We study the fair and truthful allocation of m divisible public items among n agents, each with distinct preferences for the items. To aggregate agents' preferences fairly, we follow the literature on the fair allocation of public goods and aim to find a core solution. For divisible items, a core solution always exists and can be calculated efficiently by maximizing the Nash welfare objective. However, such a solution is easily manipulated; agents might have incentives to misreport their preferences. To mitigate this, the current state-of-the-art finds an approximate core solution with high probability while ensuring approximate truthfulness. However, this approach has two main limitations. First, due to several approximations, the approximation error in the core could grow with n, resulting in a non-asymptotic core solution. This limitation is particularly significant as public-good allocation mechanisms are frequently applied in scenarios involving a large number of agents, such as the allocation of public tax funds for municipal projects. Second, implementing the current approach for practical applications proves to be a highly nontrivial task. To address these limitations, we introduce PPGA, a (differentially) Private Public-Good Allocation algorithm, and show that it attains asymptotic truthfulness and finds an asymptotic core solution with high probability. Additionally, to demonstrate the practical applicability of our algorithm, we implement PPGA and empirically study its properties using municipal participatory budgeting data.

翻译：我们研究在n个具有不同物品偏好的智能体间公平且真实地分配m个可分割公共品的问题。为公平聚合智能体偏好，我们遵循公共品公平分配文献的思路，致力于寻找核解。对于可分割物品，核解总是存在且能通过最大化纳什福利目标高效计算。然而此类解易受操纵——智能体可能存在虚报偏好的动机。为缓解此问题，现有最优方法能以高概率获得近似核解并保证近似真实性，但存在两大局限：其一，由于多重近似，核解的近似误差可能随n增长，导致非渐近核解——这一缺陷在公共品分配机制常应用于海量智能体场景（如市政项目的公共税收资金分配）时尤为突出；其二，将该方法应用于实际场景难度极大。针对这些局限，我们提出PPGA（差分隐私保护公共品分配算法），证明其具有渐近真实性且能以高概率收敛到渐近核解。此外，为展示算法的实际应用性，我们利用市政参与式预算数据实现了PPGA并实证研究了其特性。