Outer Diversity of Structured Domains

2026-02-17

AI Summary

This work proposes a novel metric termed “external diversity” to quantify the extent of preference diversity that structured preference domains—such as single-peaked, single-crossing, group-separable, and Euclidean domains—can accommodate beyond the range of preferences they explicitly allow voters to express. By leveraging combinatorial and social choice-theoretic methods, the study formally defines this measure for the first time and systematically computes its values across several classical structured domains. The analysis reveals significant differences among these domains in terms of expressive flexibility, thereby offering a new theoretical lens and analytical tool for evaluating and comparing the expressive capacity of structured preference models in social choice theory.

Technology Category

• Knowledge Representation and Reasoning: Preferences
• Game Theory and Economic Paradigms: Social Choice / Voting
• Machine Learning: Learning Preferences or Rankings

Application Category

• Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments
• Web Mining and Content Analysis: Bridging structured and unstructured data
• User Modeling, Personalization and Recommendation: Metrics for user behavior and evaluating success

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.

Problem

• ordinal preference domain
• outer diversity
• structured domains
• single-peaked
• single-crossing

Innovation

• outer diversity
• structured preference domains
• ordinal preferences
• single-peaked
• preference domain theory