[Paper Review] Fairness Behind a Veil of Ignorance: A Welfare Analysis for Automated Decision Making

Hoda Heidari, Claudio Ferrari+2 more|arXiv (Cornell University)|Jun 13, 2018

Ethics and Social Impacts of AI27 references45 citations

TL;DR

The paper introduces welfare-based fairness measures rooted in a veil of ignorance, embeds them as convex constraints in learning, and analyzes tradeoffs with accuracy and other fairness notions on real datasets. It also shows that lower bounds on welfare can bound inequality in outcomes.

ABSTRACT

We draw attention to an important, yet largely overlooked aspect of evaluating fairness for automated decision making systems---namely risk and welfare considerations. Our proposed family of measures corresponds to the long-established formulations of cardinal social welfare in economics, and is justified by the Rawlsian conception of fairness behind a veil of ignorance. The convex formulation of our welfare-based measures of fairness allows us to integrate them as a constraint into any convex loss minimization pipeline. Our empirical analysis reveals interesting trade-offs between our proposal and (a) prediction accuracy, (b) group discrimination, and (c) Dwork et al.'s notion of individual fairness. Furthermore and perhaps most importantly, our work provides both heuristic justification and empirical evidence suggesting that a lower-bound on our measures often leads to bounded inequality in algorithmic outcomes; hence presenting the first computationally feasible mechanism for bounding individual-level inequality.

Motivation & Objective

• Motivate the need to consider risk and welfare, in addition to equality, when evaluating fairness in automated decision making.
• Propose a family of welfare-based fairness measures tied to cardinal social welfare and Rawlsian ideas.
• Develop a convex in-processing method that enforces a lower bound on the welfare measure during learning.
• Empirically analyze tradeoffs between welfare, accuracy, group discrimination, and individual fairness notions.

Proposed method

• Define benefit and utility functions for predictions (b(y, ŷ)) and a CRRA utility u(b) = b^α with 0 < α < 1.
• Show that the welfare measure Wα(b) = ∑i wα(bi) with wα(b) = b^α yields a convex constraint when enforcing welfare lower bounds.
• Formulate in-processing as a constrained optimization: minimize training loss L_D(h) subject to U_D(h) ≥ τ, where U_D(h) = E[u(b(y, h(x)))].
• Link the proposed measure to cardinal welfare functions and the Pigou-Dalton transfer principle, establishing theoretical properties and relationships to Atkinson’s index.
• Discuss how the framework admits optimization efficiency and can be integrated into convex loss minimization pipelines.

Experimental results

Research questions

• RQ1 How can risk and welfare be incorporated into fairness evaluation for automated decision making beyond equality-based notions?
• RQ2 What are the tradeoffs between welfare-based fairness, prediction accuracy, and other fairness notions (group, individual) in classification and regression tasks?
• RQ3 Can enforcing a lower bound on welfare effectively bound inequality in algorithmic outcomes?
• RQ4 How does the proposed framework relate to existing welfare and inequality measures (e.g., Atkinson index) under mean-preserving transformations?

Key findings

• Welfare-based fairness measures prefer distributions with lower risk and higher welfare, even when means differ, addressing scenarios where equality alone is insufficient.
• Convex in-processing constraints allow efficient optimization for enforcing welfare lower bounds in both classification and regression tasks.
• Empirical results show tradeoffs: increasing the welfare threshold τ or stronger risk aversion α reduces inequality and group disparities but can reduce accuracy.
• Lower bounds on social welfare tend to bound inequality in outcomes, suggesting a computationally feasible mechanism for limiting individual-level inequality.
• The framework exhibits consistent ranking alignment with Atkinson’s index for fixed mean when α is in (0,1), connecting welfare and inequality notions.