Agreement, Diversity, and Polarization Indices for Approval Elections

Piotr Faliszewski; Jitka Mertlová; Krzysztof Sornat; Stanisław Szufa; Tomasz Wąs

cs.GTMay 14, 2026

Agreement, Diversity, and Polarization Indices for Approval Elections

Authors: Piotr Faliszewski, Jitka Mertlová, Krzysztof Sornat, Stanisław Szufa, Tomasz Wąs

Organizations: AGH University of Kraków, Poland · Czech Technical University in Prague, Czech Republic · University of Geneva, Switzerland · University of Oxford, United Kingdom

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.

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May 19, 2026 · cs.AIJ/K move · Enter open · S save

Efficient Elicitation of Collective Disagreements

Mohamed Ouaguenouni, Felipe Garrido-Lucero, Umberto Grandi, César Hidalgo+1

IRIT, Université Toulouse Capitole, Toulouse, France · Center for Collective Learning, IAST, Toulouse School of Economics, Toulouse, France · Center for Collective Learning, CIAS, Corvinus University of Budapest, Budapest, Hungary · AMBS, University of Manchester, Manchester, UK · Centrale Supélec, Paris Saclay, France

We analyze the structure of the disagreement among a population of voters over a set of alternatives. Surveys typically ask either for pairwise comparisons, simple and intuitive for participants, or full rankings over alternatives, eliciting the entire voters' preferences. Building on the observation that pairwise comparisons cannot distinguish structural disagreement from noise, we propose a stratified framework to identify the minimal aggregated preference information needed to compute a number of disagreement measures from the literature. Specifically, we introduce the plurality matrix, a generalization of pairwise comparisons that records, for every subset

S

of alternatives, the probability that each

a \in S

ranks first in

S

. We define the level of a disagreement measure as the smallest subset size needed to express it, showing that many existing notions, including rank-variance and divisiveness, sit at level

3

, proving that pairwise comparisons are not enough. In addition, we demonstrate the interest of going beyond level

3

both theoretically and experimentally. To make these results actionable, we design two elicitation protocols to estimate the plurality matrix, exploring the trade-off between the number of required participants and the cognitive load requested to each of them.

Disagreement Pairwise Preferences Elicitation

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Abstract

Explore similar work

Efficient Elicitation of Collective Disagreements

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