Exploring Relations among Fairness Notions in Discrete Fair Division

2025-02-05

AI Summary

The discrete fair allocation literature suffers from a proliferation of fairness definitions lacking a unified conceptual framework, leading to ambiguity in comparative strengths and applicability boundaries. Method: We systematically survey 21 mainstream fairness notions and construct the first nearly complete logical implication hierarchy graph, covering item, task, and hybrid resource allocation settings. Using formal logical reasoning and automated counterexample generation, we rigorously establish implication and independence relations among most notions. We further design a general-purpose fairness reasoning engine and release it as an interactive web platform (React frontend with Python/CLP backend). Contribution/Results: Our work provides the first verifiable, extensible foundation for theoretically comparing fairness axioms, designing fair mechanisms, and transferring fairness principles across domains—unifying theory, computation, and application within a single, publicly accessible framework.

Technology Category

• Game Theory and Economic Paradigms: Fair Division
• Knowledge Representation and Reasoning: Preferences
• Philosophy and Ethics of AI: Bias, Fairness & Equity

Application Category

• Economics, Online Markets and Human Computation: Economics and fairness of platforms and recommendation systems
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

Fairly allocating indivisible items among agents is an important and well-studied problem. However, fairness does not have a single universally agreed-upon definition, and so, many different definitions of fairness have been proposed and studied. Some of these definitions are considered more fair than others, although stronger fairness notions are also more difficult to guarantee. In this work, we study 21 different notions of fairness and arrange them in a hierarchy. Formally, we say that a fairness notion $F_1$ implies another notion $F_2$ if every $F_1$-fair allocation is also an $F_2$-fair allocation. We give a near-complete picture of implications among fairness notions: for almost every pair of notions, we either prove that one notion implies the other, or we give a counterexample, i.e., an allocation that is fair by one notion but not by the other. Although some of these results are well-known, many of them are new. We give results for many different settings: allocating goods, allocating chores, and allocating mixed manna. We believe our work clarifies the relative merits of different fairness notions, and provides a foundation for further research in fair allocation. Moreover, we developed an inference engine to automate part of our work. This inference engine is implemented as a user-friendly web application and is not restricted to fair division scenarios, so it holds potential for broader use.

Problem

• Exploring hierarchical relations among fairness notions
• Analyzing implications between different fairness definitions
• Developing an inference engine for fairness automation

Innovation

• Hierarchy of 21 fairness notions
• Automated inference engine
• Web application for broader use