Agreement, Diversity, and Polarization Indices for Approval Elections

TL;DR

This paper introduces and analyzes indices to measure agreement, diversity, and polarization in approval elections, providing tools to compare elections and understand voter behavior.

Contribution

It proposes new normalized indices for approval elections, analyzes their properties, and applies them to real-world election data for insights.

Findings

New indices effectively capture agreement, diversity, and polarization.

Indices reveal similarities and differences among real-life approval elections.

Normalization ensures comparable measurements across different election sizes.

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.