cs.AIMay 19, 2026

Efficient Elicitation of Collective Disagreements

Authors: Mohamed OuaguenouniFelipe Garrido-LuceroUmberto GrandiCésar HidalgoMagdalena Tydrichova

Organizations: 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

Abstract

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 SS of alternatives, the probability that each aSa \in S ranks first in SS. 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 33, proving that pairwise comparisons are not enough. In addition, we demonstrate the interest of going beyond level 33 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.

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