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Necessary and sufficient conditions for pairwise majority decisions on path-connected domains

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  • Madhuparna Karmokar

    (Indian Statistical Institute)

  • Souvik Roy

    (Indian Statistical Institute)

  • Ton Storcken

    (University of Maastricht)

Abstract

In this paper, we consider choice functions that are unanimous, anonymous, symmetric, and group strategy-proof and consider domains that are single-peaked on some tree. We prove the following three results in this setting. First, there exists a unanimous, anonymous, symmetric, and group strategy-proof choice function on a path-connected domain if and only if the domain is single-peaked on a tree and the number of agents is odd. Second, a choice function is unanimous, anonymous, symmetric, and group strategy-proof on a single-peaked domain on a tree if and only if it is the pairwise majority rule (also known as the tree-median rule) and the number of agents is odd. Third, there exists a unanimous, anonymous, symmetric, and strategy-proof choice function on a strongly path-connected domain if and only if the domain is single-peaked on a tree and the number of agents is odd. As a corollary of these results, we obtain that there exists no unanimous, anonymous, symmetric, and group strategy-proof choice function on a path-connected domain if the number of agents is even.

Suggested Citation

  • Madhuparna Karmokar & Souvik Roy & Ton Storcken, 2021. "Necessary and sufficient conditions for pairwise majority decisions on path-connected domains," Theory and Decision, Springer, vol. 91(3), pages 313-336, October.
    • Handle: RePEc:kap:theord:v:91:y:2021:i:3:d:10.1007_s11238-021-09804-5
    DOI: 10.1007/s11238-021-09804-5
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