Fractional Pareto-Optimality in Multiwinner Voting

2026-06-09

AI Summary

This work addresses the computational intractability and lack of efficiency robustness characterizations for Pareto optimality (PO) in multiwinner voting. We introduce fractional Pareto optimality (fPO)—a committee is fPO if it is not dominated by any fractional committee (i.e., convex combination of committees)—and establish its equivalence to weighted utilitarian welfare maximization. Leveraging welfarist analysis and structural properties of preference domains, we devise a polynomial-time verification algorithm for fPO, demonstrate its robustness under uniform candidate cloning, and prove that the set of fPO committees satisfies committee monotonicity and is connected under single-candidate swaps. We further identify preference domains where PO and fPO coincide and show that Proportional Approval Voting (PAV) may violate fPO under approval ballots.

Abstract

Efficiency in multiwinner voting is most naturally captured by Pareto-optimality (PO), yet this notion is computationally and structurally difficult to handle. We therefore study fractional Pareto-optimality (fPO), under which a committee may not be dominated even by a fractional committee, i.e., any convex combination of committees. fPO turns out to be a natural refinement of PO as it retains exactly those Pareto-optimal committees whose efficiency is robust under uniform cloning of candidates. Furthermore, fPO committees are guaranteed to exist and have strong structural properties. We present a characterization of fPO in terms of weighted utilitarian welfare maximization, which yields a polynomial-time algorithm for verifying fPO and shows that the set of fPO committees satisfies committee monotonicity and is connected under single-candidate swaps. Analyzing welfarist rules through the lens of fPO, we further uncover an incompatibility between fPO and equality-oriented objectives. Most notably, we show that proportional approval voting (PAV) violates fPO in the approval setting. We close by pinpointing preference domains, including various one-dimensional ones, on which PO and fPO collapse into one notion.

Problem

• multiwinner voting
• Pareto-optim日消息ality
• fractional Pareto-optimality
• efficiency
• approval voting

Innovation

• fractional Pareto-optimality
• multiwinner voting
• welfarist rules
• proportional approval voting
• committee monotonicity