Multiwinner Temporal Voting with Aversion to Change

TL;DR

This paper investigates the complexity of selecting committees in two-stage elections with dynamic voter preferences, revealing tractability for Approval Voting and hardness for other Thiele rules, supported by theoretical and experimental analysis.

Contribution

It provides a full complexity dichotomy for Thiele rules in two-stage committee elections and extends it to greedy variants, including parameterized complexity insights.

Findings

Approval Voting allows efficient second-stage committee selection.

Hardness results for all other Thiele rules, including Proportional Approval Voting.

Experimental results on committee change dynamics and tie effects.

Abstract

We study two-stage committee elections where voters have dynamic preferences over candidates; at each stage, a committee is chosen under a given voting rule. We are interested in identifying a winning committee for the second stage that overlaps as much as possible with the first-stage committee. We show a full complexity dichotomy for the class of Thiele rules: this problem is tractable for Approval Voting (AV) and hard for all other Thiele rules (including, in particular, Proportional Approval Voting and the Chamberlin-Courant rule). We extend this dichotomy to the greedy variants of Thiele rules. We also explore this problem from a parameterized complexity perspective for several natural parameters. We complement the theory with experimental analysis: e.g., we investigate the average number of changes in the committee as a function of changes in voters' preferences and the role of ties.