2021/10/24 by Kamesh Munagala, Munagala, Kamesh, Yiheng Shen +5 · 6 citations
Decision Sciences · Economics, Econometrics and Finance · #Auction Theory and Applications #Computer Science and Game Theory (cs.GT) #Data Structures and Algorithms (cs.DS) #FOS: Computer and information sciences #FOS: Economics and business #Game Theory and Voting Systems #Theoretical Economics (econ.TH)
paper · pdf · doi:10.48550/arxiv.2110.12499
openalex publication_date 2021/10/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Motivated by civic problems such as participatory budgeting and multiwinner elections, we consider the problem of public good allocation: Given a set of indivisible projects (or candidates) of different sizes, and voters with different monotone utility functions over subsets of these candidates, the goal is to choose a budget-constrained subset of these candidates (or a committee) that provides fair utility to the voters. The notion of fairness we adopt is that of core stability from cooperative game theory: No subset of voters should be able to choose another blocking committee of proportionally smaller size that provides strictly larger utility to all voters that deviate. The core provides a strong notion of fairness, subsuming other notions that have been widely studied in computational social choice. It is well-known that an exact core need not exist even when utility functions of the voters are additive across candidates. We therefore relax the problem to allow approximation: Voters can only deviate to the blocking committee if after they choose any extra candidate (called an additament), their utility still increases by an α factor. If no blocking committee exists under this definition, we call this an α-core. Our main result is that an α-core, for α< 67.37, always exists when utilities of the voters are arbitrary monotone submodular functions, and this can be computed in polynomial time. This result improves to α< 9.27 for additive utilities, albeit without the polynomial time guarantee. Our results are a significant improvement over prior work that only shows logarithmic approximations for the case of additive utilities. We complement our results with a lower bound of α> 1.015 for submodular utilities, and a lower bound of any function in the number of voters and candidates for general monotone utilities.