Maximizing Index Diversity in Committee Elections

2026-02-11

AI Summary

This study addresses the problem of maximizing committee diversity in multi-winner elections under constraints on either total approval scores or individual voter satisfaction. To this end, the authors propose two novel models based on approval voting and labeled candidates, each tailored to handle one type of constraint. They innovatively adapt and extend ecological diversity indices to the social choice setting, introducing a new index that satisfies desirable axiomatic properties and providing a complete axiomatic characterization. Through computational complexity analysis and empirical evaluation, the work delineates the tractability boundaries of the proposed models under mainstream voting rules and demonstrates that moderately relaxing the constraints can substantially enhance diversity outcomes.

Technology Category

• Game Theory and Economic Paradigms: Social Choice / Voting
• Constraint Satisfaction and Optimization: Satisfiability
• Humans and AI: Voting

Application Category

• Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics

Abstract

We introduce two models of multiwinner elections with approval preferences and labelled candidates that take the committee's diversity into account. One model aims to find a committee with maximal diversity given a scoring function (e.g. of a scoring-based voting rule) and a lower bound for the score to be respected. The second model seeks to maximize the diversity given a minimal satisfaction for each agent to be respected. To measure the diversity of a committee, we use multiple diversity indices used in ecology and introduce one new index. We define (desirable) properties of diversity indices, test the indices considered against these properties, and characterize the new index. We analyze the computational complexity of computing a committee for both models and scoring functions of well-known voting rules, and investigate the influence of weakening the score or satisfaction constraints on the diversity empirically.

Problem

• committee elections
• diversity maximization
• approval preferences
• multiwinner voting
• diversity indices

Innovation

• diversity index
• multiwinner elections
• approval preferences
• computational complexity
• satisfaction constraints