强化参与式预算中加性效用的比例代表性

中文摘要 AI 辅助

比例代表制是参与式预算的一个核心目标，其中选民在共享预算约束下选择公共项目。完全正当代表（FJR）考虑了其成员可能重视不同项目的群体，但对于加性效用，计算FJR结果在强NP难意义下是困难的。我们证明，对于任意非负加性效用和项目成本，可以在多项式时间内实现至多一个项目的FJR。我们的方法扩展了剩余预算贪心算法，并满足一个更强的分数公理，该公理也可以在多项式时间内验证。对于批准效用，该公理与FJR+一致，从而在该设置中提供精确的FJR。我们进一步证明，算法所选集合的每个可行补全都保持代表保证，从而在分配剩余预算时提供灵活性。特别地，我们给出了一种补全方法，确保在原始预算下满足可价格性。对于单位成本项目，我们将代表保证强化到德鲁普配额，并在有足够多正价值项目填满预算时，将其与可价格性相结合。

英文摘要

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.

发表机构

• Harvard University（哈佛大学）
• University of Oxford（牛津大学）

机构由 AI 辅助整理，请以论文原文为准。