Agreement, Diversity, and Polarization Indices for Approval Elections
Provides tools for political scientists and social choice theorists to quantitatively compare approval elections across different contexts.
The paper proposes new indices for measuring agreement, diversity, and polarization in approval elections, normalized for saturation, and demonstrates their utility by analyzing real-world election data from multiple sources.
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.