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Fairness in Algorithmic Decision Making: An Excursion Through the Lens of Causality
Aria Khademi, Sanghack Lee, David Foley, Vasant Honavar
TL;DR
Algorithmic decisions can discriminate on protected attributes, while fairness criteria based only on observed distributions may not detect discrimination. The paper uses potential-outcomes methods to estimate two causal group-fairness measures, FACE and FACT. Its real-world analyses find that their conclusions can differ, and that group fairness does not necessarily imply individual-level fairness.
Problem
Fairness criteria based only on joint distributions may not detect discrimination, motivating the question of whether protected attributes causally affect algorithmic decisions.
Source: §1 · p. 1Method
The paper introduces FACE and FACT and uses the Rubin-Neyman potential outcomes framework, including inverse probability weighting to estimate FACE.
Source: §3.1 · p. 3, §5 · p. 5Results
On real-world data, FACE and FACT estimates are robust to unmeasured confounding, but their findings do not always agree.
Source: §5 · p. 6Takeaways & Limitations
FACT analyses show that group fairness or discrimination does not necessarily imply individual-level fairness or discrimination.
Source: §5 · p. 6The reported FACE and FACT estimates are likely to represent direct rather than total causal effects.
Source: §5 · p. 6
Abstract
from arXiv · showhide
As virtually all aspects of our lives are increasingly impacted by algorithmic decision making systems, it is incumbent upon us as a society to ensure such systems do not become instruments of unfair discrimination on the basis of gender, race, ethnicity, religion, etc. We consider the problem of determining whether the decisions made by such systems are discriminatory, through the lens of causal models. We introduce two definitions of group fairness grounded in causality: fair on average causal effect (FACE), and fair on average causal effect on the treated (FACT). We use the Rubin-Neyman potential outcomes framework for the analysis of cause-effect relationships to robustly estimate FACE and FACT. We demonstrate the effectiveness of our proposed approach on synthetic data. Our analyses of two real-world data sets, the Adult income data set from the UCI repository (with gender as the protected attribute), and the NYC Stop and Frisk data set (with race as the protected attribute), show that the evidence of discrimination obtained by FACE and FACT, or lack thereof, is often in agreement with the findings from other studies. We further show that FACT, being somewhat more nuanced compared to FACE, can yield findings of discrimination that differ from those obtained using FACE.
1 INTRODUCTION
The paper motivates causal analysis as a way to detect group discrimination that fairness criteria based only on joint distributions may miss. It introduces FACE and FACT, then applies them to synthetic and real-world data.
1 INTRODUCTION
- Procedural fairness, which bars using a protected attribute in decisions, does not guarantee outcome fairness between protected groups.The introduction also situates the work amid many existing fairness definitions, including demographic parity and equalized odds.Source: §1 · p. 1
- Because fairness criteria based only on joint distributions may fail to detect discrimination, the paper approaches fairness through causal effects of protected attributes on decisions.The authors note that fairness definitions can conflict and that enforcing some definitions may increase discrimination.Source: §1 · p. 1
- Causal fairness asks whether a protected attribute affects a decision, but establishing that effect generally requires experimental manipulation or causal estimates from observational data.The paper focuses on detecting and quantifying discrimination as a prerequisite for developing predictive models that are provably non-discriminatory.Source: §1 · pp. 1–2
Contributions.
- The paper introduces FACE for population-average fairness and FACT for fairness within a protected group, using the Rubin-Neyman potential outcomes framework to estimate both.Its analyses cover synthetic data, Adult income data with gender as the protected attribute, and NYC Stop and Frisk data with race as the protected attribute.Source: Contributions · p. 2
2 FAIRNESS: A CAUSAL PERSPECTIVE
The paper frames group fairness as a causal question: whether changing a protected attribute would change outcomes. It distinguishes population-wide effects from effects assessed within a protected group.
2 FAIRNESS: A CAUSAL PERSPECTIVE
- The causal fairness question is whether changing the protected attribute would change outcomes on average, with causal effects estimated from observational data when possible.The paper describes potential outcomes as results of hypothetical interventions and uses a decision function or predictive model to support decisions.Source: §2 · p. 2
Example.
- In the hiring example, FACE compares expected hiring for men and women across applicants, while FACT compares women's hiring with their estimated outcomes had their gender differed.The FACT comparison holds the applicants' other attributes unchanged.Source: Example · p. 2
2 FAIRNESS: A CAUSAL PERSPECTIVE
- FACE compares expected outcomes across the population, whereas FACT compares a protected group's outcomes with that group's counterfactual outcomes under another attribute value.For FACT, the expectation is taken over members of the protected group; the counterfactual outcomes must be estimated.Source: Example · p. 2, §2 · p. 2
3 ESTIMATING FACE AND FACT
The section estimates group-level causal fairness measures under potential-outcome assumptions, using weighting for FACE and matching for FACT. It describes diagnostics and sensitivity analysis to assess match quality and robustness to hidden bias.
3 ESTIMATING FACE AND FACT
- The potential-outcome framework relies on consistency, positivity, SUTVA, and unconfoundedness; the paper assumes strong ignorability, combining positivity and unconfoundedness.Unconfoundedness cannot be verified from observational data alone, and sensitivity analysis can examine its possible violation.Source: §3 · pp. 2–3
3.1 Estimating and Interpreting FACE
- Under strong ignorability, FACE is estimated by inverse-probability weighting and weighted regression; without unmeasured confounding, either correctly specified model yields an unbiased estimate.For binary outcomes, the weighted model is logistic; for continuous outcomes, it is linear.Source: §3.1 · p. 3
Matching Methods.
- Matching choices include exact matching, propensity-score nearest neighbors, caliper-constrained matching, Mahalanobis matching within a propensity caliper, and full matching.The described nearest-neighbor procedure uses replacement and discards observations outside the propensity-score support; the caliper is 0.25 standard deviations.Source: Matching Methods · p. 3
Quality of Matches.
- Match quality is assessed numerically by treated-control differences in the distance measure and graphically with QQ and jitter plots.A good match has a post-match difference in means close to zero.Source: Quality of Matches · p. 3
Outcome Analysis After Matching.
- FACT uses matched treated and control individuals, then weighted regression on the matched data to estimate the protected attribute’s effect.The coefficient for A estimates FACT; the estimate is doubly robust if either the matching or outcome model is correctly specified.Source: Outcome Analysis After Matching · p. 3
Interpreting ˆγ as a Measure of FACT.
- For continuous outcomes, γ̂ measures the average matched-group outcome difference; for binary outcomes, it is the causal odds ratio for similar treated and control individuals.The paper interprets a statistically significant nonzero γ̂ as evidence of discrimination for the protected group under consideration.Source: Interpreting ˆγ as a Measure of FACT · pp. 3–4
Impact of Unmeasured Confounders on
- Sensitivity analysis varies Γ, the odds ratio in treatment assignment between matched individuals, to assess when hidden bias changes γ̂’s statistical significance.The reported robustness threshold is the Γ at which the upper-bound p-value crosses the significance threshold.Source: Impact of Unmeasured Confounders on · p. 4
4 EXPERIMENTS AND RESULTS
The experiments evaluate FACE and FACT on synthetic and real-world datasets, using statistical significance tests at α = 0.05. The synthetic data are constructed so the protected attribute has no causal effect on the outcome.
4 EXPERIMENTS AND RESULTS
- The experiments estimate FACE and FACT on synthetic and two previously studied real-world datasets, with α = 0.05 for significance tests.The protected attribute is designated separately for each dataset.Source: §4 · p. 4
Synthetic data set.
- The synthetic generative model ensures no hidden confounders and no discrimination by FACE or FACT with respect to the protected attribute.It uses 1,000 observations with five normally distributed features and generates the protected attribute conditional on those features.Source: Synthetic data set · p. 4
- The synthetic outcome is generated from the five features and fixed randomly drawn weights, rather than from the protected attribute.The outcome construction supports the intended no-discrimination setting for the experiment.Source: Synthetic data set · p. 4
The Adult data set.
The Adult income dataset is used to examine gender-based differences in salary, with annual income above $50K as the binary outcome.
The Adult data set.
- The Adult dataset contains 48,842 individuals and 14 attributes, including demographic and work-related information such as age, gender, and weekly work hours.Six attributes are continuous and eight are categorical.Source: The Adult data set · p. 4
- After one-hot encoding categorical variables and removing records with missing values, the analysis dataset contains 46,033 individuals and 45 features excluding gender.Source: The Adult data set · p. 4
- Gender is the protected attribute, and the outcome is whether annual salary exceeds $50K.Y = 1 denotes salary above $50K; Y = 0 denotes salary at or below $50K.Source: The Adult data set · p. 4
The NYC Stop and Frisk (NYCSF) data set.
For the 2014 NYC Stop and Frisk data, the analysis uses race as the protected attribute and arrest after a stop as the outcome. FACE estimates indicate higher arrest odds for Black-Hispanic men than White men in the analyzed data.
The NYC Stop and Frisk (NYCSF) data set.
- The 2014 analysis is restricted to Black-Hispanic and White men; after cleaning and one-hot encoding, it contains 7,593 records and 73 features excluding race.The original 2014 records numbered 45,787 before restricting the sample and removing missing values.Source: The NYC Stop and Frisk (NYCSF) data set · p. 4
4.2 FACE Check: Fairness Analysis Using FACE
- FACE estimates an average causal effect of 0.273 for race; the odds of arrest after a stop for Black-Hispanic individuals are about 1.31 times those for White individuals, suggesting possible racial bias.The authors reject the null hypothesis that the FACE estimate is zero.Source: §4.2 · p. 4, Table 1 · p. 4
- Across the reported FACE analyses, the synthetic data do not reject the zero-effect null, while Adult income shows an estimate of −1.069 for gender.The Adult result suggests gender-based salary discrimination against women; the synthetic outcome was designed to be fair.Source: §4.2 · p. 4
4.3 FACT Check: Fairness Analysis Using FACT
The section reports FACT analyses for the synthetic, Adult, and NYCSF data sets.
4.3 FACT Check: Fairness Analysis Using FACT
- FACT analyses are reported for the synthetic, Adult, and NYCSF data sets.The passage introduces the analysis without giving its results.Source: §4.3 · p. 4
Matching Quality Analyses.
The authors assess whether matching produces sufficiently balanced data for FACT estimation, comparing matching methods across three data sets.
Matching Quality Analyses.
- Matching sharply reduced imbalance across all data sets, with NNM and FM achieving the lowest imbalance.Before matching, Da,a′ was 1.6400 for synthetic data, 3.3508 for Adult, and 1.1616 for NYCSF.Source: Matching Quality Analyses · p. 5
- FM yielded higher-quality matches than other methods across all data sets, but more matched pairs made balance harder and the trade-off depended on the application.The authors note that considering the trade-off between match count and imbalance, FM yields higher-quality matches across data sets.Source: Matching Quality Analyses · p. 5
- After FM, synthetic-data features aligned more closely with the QQ-plot diagonal, and treated and control propensity-score distributions were similar.The authors use these diagnostics to judge match quality adequate before estimating FACT.Source: Matching Quality Analyses · p. 5, Figure 1 · p. 5
FACT Estimates.
FACT finds evidence of gender-based salary discrimination in Adult, no evidence of racial bias in NYCSF arrests after stops, and average fairness in the synthetic data.
FACT Estimates.
- For synthetic data, NNM and MMMPC did not reject γ=0, while NNMPC and FM had p-values below 0.05 but near-zero estimates; the authors conclude average fairness.EM produced no matches and was omitted from the FACT results table.Source: FACT Estimates · p. 5
- Using FM, the Adult estimate was γ̂ = −0.573; women’s odds of earning over $50K were about 0.56 times those of matched men.The authors conclude there is evidence of gender-based salary discrimination against women on average.Source: FACT Estimates · p. 5
- For NYCSF arrests after stops, FACT found no evidence of racial bias on average, unlike FACE and counterfactual fairness analyses.FACT compares Black-Hispanics with matched Whites; the authors suggest its protected-group average differs from FACE’s population-wide comparison.Source: FACT Estimates · p. 5
Impact of Unmeasured Confounders.
Sensitivity analyses indicate that FACT estimates are generally robust to hidden-confounder bias, with robustness varying by data set and matching method.
Impact of Unmeasured Confounders.
- FACT estimates were robust to hidden-confounder bias across most methods; FM robustness extended to Γ=4.5 on Adult and Γ=3 on NYCSF.On NYCSF, NNM and MMMPC estimates were robust, while NNMPC robustness extended to Γ=8.5; on Adult, all methods except FM were robust over the tested range.Source: Impact of Unmeasured Confounders · p. 5
5 SUMMARY AND DISCUSSION
The Adult and NYCSF analyses often agree with prior studies, but FACE and FACT do not always agree; FACT also shows that group fairness need not imply individual fairness.
5 SUMMARY AND DISCUSSION
- Synthetic-data experiments show the proposed methods effectively detect and quantify group fairness.Source: §5 · p. 5
- The methods adjust for potential confounders, although that adjustment may be unnecessary for gender and race because these attributes are unlikely to be caused by other covariates.Source: §5 · p. 5
- On Adult and NYCSF, FACE/FACT findings often agree with prior studies but do not always agree with each other; FACT also shows group fairness need not imply individual fairness.The authors report that real-world estimates are robust to unmeasured confounding.Source: §5 · pp. 5–6
- Further research directions include relaxing the i.i.d. assumption for related individuals and examining relationships among causal notions of fairness.Source: §5 · p. 6
- The reported FACE and FACT estimates are likely to represent direct causal effects rather than total causal effects.Source: §5 · p. 6