Social Welfare Maximization in Approval-Based Committee Voting under Uncertainty

2025-03-02

AI Summary

This study addresses multi-winner approval voting under uncertain voter preferences, with the objective of maximizing social welfare probabilistically and robustly. We introduce the first systematic formalization of preference uncertainty in approval voting and propose a unified computational framework enabling: (1) identification of the outcome most likely to maximize social welfare; (2) inference of the full probability distribution over social welfare values for any given outcome; (3) computation of the probability that an outcome maximizes social welfare; and (4) quantification of its robustness against preference perturbations. Integrating techniques from combinatorial optimization, probabilistic reasoning, and computational social choice—alongside counting complexity analysis—we design both exact and approximation algorithms. Several of our algorithms achieve theoretical optimality in time complexity; notably, this work is the first to enable high-probability optimal outcome computation, guaranteed distributional computability, and rigorous robustness quantification.

Technology Category

• Game Theory and Economic Paradigms: Social Choice / Voting
• Reasoning under Uncertainty: Decision/Utility Theory
• Knowledge Representation and Reasoning: Preferences

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

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.

Problem

• Maximizing social welfare in uncertain approval voting scenarios
• Computing probability of social welfare maximizing outcomes
• Assessing robustness of outcomes in social welfare maximization

Innovation

• Maximizes social welfare under voter preference uncertainty
• Computes probability distribution of social welfare outcomes
• Assesses robustness of outcomes in welfare maximization