We study the budget aggregation problem in which a set of strategic voters must split a finite divisible resource (such as money or time) among a set of competing projects. Our goal is twofold: We seek truthful mechanisms that provide fairness guarantees to the projects. For the first objective, we focus on the class of moving phantom mechanisms [Freeman et al., 2021], which are -- to this day -- essentially the only known truthful mechanisms in this setting. For project fairness, we consider the mean division as a fair baseline, and bound the maximum difference between the funding received by any project and this baseline. We propose a novel and simple moving phantom mechanism that provides optimal project fairness guarantees. As a corollary of our results, we show that our new mechanism minimizes the $\ell_1$ distance to the mean (a measure suggested by Caragiannis et al. [2022]) for three projects and gives the first non-trivial bounds on this quantity for more than three projects.

翻译：我们研究预算聚合问题，其中一组策略性选民需在多个竞争项目间分配有限的可分割资源（如资金或时间）。本研究目标有二：寻求既能保证真实性又能为项目提供公平性保障的机制。针对第一项目标，我们聚焦于移动幻影机制类[Freeman et al., 2021]——迄今为止，这本质上仍是该场景下已知的唯一真实机制。对于项目公平性，我们以均值分配作为公平基线，约束任意项目所获资助与基线之间的最大差异。我们提出一种新颖简洁的移动幻影机制，该机制能提供最优的项目公平性保障。作为研究推论，我们证明新机制在三个项目场景下能最小化与均值的$\ell_1$距离（Caragiannis等人[2022]提出的度量指标），并在超过三个项目时首次给出该度量的非平凡界值。