Shapley meets Rawls: an integrated framework for measuring and explaining unfairness

Fadoua Amri-Jouidel; Emmanuel Kemel; Stéphane Mussard

cs.LGMar 27, 2026

Shapley meets Rawls: an integrated framework for measuring and explaining unfairness

Authors: Fadoua Amri-Jouidel, Emmanuel Kemel, Stéphane Mussard

Organizations: UM6P Airess · Greghec, Crns HEC Paris

Abstract

Explainability and fairness have mainly been considered separately, with recent exceptions trying the explain the sources of unfairness. This paper shows that the Shapley value can be used to both define and explain unfairness, under standard group fairness criteria. This offers an integrated framework to estimate and derive inference on unfairness as-well-as the features that contribute to it. Our framework can also be extended from Shapley values to the family of Efficient-Symmetric-Linear (ESL) values, some of which offer more robust definitions of fairness, and shorter computation times. An illustration is run on the Census Income dataset from the UCI Machine Learning Repository. Our approach shows that Age", Number of hours" and ``Marital status" generate gender unfairness, using shorter computation time than traditional Bootstrap tests.

Figures & tables

Figure 1: Two-stage Shapley attribution method

ESL value	$v^{(TPR)}(X\big\|_{\mathcal{A}}(\mathcal{N}))$	$\varphi_{g}^{ESL}(\mathbf{X},v^{(TPR)})$
	$v^{(TPR)}(X\big\|_{\mathcal{A}}(\mathcal{N}))$	(men)	(women)
ES, Shapley, Consensus, LSP	1.61	1,047 (64.95%)	0.565 (35.05%)
Solidarity	1.61	0.926 (57,48%)	0.685 (42,52%)

Table 1: Summary of ESL values for men and women group

Method	Feature	$\mathcal{C}^{k}_{g=1}(v^{(TPR)})$	CI ( $g=1$ )	$\mathcal{C}^{k}_{g=2}(v^{(TPR)})$	CI ( $g=2$ )
ES	Age	$0.681^{***}$	$[0.615,0.747]$	$-0.137^{***}$	$[-0.201,-0.072]$
	Educ Num	0.009	$[-0.09,0.109]$	$0.161^{**}$	$[0.061,0.261]$
	Hours/Week	$0.126^{***}$	$[0.056,0.196]$	$-0.092^{**}$	$[-0.161,-0.023]$
	Marital status	$0.231^{***}$	$[0.128,0.334]$	$0.633^{***}$	$[0.527,0.738]$
Shapley	Age	$0.424^{***}$	$[0.380.0.468]$	$-0.006$	$[-0.036,0.024]$
	Educ Num	$0.181^{***}$	$[0.123,0.238]$	$0.114^{***}$	$[0.058,0.169]$

Table 2: Feature contributions to group-ESL

Method	Feature	$\Delta\mathcal{C}^{k}_{g}$	95%CI	$\mu_{bootstrap}(\Delta\mathcal{C}^{k}_{g})$	95% Bootstrap CI
ES	Age	$0.817^{***}$	$[0.707,\,0.928]$	0.818	$[0.784,0.851]$
	Educ Num	$-0.152$	$[-0.337,\,0.033]$	-0.152	$[-0.218,-0.086]$
	Hours/Week	$0.218^{***}$	$[0.100,\,0.337]$	0.218	$[0.181,0.255]$
	Marital status	$-0.402^{***}$	$[-0.598,\,-0.205]$	-0.400	$[-0.476,-0.314]$
Shapley	Age	$0.430^{***}$	$[0.366,0.493]$	0.430	$[0.399,0.459]$
	Educ Num	$0.067$	$[-0.035,0.169]$	0.067	$[0.012,0.125]$

Table 3: Asymptotic confidence intervals and bootstrap confidence intervals

Time complexity	Two-stage ESL	Bootstrap (two stage)
ES	8 min	1 h 37 min
Shapley		1 h 34 min
Solidarity		1 h 18 min
Consensus		1 h 36 min
LSP		1 h 39 min

Table 4: Summary of time complexity for different methods

ESL value	$v^{(TPR)}(X\big\|_{\mathcal{A}}(\mathcal{N}))$	$\varphi_{g}^{ESL}(\mathbf{X},v^{(TPR)})$
	$v^{(TPR)}(X\big\|_{\mathcal{A}}(\mathcal{N}))$	(men)	(women)
ES, Shapley, Consensus, LSP	1.365	0.706 (51.72%)	0.659 (48.28%)
Solidarity	1.365	0.694 (50.84%)	0.671 (49.16%)

Table 5: ESL group contributions (after fairness mitigation).

Method	Feature	$\mathcal{C}^{k}_{g=1}(v^{(TPR)})$	$\mathcal{C}^{k}_{g=2}(v^{(TPR)})$	$\Delta\mathcal{C}^{k}$	95% CI
ES	Age	-0.099	-0.097	-0.002	$[-0.100,0.096]$
	Educ Num	0.192	0.168	0.024	$[-0.164,0.212]$
	Hours/Week	-0.099	-0.098	-0.001	$[-0.096,0.094]$
	Marital status	0.712	0.685	0.027	$[-0.150,0.204]$
Shapley	Age	0.027	0.009	0.018	$[-0.062,0.098]$
	Educ Num	0.132	0.131	0.001	$[-0.103,0.105]$

Table 6: Contributions of features to group-ESL after fairness correction.

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May 15, 2024J/K move · Enter open · S save

When fairness metrics fail: A utility-based perspective on $\varepsilon$ -fairness

Tolulope Fadina, Thorsten Schmidt

Actuarial Science and Risk Management, University of Illinois Urbana Champaign, Illinois, USA · Department of Mathematical Stochastics, University of Freiburg, Ermst-Zermelo Str. 2, 79104 Freiburg, Germany

Algorithmic Fairness Group Fairness Credit Scoring

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Fairness in decision-making processes is often quantified using probabilistic metrics. However, these metrics need not reflect the consequences of decisions for the affected individuals and groups. We develop a utility-based framework that incorporates these consequences into the assessment of fairness. Our main result shows that a decision-making process can satisfy

\varepsilon

-fairness while nevertheless being maximally unfair once the utilities associated with its outcomes are taken into account. To address applications in which information on false negatives is unavailable, we also formulate a reduced setting that retains the essential elements of the utility-based fairness assessment. We illustrate the framework through two applications: college admissions and credit-risk assessment. In both cases, probabilistic metrics may classify a decision-making process as approximately fair even though the corresponding utility outcomes are highly unequal. In the college-admissions example, our analysis shows that improving completion rates is necessary to achieve equality of utility across groups, while in the mortgage example, mitigating unfairness requires not only adjusting approval rates but also reducing the adverse consequences of default. These findings demonstrate that fairness assessments should account not only for the probabilities of different decisions but also for the consequences of those decisions.

Abstract

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