Approval-Based Committee Voting under Uncertainty
Hariz Aziz, Venkateswara Rao Kagita, Baharak Rastegari, Mashbat Suzuki
TL;DR
This work extends approval-based committee voting to settings with uncertain voter preferences by introducing four probabilistic models of uncertainty and studying how to maximize or verify justified representation (JR) under that uncertainty. The authors define a suite of problems (JR-Probability, IsPossJR, IsNecJR, ExistsNecJR, MaxJR) and their PJR/EJR variants, and provide a comprehensive computational complexity landscape across models, including NP-completeness, coNP-hardness, and #P-completeness results. Key findings include NP-completeness of ExistsNecJR across all models, polynomial-time solvability for certain IsPossJR cases (except Lottery), and #P-completeness of JR-Probability in the 3VA model, with several tractability and hardness results depending on model and parameter regimes (e.g., $k=n$). The paper highlights the theoretical implications for designing fair, robust ABC rules under uncertainty and suggests directions such as approximation and fixed-parameter tractable approaches for MaxJR, as well as extending the analysis to other fairness notions.
Abstract
We study approval-based committee voting in which a target number of candidates are selected based on voters' approval preferences over candidates. In contrast to most of the work, we consider the setting where voters express uncertain approval preferences and explore four different types of uncertain approval preference models. For each model, we study the problems such as computing a committee with the highest probability of satisfying axioms such as justified representation.