Truthful Aggregation of Budget Proposals with Proportionality Guarantees

Abstract

We study a participatory budgeting problem, where a set of strategic agents wish to split a divisible budget among different projects by aggregating their proposals on a single division. Unfortunately, the straightforward rule that divides the budget proportionally is susceptible to manipulation. Recently, a class of truthful mechanisms has been proposed, namely the moving phantom mechanisms. One such mechanism satisfies the proportionality property, in the sense that in the extreme case where all agents prefer a single project to receive the whole amount, the budget is assigned proportionally. While proportionality is a naturally desired property, it is defined over a limited type of preference profiles. To address this, we expand the notion of proportionality, by proposing a quantitative framework that evaluates a budget aggregation mechanism according to its worst-case distance from the proportional allocation. Crucially, this is defined for every preference profile. We study this measure on the class of moving phantom mechanisms, and we provide approximation guarantees. For two projects, we show that the Uniform Phantom mechanism is optimal among all truthful mechanisms. For three projects, we propose a new, proportional mechanism that is optimal among all moving phantom mechanisms. Finally, we provide impossibility results regarding the approximability of moving phantom mechanisms.

Project-Fair and Truthful Mechanisms for Budget Aggregation

“…As a corollary of our result, we show that our new mechanism guarantees an ℓ 1 distance from the mean of no more than 2 3 for instances with three projects, which matches the known lower bound. This closes a (very small) gap that was left open by Caragiannis, Christodoulou, and Protopapas (2022), who obtained an upper bound of 2 3 +10 −5 by a complex proof that involved characterizing worst case instances and then solving a non-linear program. In contrast, our proof is combinatorial and relatively simple in comparison.…”

“…Freeman et al (2021) introduced the Independent Markets mechanism, which is guaranteed to agree with the mean when all voters want to fund only a single project (a mechanism with this property is said to be proportional). However, as Caragiannis, Christodoulou, and Protopapas (2022) showed in subsequent work, on other inputs it may produce outcomes that are far from the mean according to the ℓ 1 distance. They propose a different moving phantom mechanism, the Piecewise Uniform mechanism, which never outputs budget divisions that have an ℓ 1 distance from the mean larger than 2 3 when there are only three projects.…”

“…2 No positive results are known for higher numbers of projects. Caragiannis, Christodoulou, and Protopapas (2022) measure the quality of an outcome by its ℓ 1 distance to the mean. However, this measure does not capture how the deviation from the mean is distributed over the projects.…”

“…We introduce the notion of project fairness for the budget aggregation problem. While our definition is technically similar to the proportionality measure of Caragiannis, Christodoulou, and Protopapas (2022) in that we are interested in the worst case distance (according to some metric) from the mean, the two metrics can differ substantially in which outcomes they prefer. That said, they are related in that an upper bound on the ℓ ∞ distance implies an upper bound on the ℓ 1 distance and vice versa; see Section 6.…”

The (Computational) Social Choice Take on Indivisible Participatory Budgeting

“…Its study dates back to Bogomolnaia, Moulin and Stong (2005) and has since then received substantial a ention. Perspectives that have been considered includes welfare maximisation (Goel, Krishnaswamy, Sakshuwong and Aitamurto, 2019;Michorzewski, Peters and Skowron, 2020), fairness guarantees (Fain, Goel and Munagala, 2016;Caragiannis, Christodoulou and Protopapas, 2022;Airiau, Aziz, Caragiannis, Kruger, Lang and Peters, 2023), strategic behaviours (Aziz, Bogomolnaia and Moulin, 2019;Freeman, Pennock, Peters and Vaughan, 2021). is se ing is also closely related to that of probabilistic social choice (Brandt, 2018).…”