Project-Fair and Truthful Mechanisms for Budget Aggregation

TL;DR

This paper introduces a new truthful mechanism for budget aggregation among strategic voters, achieving optimal fairness guarantees and minimizing deviation from the mean distribution, especially for three or more projects.

Contribution

It proposes a novel moving phantom mechanism that ensures fairness and truthfulness, improving upon existing methods in budget allocation problems.

Findings

The new mechanism provides optimal project fairness guarantees.

It minimizes the $\,ell_1$ distance to the mean for three projects.

First non-trivial bounds on fairness for more than three projects.

Abstract

We study the budget aggregation problem in which a set of strategic voters must split a finite divisible resource (such as money or time) among a set of competing projects. Our goal is twofold: We seek truthful mechanisms that provide fairness guarantees to the projects. For the first objective, we focus on the class of moving phantom mechanisms [Freeman et al., 2021], which are -- to this day -- essentially the only known truthful mechanisms in this setting. For project fairness, we consider the mean division as a fair baseline, and bound the maximum difference between the funding received by any project and this baseline. We propose a novel and simple moving phantom mechanism that provides optimal project fairness guarantees. As a corollary of our results, we show that our new mechanism minimizes the $\ell_1$ distance to the mean (a measure suggested by Caragiannis et al. [2022]) for three projects and gives the first non-trivial bounds on this quantity for more than three projects.