#### Title

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

#### Article Type

Research Article

#### Publication Title

Theory and Decision

#### 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.

#### First Page

313

#### Last Page

336

#### DOI

10.1007/s11238-021-09804-5

#### Publication Date

10-1-2021

#### Recommended Citation

Karmokar, Madhuparna; Roy, Souvik; and Storcken, Ton, "Necessary and sufficient conditions for pairwise majority decisions on path-connected domains" (2021). *Journal Articles*. 1782.

https://digitalcommons.isical.ac.in/journal-articles/1782

## Comments

Open Access, Hybrid Gold