Agreement, Diversity, and Polarization Indices for Approval Elections

摘要

An index is a function that measures the extent to which an election has a particular feature. We seek indices that capture agreement, diversity, and polarization among voters in approval elections, normalized with respect to saturation. The latter means 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 derive a new map of approval elections, and compare various real-life elections from Pabulib, Preflib and other sources.