Основні поняття
The core message of this article is to introduce models and algorithms for the participatory budgeting problem when projects can interact with each other, either positively or negatively. The authors propose a utility function that captures these project interactions and study the computational complexity of optimizing different aggregation criteria (sum, product, and minimum) using this utility function.
Анотація
The article addresses the participatory budgeting problem, where community members propose projects and vote on them, and the authorities select a set of projects that fit within a given budget. The key contribution is to consider the case where projects can have positive or negative interactions with each other, rather than assuming projects are independent.
The authors first define desirable properties for utility functions in the presence of project interactions, such as cost consistency, super-set monotonicity, and the effects of positive and negative synergies. They then propose a specific utility function, called uM, that fulfills these properties. uM uses Möbius transforms to capture the synergies between projects based on their co-occurrence in the voters' preferences.
The authors then study the computational complexity of optimizing different aggregation criteria (sum, product, and minimum) using the uM utility function. They show that these problems are NP-hard, even with the k-additivity assumption (where only synergies between groups of up to k projects are considered). Finally, they propose a branch-and-bound algorithm to solve these problems exactly.
The key insights from the article are:
Detecting project interactions is important in participatory budgeting, as it can lead to better selection of projects that complement each other.
The uM utility function, based on Möbius transforms, can effectively capture positive and negative synergies between projects.
Optimizing classical aggregation criteria (sum, product, minimum) with project interactions is computationally hard, but can be solved exactly using a branch-and-bound approach.