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Identifying the desert decision rule to assess and achieve fairness

Ping Zhang, Naiwen Ying, Wang Miao

Abstract

We study fairness in decision-making when the data may encode systematic bias. Existing approaches typically impose fairness constraints while predicting the observed decision, which may itself be unfair. We propose a novel framework for characterising and addressing fairness issues by introducing the notion of desert decision, a latent variable representing the decision an individual rightfully deserves based on their actions, efforts, or abilities. This formulation shifts the prediction target from the potentially biased observed decision to the desert decision. We advocate achieving fair decision-making by predicting the desert decision and assessing unfairness by the discrepancy between desert and observed decisions. We establish nonparametric identification results under causally interpretable assumptions on the fairness of the desert decision and the unfairness mechanism of the observed decision. For estimation, we develop a sieve maximum likelihood estimator for the desert decision rule and an influence-function-based estimator for the degree of unfairness. Sensitivity analysis procedures are further proposed to assess robustness to violations of identifying assumptions. Our framework connects fairness with measurement error models, aligning predictive accuracy with fairness relative to an appropriate target, and providing a structural approach to modelling the unfairness mechanism.

Identifying the desert decision rule to assess and achieve fairness

Abstract

We study fairness in decision-making when the data may encode systematic bias. Existing approaches typically impose fairness constraints while predicting the observed decision, which may itself be unfair. We propose a novel framework for characterising and addressing fairness issues by introducing the notion of desert decision, a latent variable representing the decision an individual rightfully deserves based on their actions, efforts, or abilities. This formulation shifts the prediction target from the potentially biased observed decision to the desert decision. We advocate achieving fair decision-making by predicting the desert decision and assessing unfairness by the discrepancy between desert and observed decisions. We establish nonparametric identification results under causally interpretable assumptions on the fairness of the desert decision and the unfairness mechanism of the observed decision. For estimation, we develop a sieve maximum likelihood estimator for the desert decision rule and an influence-function-based estimator for the degree of unfairness. Sensitivity analysis procedures are further proposed to assess robustness to violations of identifying assumptions. Our framework connects fairness with measurement error models, aligning predictive accuracy with fairness relative to an appropriate target, and providing a structural approach to modelling the unfairness mechanism.

Paper Structure

This paper contains 16 sections, 10 theorems, 32 equations, 5 figures, 5 tables.

Table of Contents

  1. Introduction
  2. Fairness and the desert decision framework
  3. Existing fairness criteria and methods
  4. Desert decision and parameters of interest
  5. Identification
  6. Assumptions on the mechanism of unfairness
  7. Nonparametric identification
  8. Estimation
  9. Estimation of the desert decision rule
  10. Estimation of the degree of unfairness
  11. Extensions: legitimate differential treatment and sensitivity analysis
  12. Incorporating legitimate differential treatment
  13. Sensitivity analysis against violations of the unfairness mechanism
  14. Simulation
  15. Application
  16. ...and 1 more sections

Key Result

Proposition 1

Under Assumption ass:fair, (i) $\tau(V)$ is the best predictor of the desert decision under the cross-entropy risk: (ii) $\tau(V)$ satisfies calibration for predicting the desert decision: $Y^* \mathbin{ {$⊥$} {$=$} {$$} {} } S \mid \tau(V).$

Figures (5)

  • Figure 1: Desert decision in a standard loan approval procedure.
  • Figure 2: Causal diagrams satisfying Assumptions \ref{['ass:fair']} and \ref{['ass:aux']}, conditional on $X$.
  • Figure 3: (a) Estimation error of $\hat{\tau}$ and (b) bias of $\hat{\theta}$.
  • Figure 4: Histograms of the estimated unfairness mechanism $\hat{\alpha}$ and $\hat{\beta}$.
  • Figure 5: Histogram of $\hat{\alpha}$ for applicants targeting sales representative positions.

Theorems & Definitions (12)

  • Example 1
  • Proposition 1
  • Example 2
  • Theorem 1
  • Theorem 2
  • Proposition 2
  • Theorem 3
  • Theorem 4
  • Theorem 5
  • Theorem 6
  • ...and 2 more