On the Fairness of Causal Algorithmic Recourse

Julius von KügelgenAmir-Hossein KarimiUmang BhattIsabel ValeraAdrian WellerBernhard Schölkopf

article2022AAAI111 citations

Introduces causal criteria for algorithmic recourse to account for downstream intervention effects across protected groups, proving that fair recourse is distinct from predictive fairness and can motivate societal policy interventions over mere classifier adjustments.

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Algorithmic decision-making systems increasingly impact critical life outcomes, such as credit approvals and employment. While traditional fairness research focuses on predictive parity across demographic groups, algorithmic recourse focuses on providing rejected applicants with actionable steps to achieve a favorable outcome. However, existing recourse approaches assume features can change independently and measure fairness simply through the geometric distance to a decision boundary, ignoring the downstream causal effects that real-world actions trigger.

The article develops a causal framework to evaluate and enforce fairness in algorithmic recourse at both the group and individual levels. It aims to demonstrate that recourse fairness is distinct from predictive fairness and to explore mechanisms—both algorithmic modifications and policy-level societal interventions—for eliminating disparities in the effort required to overturn unfavorable decisions.

To evaluate this framework, the authors conducted theoretical proofs alongside empirical numerical simulations using synthetic linear and non-linear datasets with 500 samples. They also analyzed an observational sample of over 45,000 records from the standard Adult benchmark dataset. The approach modeled causal dependencies using structural causal models to simulate downstream feature changes and calculated the optimal intervention costs for negatively classified individuals.

The investigation produced four central findings. First, predictive fairness and fair recourse are complementary: an algorithm can be perfectly fair in its predictions while still imposing substantially higher effort on one demographic group to reverse a negative decision. Second, traditional distance-based recourse metrics fail to capture true effort in interconnected systems, whereas causally informed metrics accurately detect hidden disparities. Third, satisfying group-level recourse fairness does not guarantee fairness for individuals, as within-group advantages can mask severe individual-level penalties. Fourth, an empirical evaluation on the Adult dataset revealed substantial discrimination across sex, age, and nationality, yielding an average individual counterfactual cost disparity of 24.32 and a maximum individual gap of 61.53.

These results demonstrate that organizations relying solely on predictive fairness criteria face hidden compliance, ethical, and reputation risks by placing disproportionate burdens on protected classes attempting to reverse automated denials. Furthermore, the analysis indicates that altering the predictive model is not always the best remedy: when disparities stem from underlying systemic conditions, restricting classifiers can severely degrade predictive accuracy. Instead, the authors highlight targeted societal interventions, such as subsidies or policy adjustments, as an effective means to equalize recourse costs without compromising algorithmic performance.

Decision-makers and system designers should audit deployed recourse mechanisms using causal metrics rather than simple geometric distances to ensure genuine equality of effort. Where algorithmic adjustments are required, developers can guarantee individual fairness by restricting models to non-descendant features or latent background factors, weighing the potential drop in accuracy against institutional priorities. When inequalities reflect broader systemic barriers, leadership should evaluate targeted policy interventions rather than forcing artificial constraints onto predictive models.

Confidence in the mathematical findings and synthetic benchmarks is high, but real-world implementation depends on having an accurately specified causal graph, as unobserved confounding or incorrect causal assumptions can lead to suboptimal recourse recommendations. Future work should focus on estimating robust causal models and formalizing multi-stakeholder cost-benefit trade-offs before deploying these methods in high-stakes operational environments.

ETH Zurich Max Planck Institute for Intelligent Systems Saarland University The Alan Turing Institute University of Cambridge multi-objective optimisation optimization problems causal algorithmic recourse recourse fairness counterfactual fairness

arXiv: 2010.06529 amirhk/recourse

Paper: Counterfactual Fairness, Matt J. Kusner et al. (2017). Introduces the causal framework of counterfactual fairness upon which the paper establishes its causal foundations and compares recourse criteria.
Paper: Counterfactual Explanations without Opening the Black Box: Automated Decisions and the GDPR, Sandra Wachter et al. (2017). Establishes the optimization framework for generating counterfactual explanations and algorithmic recourse to reverse unfavorable decisions.
Paper: Explaining machine learning classifiers through diverse counterfactual explanations, Ramaravind Kommiya Mothilal et al. (2019). Explores actionable and diverse counterfactual recourse methods that the paper generalizes to incorporate downstream causal mechanisms.
Paper: Fairness through awareness, Cynthia Dwork et al. (2012). Provides the foundational definitions for individual fairness and metric-based equal treatment that motivate individual-level recourse fairness.
Paper: Direct and Indirect Effects, Judea Pearl (2001). Formulates the foundational structural equation and path-specific causal modeling necessary to evaluate downstream physical interventions.
Paper: Equality of Opportunity in Supervised Learning, Moritz Hardt et al. (2016). Defines standard group-level prediction fairness criteria that the paper shows to be distinct and complementary to recourse fairness.
Paper: Fairness Constraints: Mechanisms for Fair Classification, Muhammad Bilal Zafar et al. (2015). Demonstrates how to alter classifier decision boundaries under constrained optimization to satisfy mathematical fairness guarantees.

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Cover for On the Fairness of Causal Algorithmic Recourse

Abstract

Algorithmic fairness is typically studied from the perspective of predictions. Instead, here we investigate fairness from the perspective of recourse actions suggested to individuals to remedy an unfavourable classification. We propose two new fairness criteria at the group and individual level, which—unlike prior work on equalising the average group-wise distance from the decision boundary—explicitly account for causal relationships between features, thereby capturing downstream effects of recourse actions performed in the physical world. We explore how our criteria relate to others, such as counterfactual fairness, and show that fairness of recourse is complementary to fairness of prediction. We study theoretically and empirically how to enforce fair causal recourse by altering the classifier and perform a case study on the Adult dataset. Finally, we discuss whether fairness violations in the data generating process revealed by our criteria may be better addressed by societal interventions as opposed to constraints on the classifier.

Topics

multi-objective optimisation optimization problems

Keywords

causal algorithmic recourse recourse fairness counterfactual fairness causal fairness causal recourse optimisation problem algorithmic fairness counterfactual explanations disparate impact recourse cost causal model

1 Introduction
2 Preliminaries & Background
3 Fair Causal Recourse
3.1 Group-Level Fair Causal Recourse
3.2 Individually Fair Causal Recourse
3.3 Relation to Counterfactual Fairness
3.4 Achieving Fair Causal Recourse
4 Experiments
4.1 Numerical Simulations
4.2 Case Study on the Adult Dataset
5 On Societal Interventions
6 Discussion
Acknowledgements
References

Knowls

Knowl 1 — Group-Level Fair Causal Recourse
definition
Let $V = (X, A)$ be the set of observable features where $X = (X_1, \dots, X_n) \in \mathcal{X} \subseteq \mathbb{R}^n$ are non-protected features and $A \in \mathcal{A} = \{1, \dots, K\}$ denotes a protected attribute. Let $\mathcal{M} = (S, P_U)$ be a structural causal model (SCM) over $V$ with structural assignments $S = \{V_i := f_i(\mathrm{PA}_i, U_i)\}_{i=1}^{n+1}$ and mutually independent background noise terms $U = \{U_i\}_{i=1}^{n+1} \sim P_U$ . Let $h: \mathcal{X} \times \mathcal{A} \to \{-1, +1\}$ be a binary classifier.

For a factual observation $v^F = (x^F, a^F)$ with unfavorable prediction $h(v^F) = -1$ , the minimal causal recourse cost $r^{\mathrm{CAU}}(v^F)$ w.r.t. a cost function $c(\cdot; v^F)$ and feasible action set $\Theta(v^F)$ is defined as: $r^{\mathrm{CAU}}(v^F) = \min_{\theta_I \in \Theta(v^F)} c(\theta_I; v^F) \quad \text{subject to} \quad h(v_{\theta_I}(u^F)) = 1$ where $u^F$ is the exogenous noise inferred via abduction $P(U \mid V = v^F)$ , $\theta_I$ is an intervention on a subset of actionable features $X_I \subseteq X$ with indices $I \subseteq \{1, \dots, n\}$ , and $v_{\theta_I}(u^F)$ is the counterfactual state under the atomic intervention $\mathrm{do}(X_I := \theta_I)$ .

Given a dataset $\mathcal{D}$ , let $G_a^- = \{v^i \in \mathcal{D} : a^i = a, h(v^i) = -1\}$ denote the subset of negatively classified individuals belonging to group $a$ , and let $r^{\mathrm{CAU}}(G_a^-) = \frac{1}{|G_a^-|} \sum_{v^i \in G_a^-} r^{\mathrm{CAU}}(v^i)$ denote the group average causal recourse cost. The group-level unfairness of causal recourse $\Delta_{\mathrm{cost}}$ is defined as: $\Delta_{\mathrm{cost}}(\mathcal{D}, h, c, \mathcal{M}) := \max_{a, a' \in \mathcal{A}} \left| r^{\mathrm{CAU}}(G_a^-) - r^{\mathrm{CAU}}(G_{a'}^-) \right|$ Recourse for $(\mathcal{D}, h, c, \mathcal{M})$ is defined to be group CAU-fair if $\Delta_{\mathrm{cost}}(\mathcal{D}, h, c, \mathcal{M}) = 0$ .
Knowl 2 — Individually Fair Causal Recourse
definition
Let $V = (X, A)$ be observable features with non-protected attributes $X \in \mathcal{X}$ and protected attribute $A \in \mathcal{A} = \{1, \dots, K\}$ , governed by a structural causal model $\mathcal{M} = (S, P_U)$ . For a factual individual $v^F = (x^F, a^F)$ with inferred exogenous variables $u^F$ , let $v_a(u^F)$ denote the counterfactual twin of $v^F$ had their protected attribute been set to $a \in \mathcal{A}$ via intervention $\mathrm{do}(A := a)$ . Let $r^{\mathrm{CAU}}(v)$ denote the minimal causal recourse cost required to obtain a positive prediction $h = 1$ from binary classifier $h$ for an individual with observation $v$ and background noise $u$ : $r^{\mathrm{CAU}}(v) = \min_{\theta_I \in \Theta(v)} c(\theta_I; v) \quad \text{subject to} \quad h(v_{\theta_I}(u)) = 1$ where $\Theta(v)$ is the feasible intervention space and $c(\cdot; v)$ is the recourse cost function.

For a dataset $\mathcal{D}$ , the individual-level unfairness of causal recourse $\Delta_{\mathrm{ind}}$ is defined as: $\Delta_{\mathrm{ind}}(\mathcal{D}, h, c, \mathcal{M}) := \max_{a \in \mathcal{A}, v^F \in \mathcal{D}} \left| r^{\mathrm{CAU}}(v^F) - r^{\mathrm{CAU}}(v_a(u^F)) \right|$ Recourse for $(\mathcal{D}, h, c, \mathcal{M})$ is defined to be individually CAU-fair if $\Delta_{\mathrm{ind}}(\mathcal{D}, h, c, \mathcal{M}) = 0$ , meaning that every individual incurs the exact same optimal recourse cost as they would have incurred had they belonged to any other protected group.
Knowl 3 — Insufficiency of Group Fair Recourse for Individual Fair Causal Recourse
theoretical result
Neither group-level independently-manipulable feature (IMF) fair recourse (where average distance to the decision boundary is equalized across groups, $\Delta_{\mathrm{dist}} = 0$ ) nor group-level causal (CAU) fair recourse (where average causal intervention cost is equalized across groups, $\Delta_{\mathrm{cost}} = 0$ ) is a sufficient condition for individually fair causal recourse ( $\Delta_{\mathrm{ind}} = 0$ ). That is: $\text{Group IMF-fair} \not\Rightarrow \text{Individually CAU-fair}$ $\text{Group CAU-fair} \not\Rightarrow \text{Individually CAU-fair}$

This separation holds because group-level metrics average recourse costs over entire subgroups, allowing individual-level disparities to cancel out. A counterexample is given by the SCM: $A := U_A, \quad X := A U_X + (1 - A)(1 - U_X), \quad U_A, U_X \sim \mathrm{Bernoulli}(0.5)$ with binary classifier $h(X) = \mathrm{sign}(X - 0.5)$ . Here, $P(X \mid A = 0) = P(X \mid A = 1) = \mathrm{Bernoulli}(0.5)$ , so the group-average distance to the decision boundary $X = 0.5$ and the group-average causal recourse cost are identical across groups ( $\Delta_{\mathrm{dist}} = 0, \Delta_{\mathrm{cost}} = 0$ ). However, for every individual $v^F = (x^F, a^F)$ and $a \neq a^F$ , $h(x^F) = 1 - h(x_a(u_X^F))$ , meaning an individual rejected under their factual attribute would have been accepted with zero recourse cost had their attribute been swapped, yielding maximal individual recourse unfairness.
Knowl 4 — Insufficiency of Counterfactual Fairness for Fair Recourse
theoretical result
A counterfactually fair predictive classifier does not imply group-level independently-manipulable feature (IMF) fair recourse, group-level causal (CAU) fair recourse, or individual-level causal fair recourse: $h \text{ counterfactually fair} \not\Rightarrow \text{Group IMF-fair}$ $h \text{ counterfactually fair} \not\Rightarrow \text{Group CAU-fair}$ $h \text{ counterfactually fair} \not\Rightarrow \text{Individually CAU-fair}$

A counterexample is provided by the structural causal model: $A := U_A, \quad U_A \sim \mathrm{Bernoulli}(0.5)$ $X := (2 - A) U_X, \quad U_X \sim \mathcal{N}(0, 1)$ with deterministic classifier $h(X) = \mathrm{sign}(X)$ . Because $\mathrm{sign}(X) = \mathrm{sign}(U_X)$ and $U_X$ is invariant under counterfactual changes to $A$ , $h(v^F) = h(v_a(u^F))$ for all $a \in \{0, 1\}$ , satisfying counterfactual fairness of predictions.

However, $P(X \mid A = 0) = \mathcal{N}(0, 4)$ while $P(X \mid A = 1) = \mathcal{N}(0, 1)$ . Negatively classified individuals in group $A = 0$ require on average twice the distance/cost to reach the decision boundary $X = 0$ compared to group $A = 1$ ( $\Delta_{\mathrm{dist}} > 0, \Delta_{\mathrm{cost}} > 0$ ). Furthermore, under a counterfactual change in $A$ , $X$ doubles or halves, altering individual recourse cost and violating individual CAU-fairness ( $\Delta_{\mathrm{ind}} > 0$ ).
Knowl 5 — Sufficient Condition for Individually Fair Causal Recourse via Input Restriction
theoretical result
Let $V = (X, A)$ be governed by a structural causal model $\mathcal{M}$ , and let $\mathrm{desc}(A)$ denote the set of causal descendants of the protected attribute $A$ in $\mathcal{M}$ .

Assume that:
1. The binary classifier $h$ depends exclusively on a subset of non-descendants of $A$ : $\tilde{X} \subseteq V \setminus (A \cup \mathrm{desc}(A))$
2. For every individual $v^F \in \mathcal{D}$ and every protected attribute value $a \in \mathcal{A}$ , the set of feasible recourse actions $\mathcal{F}(v^F)$ and the action cost function $c(\cdot; v^F)$ remain invariant under a counterfactual change of $A$ : $\mathcal{F}(v^F) = \mathcal{F}(v_a(u^F)) \quad \text{and} \quad c(\cdot; v^F) = c(\cdot; v_a(u^F))$
Then the recourse for $(\mathcal{D}, h, c, \mathcal{M})$ is guaranteed to be individually CAU-fair: $\Delta_{\mathrm{ind}}(\mathcal{D}, h, c, \mathcal{M}) = 0$
Knowl 6 — Fair Representation via Abduction of Exogenous Variables for Causal Recourse
model/method
Restricting classifier inputs solely to non-descendants $X_{\mathrm{nd}}(A)$ guarantees individually fair causal recourse ( $\Delta_{\mathrm{ind}} = 0$ ), but often causes a sharp drop in classification accuracy because $A$ causally influences many informative features $X_{\mathrm{d}}(A)$ . To preserve predictive accuracy while satisfying individual fair recourse, descendant features $X_{\mathrm{d}}(A)$ can be replaced by their exogenous latent noise variables $U_{\mathrm{d}}(A)$ .

Under causal sufficiency ( $P_U = \prod_i P_{U_i}$ ) in an SCM with structural equations $V_i := f_i(\mathrm{PA}_i, U_i)$ , exogenous noise terms $U_i$ are by definition non-descendants of any observed variable, including $A$ . The latent variables $U_{\mathrm{d}}(A)$ capture the variations in $X_{\mathrm{d}}(A)$ that are not caused by $A$ .

The procedure is:
1. For each factual observation $v^F$ , compute the posterior distribution $P(U \mid V = v^F)$ via the abduction step of counterfactual inference to obtain latent values $u^F$ .
2. Train the classifier $h(X_{\mathrm{nd}}(A), U_{\mathrm{d}}(A))$ using the combined representation of non-descendant features and inferred exogenous variables.
Because all inputs to $h$ are non-descendants of $A$ , counterfactual changes $\mathrm{do}(A := a)$ do not alter the input representation, ensuring $\Delta_{\mathrm{ind}} = 0$ while granting the classifier access to the exogenous information in $X_{\mathrm{d}}(A)$ .

Knowl 7 — Empirical Comparison of Classifiers on Recourse Fairness Metrics

data/table

Classifiers were evaluated across three synthetic structural causal model settings with $N = 500$ training observations and $3000$ test observations:

IMF: features do not causally affect each other, but may depend on protected attribute $A \in \{0, 1\}$ .
CAU-LIN: features have linear structural assignments with additive noise, causally influencing each other and $A$ .
CAU-ANM: features have nonlinear additive noise structural assignments, causally influencing each other and $A$ .

Reported metrics include held-out test accuracy ( $\mathrm{Acc}$ ), distance-based unfairness ( $\Delta_{\mathrm{dist}}$ in margin units), causal group cost unfairness ( $\Delta_{\mathrm{cost}}$ using $L_2$ action cost), and causal individual unfairness ( $\Delta_{\mathrm{ind}}$ ).

Classifier	IMF				CAU-LIN				CAU-ANM
	Acc	$\Delta_{\mathrm{dist}}$	$\Delta_{\mathrm{cost}}$	$\Delta_{\mathrm{ind}}$	Acc	$\Delta_{\mathrm{dist}}$	$\Delta_{\mathrm{cost}}$	$\Delta_{\mathrm{ind}}$	Acc	$\Delta_{\mathrm{dist}}$	$\Delta_{\mathrm{cost}}$	$\Delta_{\mathrm{ind}}$
Linear Ground Truth & Linear Kernel SVM / Linear LR
SVM( $X, A$ )	86.5	0.96	0.40	1.63	89.5	1.18	0.44	2.11	88.2	0.65	0.27	2.32
LR( $X, A$ )	86.7	0.48	0.50	1.91	89.5	0.63	0.53	2.11	87.7	0.40	0.34	2.32
SVM( $X$ )	86.4	0.99	0.42	1.80	89.4	1.61	0.61	2.11	88.0	0.56	0.29	2.79
LR( $X$ )	86.6	0.47	0.53	1.80	89.5	0.64	0.57	2.11	87.7	0.41	0.43	2.79
FairSVM( $X, A$ )	68.1	0.04	0.28	1.36	66.8	0.26	0.12	0.78	66.3	0.25	0.21	1.50
SVM( $X_{\mathrm{nd}}$ )	65.5	0.05	0.06	0.00	67.4	0.15	0.17	0.00	65.9	0.31	0.37	0.00
LR( $X_{\mathrm{nd}}$ )	65.3	0.05	0.05	0.00	67.3	0.18	0.18	0.00	65.6	0.31	0.31	0.00
SVM( $X_{\mathrm{nd}}, U_{\mathrm{d}}$ )	86.5	0.96	0.58	0.00	89.6	1.07	0.70	0.00	88.0	0.21	0.14	0.00
LR( $X_{\mathrm{nd}}, U_{\mathrm{d}}$ )	86.7	0.43	0.90	0.00	89.5	0.35	0.77	0.00	87.8	0.14	0.34	0.00
Nonlinear Ground Truth & Polynomial Kernel SVM / Nonlinear LR
SVM( $X, A$ )	90.8	0.05	0.00	1.09	91.1	0.07	0.03	1.06	90.6	0.04	0.03	1.40
LR( $X, A$ )	90.5	0.08	0.03	1.06	90.6	0.09	0.01	1.00	90.6	0.19	0.22	1.28
SVM( $X$ )	91.4	0.13	0.00	0.92	91.0	0.17	0.08	1.09	91.0	0.02	0.03	1.64
LR( $X$ )	91.0	0.12	0.03	1.01	90.6	0.13	0.10	1.65	90.9	0.08	0.06	1.66
FairSVM( $X, A$ )	90.1	0.02	0.00	1.15	90.7	0.06	0.04	1.16	90.3	0.37	0.02	1.64
SVM( $X_{\mathrm{nd}}$ )	66.7	0.10	0.06	0.00	58.4	0.05	0.06	0.00	62.0	0.13	0.11	0.00
LR( $X_{\mathrm{nd}}$ )	64.7	0.02	0.04	0.00	58.4	0.02	0.02	0.00	61.1	0.02	0.03	0.00
SVM( $X_{\mathrm{nd}}, U_{\mathrm{d}}$ )	90.7	0.02	0.03	0.00	91.1	0.15	0.11	0.00	90.1	0.15	0.12	0.00
LR( $X_{\mathrm{nd}}, U_{\mathrm{d}}$ )	90.9	0.28	0.05	0.00	90.9	0.49	0.07	0.00	90.2	0.43	0.21	0.00

The table demonstrates that:

Non-causal distance metrics ( $\Delta_{\mathrm{dist}}$ ) misrepresent recourse cost unfairness when causal relationships exist between features ( $\Delta_{\mathrm{cost}}$ vs $\Delta_{\mathrm{dist}}$ ).
Only classifiers trained exclusively on non-descendants ( $X_{\mathrm{nd}}$ or $(X_{\mathrm{nd}}, U_{\mathrm{d}})$ ) achieve perfect individual causal recourse fairness ( $\Delta_{\mathrm{ind}} = 0$ ).
Training on $X_{\mathrm{nd}}$ alone severely degrades test accuracy (down to $58.4\% - 67.4\%$ ), while incorporating exogenous latent noise variables $(X_{\mathrm{nd}}, U_{\mathrm{d}})$ restores full predictive accuracy ( $86.5\% - 91.1\%$ ) while preserving $\Delta_{\mathrm{ind}} = 0$ .

Knowl 8 — Empirical Auditing of Recourse Discrimination on the Adult Dataset
empirical result
An empirical audit of causal recourse fairness was conducted on the UCI Adult dataset using an 8-variable structural causal model. The model incorporates three protected attributes (sex $\in \{\text{male}, \text{female}\}$ , binarized age $\mathbb{I}\{\text{age} \ge 38\} \in \{\text{young}, \text{old}\}$ , nationality $\in \{\text{US}, \text{non-US}\}$ ) and five non-protected variables: marital status (non-actionable), education level, working class, occupation, and weekly work hours (actionable). A nonlinear logistic regression classifier trained with feature unawareness $\mathrm{LR}(X)$ achieving $78.4\%$ test accuracy demonstrated marked recourse unfairness:
1. Discrepancy between metrics: Group distance unfairness is $\Delta_{\mathrm{dist}} = 0.89$ (maximal gap between old US males and old non-US females), whereas group causal cost unfairness is $\Delta_{\mathrm{cost}} = 33.32$ (maximal gap between old US females and old non-US females), demonstrating that non-causal distance metrics fail to identify the most disadvantaged subgroups.
2. Individual recourse unfairness: The mean difference in recourse cost between individuals and their counterfactual twins is $24.32$ , with a maximum individual disparity of $\Delta_{\mathrm{ind}} = 61.53$ .
3. Qualitative disparities in recourse actions: For an older non-US female individual whose factual cost of recourse is $67.0$ (suggested action: $\mathrm{do}(\text{Hrs}: 92.0)$ ), her counterfactual twin had she been an older US male requires a cost of only $5.5$ (suggested action: $\mathrm{do}(\text{Edu}: \text{Prof-school}, \text{WC}: \text{Private})$ ). Suggested recourse systematically favors male, older, and US individuals via lower-cost educational interventions, while prescribing extreme increases in working hours to female and non-US individuals.
Knowl 9 — Societal Interventions on Structural Causal Models for Fair Recourse
model/method
As an alternative to constraining or altering the classifier $h$ , fair causal recourse can be achieved by altering the data-generating structural causal model $\mathcal{M}$ through societal interventions $i_k$ , transforming $\mathcal{M}$ into a modified model $\mathcal{M}'_k = i_k(\mathcal{M})$ that equalizes recourse effort while keeping $h$ fixed.

For a generative process $X := (2 - A) U_X$ with $A \sim \mathrm{Bernoulli}(0.5)$ , $U_X \sim \mathcal{N}(0, 1)$ , and classifier $h(X) = \mathrm{sign}(X)$ , a targeted subsidy policy $i_k = (p, t, s)$ alters the structural assignments to: $T := (1 - A) \mathbb{I}\{U_T < p\}, \quad U_T \sim \mathrm{Uniform}[0, 1]$ $X := (2 - A) U_X + s T \mathbb{I}\{U_X < t\}, \quad U_X \sim \mathcal{N}(0, 1)$ where $p \in [0, 1]$ is the fraction of individuals in the disadvantaged group ( $A = 0$ ) receiving treatment, $t \le 0$ is an eligibility threshold on latent ability $U_X$ , and $s \le -2t$ is the subsidy magnitude chosen to prevent flipping negative factual predictions ( $X < 0$ ) into positive predictions.

The intervention shifts rejected individuals in $A=0$ closer to the decision boundary $X = 0$ , equalizing the effort required for recourse with $A=1$ . Policies $i_k$ are evaluated and selected by trading off societal cost $c_k$ (total paid-out subsidies) against societal benefit $b_k$ (reduction in the group recourse cost difference $\Delta_{\mathrm{cost}}$ ).

Coverage note — None was omitted; all contributed definitions, theoretical propositions, representation methods, experimental evaluations, and societal intervention models are fully covered.

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Citation

MLA

Kügelgen, J. von ., et al. “On the Fairness of Causal Algorithmic Recourse”. arXiv, 2020, http://arxiv.org/abs/2010.06529v5.

APA

Kügelgen, J. von ., Karimi, A.-H., Bhatt, U., Valera, I., Weller, A., & Schölkopf, B. (2020). On the Fairness of Causal Algorithmic Recourse. arXiv. http://arxiv.org/abs/2010.06529v5

Chicago

Kügelgen, J. von ., A.-H. Karimi, U. Bhatt, I. Valera, A. Weller, and B. Schölkopf. 2020. “On the Fairness of Causal Algorithmic Recourse”. arXiv. http://arxiv.org/abs/2010.06529v5.

Harvard

Kügelgen, J. von . et al. (2020) “On the Fairness of Causal Algorithmic Recourse”, arXiv [Preprint]. Available at: http://arxiv.org/abs/2010.06529v5.

Vancouver

1. Kügelgen J von, Karimi A-H, Bhatt U, Valera I, Weller A, Schölkopf B (2020) On the Fairness of Causal Algorithmic Recourse. arXiv

BibTeX

@article{kugelgen2020the,
  title = {On the Fairness of Causal Algorithmic Recourse},
  author = {Kügelgen, Julius von and Karimi, Amir-Hossein and Bhatt, Umang and Valera, Isabel and Weller, Adrian and Schölkopf, Bernhard},
  year = {2020},
  journal = {arXiv},
  url = {http://arxiv.org/abs/2010.06529v5},
  eprint = {2010.06529}
}

Metadata:arXiv

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On the Fairness of Causal Algorithmic Recourse

Abstract

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Table of Contents

Knowls

Knowl 1 — Group-Level Fair Causal Recourse

Knowl 2 — Individually Fair Causal Recourse

Knowl 3 — Insufficiency of Group Fair Recourse for Individual Fair Causal Recourse

Knowl 4 — Insufficiency of Counterfactual Fairness for Fair Recourse

Knowl 5 — Sufficient Condition for Individually Fair Causal Recourse via Input Restriction

Knowl 6 — Fair Representation via Abduction of Exogenous Variables for Causal Recourse