Participatory budgeting (PB) has been widely adopted and has attracted significant research efforts; however, there is a lack of mechanisms for PB which elicit project interactions, such as substitution and complementarity, from voters. Also, the outcomes of PB in practice are subject to various minimum/maximum funding constraints on 'types' of projects. We propose a novel preference elicitation scheme for PB which allows voters to express how their utilities from projects within 'groups' interact. We consider preference aggregation done under minimum and maximum funding constraints on 'types' of projects, where a project can have multiple type labels as long as this classification can be defined by a 1-laminar structure (henceforth called 1-laminar funding constraints). Overall, we extend the Knapsack voting model of Goel et al. [26] in two ways - enriching the preference elicitation scheme to include project interactions and generalizing the preference aggregation scheme to include 1-laminar funding constraints. We show that the strategyproofness results of Goel et al. [26] for Knapsack voting continue to hold under 1-laminar funding constraints. Moreover, when the funding constraints cannot be described by a 1-laminar structure, strategyproofness does not hold. Although project interactions often break the strategyproofness, we study a special case of vote profiles where truthful voting is a Nash equilibrium under substitution project interactions. We then study the computational complexity of preference aggregation. Social welfare maximization under project interactions is NP-hard. As a workaround for practical instances, we give a fixed parameter tractable (FPT) algorithm for social welfare maximization with respect to the maximum number of projects in a group when the overall budget is specified in a fixed number of bits.

翻译：参与式预算（PB）已被广泛采用并吸引了大量研究关注；然而，现有PB机制缺乏从选民中揭示项目间交互关系（如替代性与互补性）的能力。此外，实践中PB的结果受到针对项目“类型”的各类资金上下限约束。我们提出了一种新型PB偏好揭示方案，允许选民表达同一“组”内项目效用之间的交互关系。我们考虑在项目“类型”的最小/最大资金约束下进行偏好聚合，其中只要项目分类可由1-层状结构定义，则一个项目可拥有多个类型标签（以下简称1-层状资金约束）。总体而言，我们从两个方向扩展了Goel等人[26]的背包投票模型：丰富偏好揭示方案以纳入项目交互，以及推广偏好聚合方案以包含1-层状资金约束。我们证明，在1-层状资金约束下，Goel等人[26]关于背包投票的策略证明性结果仍然成立。此外，当资金约束无法通过1-层状结构描述时，策略证明性不再成立。尽管项目交互常破坏策略证明性，我们研究了一种特殊情况：在替代性项目交互下，真实投票构成纳什均衡的投票剖面。随后研究了偏好聚合的计算复杂度。在项目交互条件下，社会福利最大化是NP难的。作为实际场景的应对方案，我们提出了一种固定参数可解（FPT）算法，该算法以最大分组项目数为参数，在总预算以固定比特数指定的情况下实现社会福利最大化。