A simple characterization of single-peaked domains

2026-04-29

AI Summary

This study investigates how to characterize single-peaked preference domains on tree structures that admit strategy-proof mechanisms. By introducing extreme rules—a class of social choice rules satisfying consistency and anonymity—the authors provide the first concise characterization of single-peaked domains on trees through the lens of strategy-proofness. The central contribution establishes that an extreme rule is strategy-proof on a given preference domain if and only if the domain consists precisely of preferences that are single-peaked with respect to the underlying tree. This result yields a direct equivalence between the structural property of preferences and the strategic property of mechanisms, offering a novel theoretical tool for identifying single-peaked domains in tree-structured settings.

Abstract

This paper characterizes the single-peaked domain on a tree via the strategy-proofness of extreme rules defined on that tree. For any tree, these rules are unanimous and anonymous on any preference domain. In particular, we show that they are strategy-proof only on the single-peaked domain associated with that tree.

Problem

• single-peaked domain
• strategy-proofness
• extreme rules
• tree
• preference domain

Innovation

• single-peaked domain
• strategy-proofness
• extreme rules
• tree structure
• preference domain