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

Madhuparna Karmokar (), Souvik Roy () and Ton Storcken ()
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Madhuparna Karmokar: Indian Statistical Institute
Souvik Roy: Indian Statistical Institute
Ton Storcken: University of Maastricht

Theory and Decision, 2021, vol. 91, issue 3, No 2, 313-336

Abstract: 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.

Keywords: Pairwise majority rule; Single-peaked domains on trees; Unanimity; Anonymity; Group strategy-proofness; Strategy-proofness (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s11238-021-09804-5

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