Abstract
We study the robustness of approval-based participatory budgeting (PB) rules to random noise in the votes. First, we analyze the computational complexity of the #Flip-Bribery problem, where given a PB instance we ask for the number of ways in which we can flip a given number of approvals in the votes, so that a specific project is selected. This problem captures computing the funding probabilities of projects in case random noise is added. Unfortunately, it is intractable even for the simplest PB rules. Second, we analyze the robustness of several prominent PB rules (including the basic greedy rule and the Method of Equal Shares) on real-world instances from Pabulib. Using sampling, we quantify the extent to which simple, greedy PB rules are more robust than proportional ones, and we identify three types of (very) non-robust projects in real-world PB instances.
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Notes
- 1.
Note that the difference between at most r and exactly r is immaterial here from the point of view of computational complexity: Both variants are Turing-reducible to each other.
- 2.
To maintain focus, we do not consider MES-Apr here. The reason why we examine MES-Cost is that this is the variant that has been used in practice [20].
- 3.
We describe, analyze, and compare other existing completion variants in our full version [4].
- 4.
Our choice of focusing on resampling probabilities up to \(25\%\) is in some sense arbitrary. However, we believe that this range captures practically relevant cases. Indeed, if we need to introduce more than \(25\%\) of noise to affect the results, then it is natural to consider the original results to be robust.
- 5.
We sometimes refer to projects by the color of their lines. Doing so for the first time, we often specify the number of approvers of the project and its cost in brackets.
- 6.
Note that in these plots we only consider averaged values. We did not include other statistical quantities for the sake of readability and their lack of relevance to the goal of our study.
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Acknowledgments
NB was supported by the DFG project ComSoc-MPMS (NI 369/22). This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 101002854).
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Boehmer, N., Faliszewski, P., Janeczko, Ł., Kaczmarczyk, A. (2023). Robustness of Participatory Budgeting Outcomes: Complexity and Experiments. In: Deligkas, A., Filos-Ratsikas, A. (eds) Algorithmic Game Theory. SAGT 2023. Lecture Notes in Computer Science, vol 14238. Springer, Cham. https://doi.org/10.1007/978-3-031-43254-5_10
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