Maximizing Index Diversity in Committee Elections

TL;DR

This paper proposes models for multiwinner approval elections that optimize committee diversity using various indices, analyzing their properties, computational complexity, and empirical behavior under different constraints.

Contribution

It introduces two novel models for diversity-aware committee selection, evaluates multiple diversity indices, and analyzes their computational and empirical aspects.

Findings

Diversity indices satisfy key desirable properties

Computational complexity results for committee selection models

Empirical analysis of diversity under relaxed constraints

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.