AI 中文总结
本文针对预算聚合问题，定义两种个体公平份额保障，证明t≥1时ℓ_t效用下可同时满足帕累托效率且多项式时间可计算，还得出ℓ_1、ℓ_2效用下的相关不可能性结果。
AI 中文摘要
我们考虑将n个关于m个备选方案的个体分布聚合为一个集体分布的问题，这也被称为预算聚合。该领域现有的公平性概念通常无法保证对个体代理的公平性。为解决这一问题，我们定义了两种版本的个体公平份额保障。我们证明，当代理的效用来自任意t≥1的ℓ_t度量时，这两种保障均可与帕累托效率同时满足，且对应的分布可在多项式时间内计算。另一方面，对于ℓ_1效用，我们证明当n,m≥3时，帕累托效率、策略防伪性以及一种名为单意图正份额的极弱公平概念并不总是兼容；对于更小的参数，我们提供了满足这三个公理的规则。我们还针对ℓ_2效用建立了类似的不可能性结果。
英文摘要
We consider the problem of aggregating $n$ individual distributions over $m$ alternatives into a collective distribution, also known as budget aggregation. Existing fairness notions in this literature typically do not guarantee fairness to individual agents. To address this, we define two versions of individual fair share guarantees. We show that when agents' utilities are derived from $\ell_t$ metrics for any $t\geq 1$, both these guarantees can be satisfied along with Pareto efficiency, and the corresponding distributions can be computed in polynomial time. On the other hand, for $\ell_1$ utilities, we prove that Pareto efficiency, strategyproofness, and a very weak fairness notion called single-minded positive share are not always compatible for $n,m \ge 3$. For smaller parameters, we provide rules that satisfy these three axioms. We also establish similar impossibility results for $\ell_2$ utilities.
