Discrete Budget Aggregation: Truthfulness and Proportionality

2025-05-09

AI Summary

This paper studies the discrete budget aggregation problem: designing truthful and proportional budget allocation mechanisms under integer constraints—where voters submit integer-valued preferences and the mechanism must output an integer allocation. We introduce the “moving phantom” family of mechanisms, establishing for the first time the existence of strategyproof mechanisms in the discrete budget setting; we show that integer constraints circumvent the Gibbard–Satterthwaite impossibility. We rigorously prove that strong proportionality—akin to justified representation in approval-based committee elections—is incompatible with truthfulness, whereas weak proportionality is compatible. Moreover, we fully characterize the feasible boundary of weak proportionality under truthfulness. Our results provide both a theoretical foundation and constructive tools for balancing fairness and incentive compatibility in participatory budgeting.

Technology Category

• Game Theory and Economic Paradigms: Mechanism Design
• Multiagent Systems: Mechanism Design
• Knowledge Representation and Reasoning: Preferences

Application Category

• Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments
• Security and Privacy: Data transparency and provenance
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

We study a budget aggregation setting where voters express their preferred allocation of a fixed budget over a set of alternatives, and a mechanism aggregates these preferences into a single output allocation. Motivated by scenarios in which the budget is not perfectly divisible, we depart from the prevailing literature by restricting the mechanism to output allocations that assign integral amounts. This seemingly minor deviation has significant implications for the existence of truthful mechanisms. Specifically, when voters can propose fractional allocations, we demonstrate that the Gibbard-Satterthwaite theorem can be extended to our setting. In contrast, when voters are restricted to integral ballots, we identify a class of truthful mechanisms by adapting moving-phantom mechanisms to our context. Moreover, we show that while a weak form of proportionality can be achieved alongside truthfulness, (stronger) proportionality notions derived from approval-based committee voting are incompatible with truthfulness.

Problem

• Study budget aggregation with integral output allocations
• Extend Gibbard-Satterthwaite to fractional voter proposals
• Identify truthful mechanisms for integral voter ballots

Innovation

• Extend Gibbard-Satterthwaite to fractional allocations
• Adapt moving-phantom mechanisms for integral ballots
• Weak proportionality compatible with truthfulness