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Centralized Selection with Preferences in the Presence of Biases
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Studies centralized multi-institution selection with candidate preferences under group-wise utility bias, showing Gale-Shapley-style selection can hurt preference fairness and utility, and proposes institution-wise proportional constraints that restore near-optimal preference fairness and utility under i.i.d. assumptions.
Problem
Centralized selection of candidates to multiple capacity-limited institutions when candidates' observed utilities are biased against a disadvantaged group, harming preference-based and representational fairness as well as true utility.
Approach
Replaces group-wise constraints (which only fix representation) with institution-wise proportional quotas: each institution reserves capacity proportional to each group's size, and a serial-dictatorship (stable) assignment is run independently per group. This yields near-optimal preference-based fairness, representational fairness and utility without knowing the bias parameter beta.
Key results
- Under the uniform utility case with beta near 0, the unconstrained algorithm's utility ratio approaches 2/3 and fairness metrics approach 0.
- On IIT-JEE 2009 data, institution-wise constraints achieve P^(1) >= 0.9 for all phi, while group-wise constraints achieve P^(1) <= 0.5.
- Institution-wise constraints maintain preference fairness above 0.75 across synthetic settings with distinct group preference distributions, where group-wise constraints stay at or below 0.7.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Add institution-wise proportional representation constraints instead of group-wise constraints | Centralized selection on IIT-JEE 2009 · IIT-JEE 2009 | preference-based fairness (P^(1)): ≤ 0.5 (group-wise); ≥ 0.9 (institution-wise) | Helped |
| Add institution-wise proportional representation constraints instead of group-wise constraints | Centralized selection on IIT-JEE 2009 · IIT-JEE 2009 | preference-based fairness (P^(3)): ≤ 0.7 (group-wise); ≥ 0.95 (institution-wise) | Helped |
| Add institution-wise proportional representation constraints instead of using no constraints | Centralized selection on IIT-JEE 2009 · IIT-JEE 2009 | preference-based fairness (P^(3)): ≤ 0.25 (unconstrained); ≥ 0.95 (institution-wise) | Helped |
| Add institution-wise proportional representation constraints instead of group-wise constraints | Centralized selection with distinct group preference distributions · Synthetic, distinct preference distributions | preference-based fairness (P^(1)): ≤ 0.7 (group-wise); ≥ 0.75 (institution-wise) | Helped |
| Apply unconstrained stable assignment under decreasing disadvantaged-group utility estimates | Stable assignment · Synthetic, utilities uniform on [0,1], β approaching 0 | representational fairness (R): \beta \pm O \left( \frac{\sqrt{\log n}}{{\sqrt{n}}} \right) | Hurt |
| Apply unconstrained stable assignment under decreasing disadvantaged-group utility estimates | Stable assignment · Synthetic, utilities uniform on [0,1], β approaching 0 | utility ratio (U): \frac{2}{3} + \frac{ 4 \beta}{3(\beta+1)^2} \pm O \left( \frac{\sqrt{\log n}}{{\sqrt{n}}} \right) | Hurt |
| Add institution-wise proportional representation constraints | Centralized selection · Synthetic, arbitrary utility and preference distributions | representational fairness (R): 1 | Helped |
| Relax institution-wise capacity reservations using α rather than enforcing strict reservations (ablation) | Institution-wise constraints · Synthetic, Pareto utilities | preference-based fairness (P^(1)): 0.45 to 0.90 | Helped |
| Relax group-wise representation bounds using α (ablation) | Group-wise constraints · Synthetic, Pareto utilities | preference-based fairness (P^(1)): 0.45 to 0.55 | Helped |
| Relax institution-wise capacity reservations using α rather than enforcing strict reservations (ablation) | Institution-wise constraints · Synthetic, truncated Gaussian utilities | preference-based fairness (P^(1)): 0.55 to 0.90 | Helped |
| Relax group-wise representation bounds using α (ablation) | Group-wise constraints · Synthetic, truncated Gaussian utilities | preference-based fairness (P^(1)): 0.55 to 0.60 | Helped |
| Vary preference dispersion φ (ablation) | Institution-wise constraints · Synthetic, shared preference distribution | preference-based fairness | No clear effect |
Surprising findings
- Group-wise proportional representation constraints can lower preference-based fairness to near 0 even while achieving perfect representational fairness.
- Explicit preference-fairness-enforcing algorithms can have utility roughly half of optimal in adversarial constructions.
Limitations
- Theoretical guarantees rely on i.i.d. utilities and preference lists across candidates.
- Requires known group identities and assumes truthful group reporting; relaxed variants are needed for practical use.
- Real-world experiments use JEE scores as utility proxy and modeled Mallows preferences because individual preferences were not released.
Experimental setup
Datasets: IIT-JEE 2009 scores and seat data (JOSAA), 384,977 students synthetic utilities (truncated Gaussian, Pareto) with Mallows preferences
Benchmarks: IIT-JEE 2009 admissions simulation synthetic Mallows-preference simulations
Metrics: preference-based fairness P representational fairness R utility ratio U
Baselines: unconstrained Gale-Shapley (A*) group-wise constrained algorithm (A_group) relaxed group-wise constraints
Builds on: Gale-Shapley algorithm beta-bias model of Emelianov et al. group-wise proportional constraints (Celis et al.)
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