Approximation Algorithms for Optimization Problems with Justified Representation Constraints

Zhihao Jiang, Ashish Goel

Keywords: Multiwinner Voting, Approval Voting, Justified Representation

Abstract: Justified representation (JR) is a crucial fairness concept within the context of committee selection in the approval voting setting. When multiple committees satisfy JR, an additional quality measurement is required to select a committee among all JR committees. Optimization problems over all JR committees are NP-hard in many cases. In this paper, we consider approximation algorithms for optimization problems subject to JR constraints. Specifically, we explore algorithms and complexity related to minimizing total committee member costs and maximizing social welfare over JR committees. Our cost-minimization algorithm also works in the EJR+ and BJR setting. Our approach employs techniques such as linear programming rounding and reduction of hypergraph problems to our context.

Submission Number: 9