Specification, Application, and Operationalization of a Metamodel of Fairness

TL;DR

This work defines the AR fairness metamodel to formalize and compare fairness across scenarios by treating agents, resources, and attributes as first class primitives, with outcomes drawn from $\mathsf{A}\times \mathsf{R}$. Fairness measures are framed as functions $\tilde{f}_{\mathsf{F}}: \mathcal{P}(\mathsf{A}\times \mathsf{R}) \to [0,1]$, enabling precise instantiations of equality, equity, group fairness, and individual fairness, plus continuous indices such as Jain's fairness index and the complementary Gini index, as well as a COMPAS-style bias detector. The approach is operationalized through the Tiles framework, implemented in Soda with Lean proofs and a JVM-compatible runtime, providing a modular, readable pipeline-based representation of fairness definitions and metrics. The methodology supports rigorous comparison and verification of fairness notions across domains, and the open-source Tiles implementation invites real-world case studies and tooling enhancements to broaden practical impact.

Abstract

This paper presents the AR fairness metamodel, aimed at formally representing, analyzing, and comparing fairness scenarios. The metamodel provides an abstract representation of fairness, enabling the formal definition of fairness notions. We instantiate the metamodel through several examples, with a particular focus on comparing the notions of equity and equality. We use the Tiles framework, which offers modular components that can be interconnected to represent various definitions of fairness. Its primary objective is to support the operationalization of AR-based fairness definitions in a range of scenarios, providing a robust method for defining, comparing, and evaluating fairness. Tiles has an open-source implementation for fairness modeling and evaluation.

Theorems & Definitions (13)

• definition 1: Fairness Scenario
• definition 2: Fairness Measure
• definition 3: Equality, Equity, and Strict Equity
• proposition 1: Strict Equity Implies Equity
• proof
• proposition 2: Equality Reduced to Strict Equity
• proof
• definition 4: Ordinal Preference Function
• definition 5: Jain's Fairness Index
• proposition 3: Correctness of the Equality Pipeline