Cost Bias in Participatory Budgeting

The relatively young research field of Computational Social Choice (COMSOC) studies the computational aspects of communal decision making, such as the difficulty of election winner determinations and voting manipulation. One election type that has been studied extensively in COMSOC and originated in South America in the 1980s is called Participatory Budgeting (PB). The municipality decides on a budget, projects are proposed that could be realized with that budget, and the voters can then indicate which of these projects they approve of. As with any election, a voting rule computes the election outcome. Several voting rules exist, commonly used are greedy-style voting rules. Fairly recently, a new and proportional voting rule has been developed, called the Method of Equal Shares. Voting rules have been studied extensively, for example in regards to computational effort or proportionality. However, up until now, bias in PB elections has not received any attention in COMSOC literature. We formulate the concept of cost bias in participatory budgeting, which refers to the idea that a possible inclusion of a project is unduly dependent on if a project is relatively cheap or relatively expensive. Furthermore, we introduce the concept of the proportionality of a project, meaning the difference between the percentage of the budget that a project would cost and the percentage of possible approvals it received. We sample PB elections, extending the procedure to also include project costs, where we can influence the probability that a project is proportional. We use these created election instances to perform extensive statistical experiments measuring a possible correlation between project proportionality and inclusion of that project in the election outcome. We compare the measured correlations for both the utilitarian greedy voting rule and MES. Our findings clearly show a measurable bias of MES towards proportionally inexpensive projects if most projects are disproportionately expensive. This measured bias aligns with additional frequency analysis experiments done on real-world election data. Furthermore, we prove two new theoretical results: For two specific PB instance types it holds that under a greedy-style voting rule a smaller cost project is at least as likely to be included in the outcome as a higher cost one.