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Fairness in Matching under Uncertainty
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use the LP-based fair allocation instead of the mix of Thompson sampling and a utility-maximizing matching | Libimseti matching experiment · Libimseti | expected welfare | Helped |
| Use the LP-based solution rather than Thompson sampling at full fairness | Libimseti matching experiment · Libimseti, φ=1 | expected welfare | Helped |
| Set φ=0, leaving the principal unconstrained by fairness | LP-based allocation and A_mix baseline · Libimseti, φ=0 | expected welfare | No clear effect |
| Substitute sampled estimates directly for the true fairness requirements in the LP, without the correction (ablation) | Fair utility-maximizing matching LP · Matching under uncertainty | fairness | Hurt |
| Substitute sampled estimates directly for the true fairness requirements in the LP, without the correction (ablation) | Fair utility-maximizing matching LP · Matching under uncertainty | principal utility | Hurt |
| Add the correction widehat{ell}_{x,k}=(tilde{ell}_{x,k}+k epsilon)/(n epsilon+1) to sampled fairness requirements | Fair utility-maximizing matching LP · Matching under uncertainty | utility approximation: 1/(φ n ε + 1) | Helped |
| Add the correction widehat{ell}_{x,k}=(tilde{ell}_{x,k}+k epsilon)/(n epsilon+1) to sampled fairness requirements | Fair utility-maximizing matching LP · Matching under uncertainty | fairness: φ · (1 + ε/2)/(n ε+1) | Helped |
| Use the modified LP with the tightness construction's perturbed fairness inputs (ablation) | Sampling-based fair allocation · Fair ranking instance, φ=1 | utility approximation: 1/(n ε + 1) | Hurt |
| Use the modified LP with the tightness construction's perturbed fairness inputs (ablation) | Sampling-based fair allocation · Fair ranking instance, φ=1 | fairness: (1+ε/2)/(nε+1) | Hurt |
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