Participatory budgeting (PB) is a democratic process for allocating funds to projects based on the votes of community members. PB outcomes are commonly evaluated for how they reflect voters preferences (e.g., social welfare) and the extent to which they are fair (e.g., proportionality). Due to practical and computational reasons, voters are usually asked to report their preferences over projects separately, possibly neglecting important dependencies among projects, which causes the outcome to no longer be proportional and achieve lower satisfaction. This work is the first to suggest a polynomial-time aggregation method capable of guaranteeing proportional outcomes under substitution dependencies. The method is a variant of the Method of Equal Shares, and we further provide another variation that can guarantee a more relaxed notion of proportionality for any type of dependency, and is FPT rather than polynomial. Through simulations, we demonstrate that these aggregation methods achieve, on average, higher social welfare than their counterparts that ignore the dependencies.

翻译：参与式预算（PB）是一种基于社区成员投票为项目分配资金的民主过程。对PB结果的评估通常关注其如何反映选民偏好（例如社会福利）以及公平程度（例如比例性）。由于实践和计算上的原因，选民通常被要求分别报告对各项目的偏好，这可能忽略了项目间的重要依赖关系，从而导致结果不再具有比例性且满意度降低。本研究首次提出了一种能够在替代依赖下保证比例结果的多项式时间聚合方法。该方法为等额分配法的一种变体，并进一步提供了另一种变体，该变体可为任何类型的依赖保证一种更宽松的比例性概念，且具有固定参数可处理性而非多项式复杂度。通过模拟实验，我们证明这些聚合方法平均比忽略依赖关系的对应方法实现了更高的社会福利。