Research map / Learning theory and algorithms / Fairness
Fairness under Competition
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Shows theoretically and empirically that individually Equal-Opportunity-fair classifiers used by competing lenders can yield an unfair ecosystem, and that post-processing fairness adjustments can worsen ecosystem fairness.
Problem
Whether adopting individually fair (Equal Opportunity) classifiers across multiple competing firms yields a fair ecosystem overall, in which deserving borrowers from different groups receive offers at equal rates.
Approach
Introduces Equal Opportunity under Competition (EOC) and a welfare-based v-EOC, and characterizes how the ecosystem-level unfairness arises from differences in classifier correlations across groups and from differences in the sets of borrowers served by each lender, with closed-form levels and worst-case bounds; also shows post-processing EO adjustments can increase EOC.
Key results
- Two EO classifiers with false-negative rates beta_1, beta_2 have EOC level sigma_1*sigma_2*|rho^0-rho^1|, with worst case min(beta_1,beta_2)-max(0,beta_1+beta_2-1); with equal beta<=1/2 the worst case is beta.
- In Lending Club experiments with 100k training examples, fairness adjustment made EOC worse in 30.1%, 15.8%, and 17.4% of runs (Exp. 1-3), with mean factor increases of 19, 1.3, and 3.1.
- In a worked example, two individually EO-adjusted classifiers can have a positive EOC level while the pre-adjustment pair was EOC (e.g., fairness adjustment makes the ecosystem less fair).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Apply EO fairness adjustment to both classifiers | Competing classifiers in Lending Club Exp. 1 · Lending Club, training set 100k | Probability EOC increases (%): [26.2, 34.0] | Mixed |
| Apply EO fairness adjustment to both classifiers | Competing classifiers in Lending Club Exp. 2 · Lending Club, training set 100k | Probability EOC increases (%): [12.6, 19.0] | Mixed |
| Apply EO fairness adjustment to both classifiers | Competing classifiers in Lending Club Exp. 3 · Lending Club, training set 100k | Probability EOC increases (%): [14.2, 20.6] | Mixed |
| Apply EO fairness adjustment to the classifier serving both groups | Competing classifiers in Lending Club Exp. 4 · Lending Club, different served subsets, training set 100k | Probability EOC increases (%): [0.0, 0.0] | No clear effect |
| Apply EO fairness adjustment to both classifiers | Competing classifiers in Lending Club Exp. 5 · Lending Club, independently sampled training data, training set 100k | Probability EOC increases (%): [24.0, 31.4] | Mixed |
| Apply EO fairness adjustment to both classifiers | Competing classifiers in Lending Club Exp. 6 · Lending Club, independently sampled training data, training set 100k | Probability EOC increases (%): [28.0, 36.0] | Mixed |
| Apply fairness adjustment to both classifiers | Competing classifiers in Lending Club Exp. 3 · Lending Club, selected run | EOC level: 0.020774% -> 0.444052% | Hurt |
| Use EO classifiers whose correlations differ across protected groups | Two competing classifiers · Equal Opportunity under Competition | EOC level: σ1·σ2·|ρ0−ρ1| | Hurt |
| Use EO classifiers serving subsets with different group overlaps | Two competing classifiers · Equal Opportunity under Competition | EOC level: β·(1−β)·|γ0−γ1| | Hurt |
| Increase the number of EO classifiers with shared predictions for one group and independent errors for the other | Competing classifiers · Equal Opportunity under Competition | EOC level: β−β^n | Hurt |
| Adjust individually biased classifiers to satisfy EO | Two competing classifiers with group-dependent correlations · Equal Opportunity under Competition | EOC level | Hurt |
| Adjust the classifier serving both groups to have equal false-negative rates | Two competing classifiers serving different borrower subsets · Equal Opportunity under Competition | EOC level | Hurt |
Surprising findings
- Fairness adjustment of individual classifiers often increased the ecosystem EOC level, even though each adjusted classifier became more EO.
- Increasing the number of EO classifiers can strictly increase the ecosystem EOC level (beta - beta^n in the stylized example).
Limitations
- Theoretical results rely on simplifying assumptions such as uncorrelated classifiers on overlapping borrowers, 0-1 or 0-1-k utility preferences, and post-processing fairness adjustments.
- Experiments use simple classifiers (logistic regression, decision tree) and a protected attribute (mortgage status) that is a proxy rather than true demographic group.
- Worst-case bounds and multi-lender results are only partially extended to welfare-based and other fairness notions.
Experimental setup
Datasets: Lending Club loan data 2007-2015 Adult Census Income
Benchmarks: Lending Club loan data Adult Census Income
Metrics: EO level EOC level likelihood EOC increased after fairness adjustment effect size of EOC increase
Baselines: logistic regression decision tree
Builds on: Equal Opportunity (Hardt et al.) post-processing fairness adjustment welfare-equalizing fairness
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