Multiwinner Temporal Voting with Aversion to Change

TL;DR

This work investigates two-stage committee elections with evolving voter preferences, formalizing Resilient Committee Elections (RCE) under Thiele rules. It establishes a complete complexity dichotomy: RCE is solvable in polynomial time for Approval Voting but coNP-hard (and coW[1]-hard in k) for every other Thiele rule, a result that extends to greedy Thiele rules. The authors also provide parameterized algorithms (FPT/XP) for natural parameters and report extensive experiments on contiguity, tie-breaking, and replacement patterns, highlighting the practical impact of tie handling. Overall, the paper clarifies the computational limits of maintaining stable committees over time in approval-based settings and connects these limits to both theory and empirical behavior.

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.

Figures (18)

• Figure 1: Results of Experiment 1. $x$-axis is the percentage change between the original election $E$ and the adapted election $E'$; $y$-axis is the average distance between the two winning committees.
• Figure 2: Results of Experiment 2. Focus is only on MIX operation. Orange lines represent the median and dashed green lines the mean. $x$-axis is the percentage change between the original election $E$ and the adapted election $E'$; $y$-axis is the $\mathrm{dist}\xspace(S, S_{\mathrm{lexi}}') - \mathrm{dist}\xspace(S, S_{\mathrm{opt}}')$, where $S$, and $S_{\mathrm{lexi}}'$ are the respective winning committees in $E$ and $E'$ under lexicographic tie-breaking, and $S_{\mathrm{opt}}'$ is chosen out of $100$ tied winning committees in $E'$ to be closest to $S$.
• Figure 3: Results of Experiment $3$. Focus is only on MIX operation and changes of $2.5\%$ in relation to the original number of approvals were applied. Orange lines represent the median and dashed green lines the mean. $x$-axis corresponds to candidates from the original winning committee, ordered by when they were chosen in the given greedy Thiele rule; $y$-axis is the percentage of winning committees in the adapted elections where each candidate is replaced.
• Figure 4: Results of Experiment $1$ under the 1D model.
• Figure 5: Results of Experiment $1$ under the 2D model.

Theorems & Definitions (46)

• Proposition 2.1
• proof
• Theorem 2.2
• proof
• Theorem 2.3
• Proposition 3.1
• Theorem 3.2
• Corollary 3.3
• Theorem 3.4
• Proposition 4.1