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

Madhuparna Karmokar*, Souvik Roy, Ton Storcken

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

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.

Original languageEnglish
Pages (from-to)313-336
Number of pages24
JournalTheory and Decision
Volume91
Issue number3
Early online date26 Mar 2021
DOIs
Publication statusPublished - Oct 2021

Keywords

  • Pairwise majority rule
  • Single-peaked domains on trees
  • Unanimity
  • Anonymity
  • Group strategy-proofness
  • Strategy-proofness

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