A simple characterization of single-peaked domains

TL;DR

This paper characterizes single-peaked preference domains on trees through the strategy-proofness of extreme rules, showing these rules are strategy-proof only within the single-peaked domain on that tree.

Contribution

It provides a new characterization of single-peaked domains on trees based on the strategy-proofness of specific rules, linking domain structure to rule properties.

Findings

Extreme rules are unanimous and anonymous on any preference domain.

Extreme rules are strategy-proof only on the single-peaked domain associated with the tree.

The characterization applies to any tree structure in preference domains.

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.