Approximate-EFX Allocations with Ordinal and Limited Cardinal Information

2026-02-09

AI Summary

This work investigates the problem of achieving approximately envy-free up to any good (α-EFX) allocations under a limited information model, where only agents’ ordinal preferences over items and a small number of cardinal queries are available. By integrating ordinal preference modeling, bounded query mechanisms, and combinatorial allocation algorithms, the study provides the first systematic analysis of the feasibility of α-EFX allocations and establishes a near-optimal trade-off between the approximation factor α and query complexity. The main contributions include a constant-factor α-EFX allocation algorithm and significantly reduced query complexity in settings with a fixed number of agents or binary valuations, thereby advancing the theoretical foundations of fair division in low-information environments.

Technology Category

• Game Theory and Economic Paradigms: Fair Division
• Multiagent Systems: Mechanism Design
• Machine Learning: Learning Preferences or Rankings

Application Category

• Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments
• Graph Algorithms and Modeling for the Web: Querying, indexing, and retrieval in Web-related graphs
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

Abstract

We study a discrete fair division problem where $n$ agents have additive valuation functions over a set of $m$ goods. We focus on the well-known $\alpha$-EFX fairness criterion, according to which the envy of an agent for another agent is bounded multiplicatively by $\alpha$, after the removal of any good from the envied agent's bundle. The vast majority of the literature has studied $\alpha$-EFX allocations under the assumption that full knowledge of the valuation functions of the agents is available. Motivated by the established literature on the distortion in social choice, we instead consider $\alpha$-EFX algorithms that operate under limited information on these functions. In particular, we assume that the algorithm has access to the ordinal preference rankings, and is allowed to make a small number of queries to obtain further access to the underlying values of the agents for the goods. We show (near-optimal) tradeoffs between the values of $\alpha$ and the number of queries required to achieve those, with a particular focus on constant EFX approximations. We also consider two interesting special cases, namely instances with a constant number of agents, or with two possible values, and provide improved positive results.

Problem

• fair division
• EFX fairness
• ordinal preferences
• limited cardinal information
• approximate fairness

Innovation

• approximate EFX
• ordinal preferences
• limited cardinal information
• query complexity
• fair division