economics, University of Siena.

    More about this item

    Keywords

    social choice; restricted domains; Condorcet domains; single-peakedness; single-dippedness; majority voting; single-crossing property;

    JEL classification:

    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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