Agreement, Diversity, and Polarization Indices for Approval Elections

2026-05-14

AI Summary

This study addresses the challenge of consistently quantifying consensus, diversity, and polarization in approval elections across varying levels of voter approval saturation. It proposes a suite of novel indices normalized by saturation level and validates their robustness and effectiveness through axiomatic analysis and empirical evaluation on real-world datasets, including Pabulib and Preflib. The work offers the first systematic characterization of multidimensional group attitudes in approval voting, constructing a mapping of real election scenarios that reveals underlying similarities and differences. By doing so, it provides a new analytical toolkit for comparative election studies, enabling more nuanced insights into the structural properties of collective decision-making processes under approval-based rules.

Abstract

An index is a function that given an election outputs a value between 0 and 1, indicating the extent to which this election has a particular feature. We seek indices that capture agreement, diversity, and polarization among voters in approval elections, and that are normalized with respect to saturation. By the latter we mean that if two elections differ by the fraction of candidates approved by an average voter, but otherwise are of similar nature, then they should have similar index values. We propose several indices, analyze their properties, and use them to (a) derive a new map of approval elections, and (b) show similarities and differences between various real-life elections from Pabulib, Preflib and other sources.

Problem

• approval elections
• agreement
• diversity
• polarization
• normalization

Innovation

• approval elections
• agreement index
• diversity index
• polarization index
• saturation normalization