Approximate Strategyproofness in Approval-based Budget Division

2026-05-12

AI Summary

This work addresses the inherent trade-off among strategyproofness, efficiency, and fairness in approval-based budget allocation. To reconcile these competing objectives, the paper introduces approximate strategyproofness, measured by the incentive ratio—the maximum utility gain a voter can achieve through manipulation—and seeks mechanisms that are both efficient and fair under this relaxed notion. The authors theoretically establish that the Nash product rule achieves the optimal incentive ratio of 2 under standard fairness and efficiency conditions, and prove this bound to be tight. This result extends to settings with arbitrary concave utility functions. Through a combination of theoretical analysis and empirical evaluation, the study systematically assesses the manipulability of various allocation rules, demonstrating the Nash product rule’s superior ability to balance fairness, efficiency, and resistance to strategic manipulation.

Abstract

In approval-based budget division, the task is to allocate a divisible resource to the candidates based on the voters' approval preferences over the candidates. For this setting, Brandl et al. [2021] have shown that no distribution rule can be strategyproof, efficient, and fair at the same time. In this paper, we aim to circumvent this impossibility theorem by focusing on approximate strategyproofness. To this end, we analyze the incentive ratio of distribution rules, which quantifies the maximum multiplicative utility gain of a voter by manipulating. While it turns out that several classical rules have a large incentive ratio, we prove that the Nash product rule ($\mathsf{NASH}$) has an incentive ratio of $2$, thereby demonstrating that we can bypass the impossibility of Brandl et al. by relaxing strategyproofness. Moreover, we show that an incentive ratio of $2$ is optimal subject to some of the fairness and efficiency properties of $\mathsf{NASH}$, and that the positive result for the Nash product rule even holds when voters may report arbitrary concave utility functions. Finally, we complement our results with an experimental analysis.

Problem

• approximate strategyproofness
• approval-based budget division
• incentive ratio
• impossibility theorem
• Nash product rule

Innovation

• approximate strategyproofness
• incentive ratio
• Nash product rule
• approval-based budget division
• fair division