On the Complexity of Finding a Diverse and Representative Committee using a Monotone, Separable Positional Multiwinner Voting Rule

TL;DR

This paper analyzes the computational complexity of selecting a diverse and representative committee in multiwinner elections using a specific voting rule, establishing complexity results under minimal assumptions.

Contribution

It provides a complete complexity classification for finding such committees with a monotone, separable positional rule, removing previous restrictive assumptions.

Findings

Complexity classification is complete under P ≠ NP.

The problem remains hard even with minimal assumptions.

Clarifies the computational boundaries of diversity and fairness in multiwinner voting.

Abstract

Fairness in multiwinner elections, a growing line of research in computational social choice, primarily concerns the use of constraints to ensure fairness. Recent work proposed a model to find a diverse \emph{and} representative committee and studied the model's computational aspects. However, the work gave complexity results under major assumptions on how the candidates and the voters are grouped. Here, we close this gap and classify the complexity of finding a diverse and representative committee using a monotone, separable positional multiwinner voting rule, conditioned \emph{only} on the assumption that P $\neq$ NP.