Truthful Budget Aggregation: Beyond Moving-Phantom Mechanisms

TL;DR

This paper explores the space of truthful budget aggregation mechanisms beyond moving-phantom mechanisms, demonstrating that broader classes can exist but do not necessarily offer better fairness guarantees.

Contribution

It introduces a new class of truthful mechanisms that are not moving-phantoms and confirms that existing fairness bounds apply to all such mechanisms.

Findings

A new class of truthful mechanisms beyond moving-phantom mechanisms is identified.

Moving-phantom mechanisms are limited in fairness guarantees, which extend to all mechanisms with similar properties.

Lower bounds on fairness are shown to apply broadly, limiting improvements in fairness.

Abstract

We study a budget-aggregation setting in which a number of voters report their ideal distribution of a budget over a set of alternatives, and a mechanism aggregates these reports into an allocation. Ideally, such mechanisms are truthful, i.e., voters should not be incentivized to misreport their preferences. For the case of two alternatives, the set of mechanisms that are truthful and additionally meet a range of basic desiderata (anonymity, neutrality, and continuity) exactly coincides with the so-called moving-phantom mechanisms, but whether this space is richer for more alternatives was repeatedly stated as an open question. We answer this question in the affirmative by presenting a class of truthful mechanisms that are not moving-phantoms but satisfy the three properties. Since moving-phantom mechanisms can only provide limited fairness guarantees (measured as the worst-case distance to a fair share solution), one motivation for broadening the class of truthful mechanisms is the hope for improved fairness guarantees. We dispel this hope by showing that lower bounds holding for the class of moving-phantom mechanisms extend to all truthful, anonymous, neutral, and continuous mechanisms.