Truthful Aggregation of Budget Proposals with Proportionality Guarantees

TL;DR

This paper introduces a quantitative framework to evaluate and improve truthful budget aggregation mechanisms, extending proportionality guarantees to all preference profiles and analyzing their optimality and limitations.

Contribution

It extends the concept of proportionality to all preference profiles, proposes new mechanisms with approximation guarantees, and establishes impossibility results for moving phantom mechanisms.

Findings

Uniform Phantom mechanism is optimal for two projects.

A new proportional mechanism is nearly optimal for three projects.

Impossibility results limit the approximation of moving phantom mechanisms.

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 straight-forward rule that divides the budget proportionally is susceptible to manipulation. In a recent work, Freeman et al. [arXiv:1905.00457] proposed a class of truthful mechanisms, called moving phantom mechanisms. Among others, they propose a proportional mechanism, 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 which 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 the optimal among all truthful mechanisms. For three projects, we propose a new, proportional mechanism which is virtually optimal among all moving phantom mechanisms. Finally, we provide impossibility results regarding the approximability of moving phantom mechanisms.