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Strategic Costs of Perceived Bias in Fair Selection
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Game-theoretic all-pay contest model in which two groups with ρ-biased valuation distributions choose effort; the large-n Nash equilibrium is a single threshold policy, with closed-form representation, welfare, and revenue metrics and an intervention optimization over selectivity and bias.
Problem
Explaining how differences in perceived post-selection value across socioeconomic groups lead to rational effort and representation disparities even when selection under a meritocratic rule is symmetric.
Approach
Models a two-group all-pay-style contest where group 2 valuations are a ρ-biased scaling of group 1 valuations; in the large-agent limit, the unique symmetric Nash equilibrium is a single threshold policy determined by a mixture-CDF equation, yielding closed-form metrics and a cost-sensitive intervention optimization over selectivity c and bias ρ.
Key results
- Under uniform densities with alpha=0.5, c=0.1, representation ratio stays at or below 0.2 for rho up to 0.85, showing strategic behavior amplifies disparities in highly selective settings.
- Calibrating to JEE Advanced 2024 gender data gives rho approximately 0.882 from observed representation ratio 0.671.
- Intervention optimization: for target thresholds tau up to 0.92 increasing selectivity c is more cost-effective; above 0.92 increasing rho is preferable.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Increase valuation-bias parameter rho | Large-n two-group equilibrium · Two-group contest | representation ratio | Helped |
| Increase valuation-bias parameter rho | Large-n two-group equilibrium · Two-group contest | social welfare ratio | Helped |
| Increase selection fraction c (reduce selectivity) | Uniform-density large-n equilibrium · Uniform valuations on [0,1] and [0,rho] | representation ratio | Helped |
| Increase selection fraction c (reduce selectivity) | Uniform-density large-n equilibrium · Uniform valuations on [0,1] and [0,rho] | social welfare ratio | Helped |
| Increase selection fraction c | Large-n equilibrium · Two-group contest | average revenue | Hurt |
| Increase valuation-bias parameter rho | Large-n equilibrium · Two-group contest | average revenue | Helped |
| Increase selection fraction c | Uniform-density large-n equilibrium · Uniform valuations on [0,1] and [0,rho] | representation ratio | Helped |
| Increase selection fraction c | Uniform-density large-n equilibrium · Uniform valuations on [0,1] and [0,rho] | representation ratio: c = 0.5 | Helped |
| Increase rho to at least 0.976 | Uniform-density intervention · 80%-rule representation target | representation ratio: 0.976 | Helped |
| Increase selection fraction c rather than rho | Cost-sensitive intervention optimization · Representation target tau <= 0.92 | intervention cost-effectiveness: 0.92 | Helped |
| Increase valuation-bias parameter rho rather than c | Cost-sensitive intervention optimization · Representation target tau > 0.92 | intervention cost-effectiveness: 0.92 | Helped |
| Apply a higher group-specific merit scale or offset to G2 (x2 > x1 and y2 > y1) | Group-specific merit-mapping intervention · Highly selective settings | representation ratio: 0.8 | Helped |
Surprising findings
- Finite-n simulations show group 2 policy can exceed group 1 policy for small n, reversing the large-n ordering.
- Average revenue computed under an unbiased NE policy overestimates true revenue by about 13% at rho=0.8 in a two-agent example.
Limitations
- Model is static and captures only one stage of a feedback cycle.
- Closed-form equilibrium is derived for uniform densities; general densities require more involved analysis and finite-n equilibrium lacks explicit form.
- Intervention costs are illustrative functional forms (e.g., 5*Delta^1.1) rather than empirically estimated.
Experimental setup
Datasets: JEE Advanced 2024 admission statistics
Metrics: representation ratio social welfare ratio average revenue
Baselines: undifferentiated contest biased contest with effort bias unbiased NE policy
Builds on: all-pay auction undifferentiated contest statistical discrimination models
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