Social Welfare Maximization in Approval-Based Committee Voting under Uncertainty
Haris Aziz, Yuhang Guo, Venkateswara Rao Kagita, Baharak Rastegari, Mashbat Suzuki
TL;DR
This work advances the study of social welfare maximization in approval-based committee voting under uncertainty by systematically modeling four uncertainty paradigms and mapping a comprehensive set of computational problems (IsPossSWM, IsNecSWM, ExistsNecSWM, SWM-Prob, SW-Dist, MaxSWM, MaxExpSW). It delivers a detailed complexity landscape: polynomial-time algorithms for many problems across Joint, Candidate, and 3VA models, with #P-hardness and NP-hardness results primarily arising in the Lottery model, and it introduces dynamic-programming and dominance-graph techniques to achieve these results. The paper also extends to robustness concepts, showing that maximizing expected welfare yields provable robustness in some models, and provides practical DP procedures for distributional inquiries (SW-Dist) and probability computations (SWM-Prob). Overall, it supplies a versatile algorithmic toolkit for set selection under uncertainty with clear implications for real-world approval-based decision processes. The findings have potential applications in recommender systems, governance, and blockchain contexts where approval-based multi-winner choices must be made under partial information.
Abstract
Approval voting is widely used for making multi-winner voting decisions. The canonical rule (also called Approval Voting) used in the setting aims to maximize social welfare by selecting candidates with the highest number of approvals. We revisit approval-based multi-winner voting in scenarios where the information regarding the voters' preferences is uncertain. We present several algorithmic results for problems related to social welfare maximization under uncertainty, including computing an outcome that is social welfare maximizing with the highest probability, computing the social welfare probability distribution of a given outcome, computing the probability that a given outcome is social welfare maximizing, and understanding how robust an outcome is with respect to social welfare maximizing.