The Unfairness of $\varepsilon$-Fairness

TL;DR

This paper develops a tractable utility-based framework for fairness in binary decision settings, arguing that ε-fairness can yield highly unfair real-world outcomes when context is ignored. By defining utilities for joint outcomes and the resulting expected utilities across two groups, it shows how disparities can persist or be amplified even under parity-like constraints. The authors derive explicit expressions for expected utility and the utility difference, introduce probabilistic uncertainty handling, and illustrate the approach with college admissions and mortgage credit examples. They present sufficient conditions under which fairness in utility can be guaranteed and discuss reduced settings for data-limited scenarios, highlighting the importance of incorporating real-world consequences, uncertainty, and wealth effects into fairness analyses.

Abstract

Fairness in decision-making processes is often quantified using probabilistic metrics. However, these metrics may not fully capture the real-world consequences of unfairness. In this article, we adopt a utility-based approach to more accurately measure the real-world impacts of decision-making process. In particular, we show that if the concept of $\varepsilon$-fairness is employed, it can possibly lead to outcomes that are maximally unfair in the real-world context. Additionally, we address the common issue of unavailable data on false negatives by proposing a reduced setting that still captures essential fairness considerations. We illustrate our findings with two real-world examples: college admissions and credit risk assessment. Our analysis reveals that while traditional probability-based evaluations might suggest fairness, a utility-based approach uncovers the necessary actions to truly achieve equality. For instance, in the college admission case, we find that enhancing completion rates is crucial for ensuring fairness. Summarizing, this paper highlights the importance of considering the real-world context when evaluating fairness.

Figures (5)

• Figure 1: Confusion matrix in our setting - for each group $s$ we associate to $Y=i$ and $\hat{Y}=j$ the utility $U_{ij}$ and the probability $p^s_{ij}$. The true positives are represented by $p^s_{11}$, since $Y=1$ is considered the positive case.
• Figure 2: Utility differences for the college admission. Left:The utility difference as function of $q_1$. Even if the admission rate of the protected group equals $q_1=100\%$, there remains a disadvantage of ca. 500. Right: The case with a fixed number of admitted persons. We admit 1000 persons out of 1250, where 250 belong to the protected group. Starting from an equal admission rate of 80% we allow additional persons from the protected group, meanwhile diminishing the number of admissions from the other group. In this case one is able to achieve equal utilities by admitting 95% of the protected group.
• Figure 3: Confusion matrix in the reduced setting. The cases 00 and 10 are now collapsed to the case $0$ (where $\hat{Y}=0$).
• Figure 4: Illustration of the mortgage example
• Figure 5: Illustration of the general setting - the income $X_T$ is normally distributed and we plot the density, together with the two utility barriers - $D_1$ is between $a$ and $b$ - and the utility $U$.

Theorems & Definitions (28)

• Example 1: University admission
• Definition 2
• Proposition 3
• Proposition 4: Equal joint probabilities imply fairness
• Remark 1: Connection to risk-measures
• Proposition 5
• Proposition 6
• Proposition 7
• Proposition 8
• Proposition 9