Strengthening Proportionality in Participatory Budgeting with Additive Utilities

2026-09-08

AI Summary

研究解决了参与式预算中比例代表性问题，通过扩展残差预算贪婪算法，在多项式时间内实现几乎满足完全正当代表性的解决方案。

Abstract

Proportional representation is a central goal in participatory budgeting, where voters select public projects subject to a shared budget. Full justified representation (FJR) accounts for groups whose members may value different projects, but computing an FJR outcome is strongly NP-hard for additive utilities. We show that FJR up to one project can be achieved in polynomial time for arbitrary nonnegative additive utilities and project costs. Our approach extends Residual-Budget Greedy and satisfies a stronger fractional axiom that can also be verified in polynomial time. For approval utilities, this axiom coincides with FJR+, providing exact FJR in that setting. We further show that every feasible completion of the algorithm's selected set preserves the representation guarantee, providing flexibility in allocating the remaining budget. In particular, we give a completion that ensures priceability at the original budget. For unit-cost projects, we strengthen the representation guarantee to the Droop quota and combine it with priceability whenever there are enough positively valued projects to fill the budget.

Problem

• participatory budgeting
• proportional representation
• additive utilities
• full justified representation (FJR)

Innovation

• Proportional Representation
• Additive Utilities
• Polynomial Time
• Residual-Budget Greedy
• Fractional Axiom