Outer Diversity of Structured Domains

TL;DR

This paper introduces the concept of outer diversity in preference domains and evaluates its significance across well-known structured domains like single-peaked, single-crossing, group-separable, and Euclidean preferences.

Contribution

It defines the notion of outer diversity and assesses its importance for various classical structured preference domains.

Findings

Outer diversity varies across different structured domains.

Outer diversity provides insights into the complexity of preference domains.

The concept helps understand the limitations and capabilities of voting rules within these domains.

Abstract

An ordinal preference domain is a subset of preference orders that the voters are allowed to cast in an election. We introduce and study the notion of outer diversity of a domain and evaluate its value for a number of well-known structured domains, such as the single-peaked, single-crossing, group-separable, and Euclidean ones.