Core Concepts

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.

Abstract

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.

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by Martin Duran... at **arxiv.org** 03-29-2024

Deeper Inquiries

In participatory budgeting, positive project interactions occur when the implementation of one project enhances the benefits or outcomes of another project. For example, building a community garden and a composting facility in close proximity can create a positive synergy by reducing waste and providing fresh produce to residents. On the other hand, negative project interactions can occur when projects conflict or undermine each other's effectiveness. For instance, constructing a noisy playground next to a retirement home may lead to discomfort for the elderly residents.
The proposed uM utility function can be used to improve decision-making in these cases by quantifying the synergies between projects based on the preferences expressed by voters. By analyzing the M¨obius transforms of project subsets, the utility function can identify positive and negative interactions. This information can guide the selection of projects in a way that maximizes positive synergies and minimizes negative synergies, leading to more effective and harmonious project combinations in participatory budgeting.

To extend the authors' approach to consider more complex forms of project interactions, such as higher-order synergies beyond pairwise interactions, the utility function could be modified to incorporate interactions between larger groups of projects. By expanding the M¨obius transforms to capture synergies between multiple projects simultaneously, the utility function could assess the combined effects of project interactions at a higher level of granularity. This would enable a more nuanced understanding of how different combinations of projects interact and influence each other, allowing for more sophisticated decision-making in participatory budgeting.

Incorporating other social welfare functions and fairness considerations into the participatory budgeting problem with project interactions can further enhance the decision-making process. For example, considering equity and distributional fairness criteria could ensure that the benefits of selected projects are distributed equitably among different demographic groups or communities. Additionally, incorporating sustainability criteria could prioritize projects that have long-term positive impacts on the environment and society. By integrating a diverse range of social welfare functions and fairness considerations, participatory budgeting processes can become more comprehensive and inclusive, leading to outcomes that better reflect the needs and values of the community.

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