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. There is an insufficient understanding of how these funding constraints affect PB's strategic and computational complexities. 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. 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. for Knapsack voting continue to hold under 1-laminar funding constraints. 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 turn to the study of 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.

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，现有机制缺乏向选民征集项目间交互（如替代关系与互补关系）的能力。此外，实践中的PB结果受到针对项目"类别"的各类最低/最高资金约束的制约。目前关于这些资金约束如何影响PB的策略复杂性与计算复杂性的认识仍不充分。本文提出一种新型PB偏好征集方案，允许选民表达其从"组内"项目获得效用的交互方式。我们考虑在项目"类别"的最低与最高资金约束下进行偏好聚合，其中若项目分类可由1-层状结构（以下简称1-层状资金约束）定义，则同一项目可具有多个类别标签。总体上，我们从两方面扩展了Goel等人的背包投票模型：丰富偏好征集方案以纳入项目交互，并推广偏好聚合方案以包含1-层状资金约束。我们证明Goel等人关于背包投票的策略防御性结论在1-层状资金约束下依然成立。尽管项目交互往往会破坏策略防御性，我们研究了一种特殊投票场景，其中在替代性项目交互下真实投票构成纳什均衡。进而转向偏好聚合计算复杂度的研究：存在项目交互的社会福利最大化问题为NP难。作为实际场景的解决方案，我们给出一个以组内最大项目数为参数的固定参数可解（FPT）算法。