Individual Fairness in Budget Aggregation

2026-08-02

AI Summary

This work addresses the challenge of aggregating individual distributions over multiple options into a collective distribution while simultaneously satisfying fairness and efficiency desiderata. Existing budget aggregation methods struggle to reconcile individual fairness with Pareto efficiency. We introduce two individual fairness guarantees grounded in ℓₜ (t ≥ 1) utility models and develop polynomial-time algorithms that achieve compatibility between fairness and Pareto efficiency under ℓ₁ and ℓ₂ norms. For small-scale settings, we construct an aggregation rule that satisfies strategyproofness, Pareto efficiency, and a weak fairness notion. However, we prove that these three properties are incompatible in large-scale settings, thereby uncovering a fundamental trade-off inherent in the design of such mechanisms.

Abstract

We consider the problem of aggregating $n$ individual distributions over $m$ alternatives into a collective distribution, also known as budget aggregation. Existing fairness notions in this literature typically do not guarantee fairness to individual agents. To address this, we define two versions of individual fair share guarantees. We show that when agents' utilities are derived from $\ell_t$ metrics for any $t\geq 1$, both these guarantees can be satisfied along with Pareto efficiency, and the corresponding distributions can be computed in polynomial time. On the other hand, for $\ell_1$ utilities, we prove that Pareto efficiency, strategyproofness, and a very weak fairness notion called single-minded positive share are not always compatible for $n,m \ge 3$. For smaller parameters, we provide rules that satisfy these three axioms. We also establish similar impossibility results for $\ell_2$ utilities.

Problem

• Individual Fairness
• Budget Aggregation
• Fair Share
• Pareto Efficiency
• Strategyproofness

Innovation

• individual fairness
• budget aggregation
• Pareto efficiency
• strategyproofness
• impossibility results