Robustness of Participatory Budgeting Outcomes: Complexity and Experiments

TL;DR

This paper investigates the robustness of approval-based participatory budgeting rules to vote noise, revealing computational intractability of related problems and comparing the stability of different rules through experiments on real data.

Contribution

It introduces the #Flip-Bribery problem for assessing project funding probabilities and analyzes the robustness of PB rules, including the greedy rule and Method of Equal Shares, using sampling methods.

Findings

#Flip-Bribery is computationally intractable even for simple PB rules.

Greedy PB rules are more robust than proportional rules in real-life instances.

Identified three types of projects that are highly non-robust in practice.

Abstract

We study the robustness of approval-based participatory budgeting (PB) rules to random noise in the votes. Our contributions are twofold. First, we study 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. The idea is that #Flip-Bribery captures the problem of computing the funding probabilities of projects in case random noise is added. Unfortunately, the problem 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-life instances from Pabulib. Since #Flip-Bribery is intractable, we resort to sampling to obtain our results. 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-life PB instances.