The Complexity of Justified Representation with Additive Utilities

2026-09-01

AI Summary

研究了在参与式预算和委员会选举中满足正当代表性的问题，使用加法效用，并探讨了不同方法的计算复杂性。

Abstract

We study the computational complexity of satisfying proportional representation -- in particular proportional, extended, and fully justified representation (PJR, EJR, and FJR) -- in participatory budgeting and committee elections with additive utilities. First, we give a complete picture of the complexity of the axioms for a constant number of voters or voter types. Second, we show that even for committee elections with integer utilities bounded above by a small constant, satisfying FJR is intractable, giving the first strong NP-hardness result for a justified representation axiom. Third, we extend the Expanding Approvals Rule to committee elections with additive utilities and show that it satisfies PJR. Lastly, we show that no sequential voting rule can improve on the known positive result, thus proving that novel, substantially different voting rules are needed to surpass these boundaries. Beyond their theoretical merit, our results carry practical importance, as multi-winner voting with additive utilities has recently been gaining prominence in online deliberation and real-world participatory budgeting.

Problem

• proportional representation
• additive utilities
• computational complexity
• participatory budgeting
• committee elections

Innovation

• Computational Complexity
• Fully Justified Representation (FJR)
• Expanding Approvals Rule
• Additive Utilities