New indices measure agreement, diversity, and polarization in approval elections

A team of computer scientists from AGH University and other Polish institutions—Piotr Faliszewski, Jitka Mertlová, Krzysztof Sornat, Stanisław Szufa, and Tomasz Wąs—has published a new paper on arXiv proposing a family of indices for approval elections. Unlike traditional election analysis that focuses on winner selection or candidate ranking, their work targets the underlying voter behavior patterns: how much voters agree (agreement index), how diverse their preferences are (diversity index), and how polarized the electorate is (polarization index). Critically, all indices are normalized with respect to saturation—the fraction of candidates an average voter approves. This normalization ensures that an election where voters approve many candidates and one where they approve few are comparable in their structural features, avoiding distortions from differing base approval rates.

The researchers applied their indices to real-world approval election data from sources like Pabulib (participatory budgeting) and Preflib (preference and judgment data). The result is a new “map of approval elections” that clusters similar voting scenarios—showing, for instance, which participatory budgeting elections behave like political referendums and which resemble internal committee decisions. The work bridges computational social choice, game theory, and AI multiagent systems, offering tools that could improve election design, analyze voter sentiment, and detect polarization in organizational or public votes. The paper is available on arXiv under CS.GT and related subjects.