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Impact of Fairness Regulations on Institutions' Policies and Population Qualifications

Hamidreza Montaseri, Amin Gohari

TL;DR

This work analyzes how penalties for discrimination, designed to enforce demographic parity, affect policy choices of utility-maximizing institutions and the evolution of population qualifications. It introduces a convex penalty framework $\max \mathbb{E}[DY]-\lambda g(\Delta)$ with $\Delta$ as the disparity in selection rates, and derives static conditions under which penalties are effective or fully achieve parity. Dynamically, it models how qualifications evolve via a time-homogeneous Markov process and shows that myopic penalties can sometimes hinder natural convergence to equality, though sufficient transition-bias and growth assumptions can restore parity. Empirical validation on the LSAC dataset supports the static results and demonstrates the nuanced impact of penalty shapes on parity, offering guidance for constructing regulatory fairness interventions in real-world settings.

Abstract

The proliferation of algorithmic systems has fueled discussions surrounding the regulation and control of their social impact. Herein, we consider a system whose primary objective is to maximize utility by selecting the most qualified individuals. To promote demographic parity in the selection algorithm, we consider penalizing discrimination across social groups. We examine conditions under which a discrimination penalty can effectively reduce disparity in the selection. Additionally, we explore the implications of such a penalty when individual qualifications may evolve over time in response to the imposed penalizing policy. We identify scenarios where the penalty could hinder the natural attainment of equity within the population. Moreover, we propose certain conditions that can counteract this undesirable outcome, thus ensuring fairness.

Impact of Fairness Regulations on Institutions' Policies and Population Qualifications

TL;DR

This work analyzes how penalties for discrimination, designed to enforce demographic parity, affect policy choices of utility-maximizing institutions and the evolution of population qualifications. It introduces a convex penalty framework with as the disparity in selection rates, and derives static conditions under which penalties are effective or fully achieve parity. Dynamically, it models how qualifications evolve via a time-homogeneous Markov process and shows that myopic penalties can sometimes hinder natural convergence to equality, though sufficient transition-bias and growth assumptions can restore parity. Empirical validation on the LSAC dataset supports the static results and demonstrates the nuanced impact of penalty shapes on parity, offering guidance for constructing regulatory fairness interventions in real-world settings.

Abstract

The proliferation of algorithmic systems has fueled discussions surrounding the regulation and control of their social impact. Herein, we consider a system whose primary objective is to maximize utility by selecting the most qualified individuals. To promote demographic parity in the selection algorithm, we consider penalizing discrimination across social groups. We examine conditions under which a discrimination penalty can effectively reduce disparity in the selection. Additionally, we explore the implications of such a penalty when individual qualifications may evolve over time in response to the imposed penalizing policy. We identify scenarios where the penalty could hinder the natural attainment of equity within the population. Moreover, we propose certain conditions that can counteract this undesirable outcome, thus ensuring fairness.
Paper Structure (18 sections, 11 theorems, 154 equations, 10 figures)

This paper contains 18 sections, 11 theorems, 154 equations, 10 figures.

Table of Contents

  1. Introduction
  2. Problem Formulation in the Static Case
  3. A simplification
  4. Related Work
  5. Effectiveness of the Discrimination Penalty in the Static Case
  6. Dynamics of the Population
  7. Dynamics of the institution's objective
  8. Stationary states
  9. Experiments
  10. Dynamics
  11. Conclusion
  12. A useful lemma
  13. Proof of Theorem \ref{['th:effective']}
  14. Proof of Theorem \ref{['th:fulldp']}
  15. Proof of Theorem \ref{['th:um']}
  16. ...and 3 more sections

Key Result

Theorem 1

The penalty function $g(\cdot)$ and scalar $\lambda$ are effective if and only if $\beta_e < \lambda \cdot g'_-(\Delta_{\text{UM}})$, where $g'_-(\cdot)$ is the left-hand derivative of $g$ and where $\mathcal{T}_e\subset\mathcal{Y}\times\{\mathscr A,\mathscr B\}$ is defined as

Figures (10)

  • Figure 1: Transition probabilities when a) getting selected and b) when not
  • Figure 2: Evolution of disparity $\Delta$ under different levels of $\lambda$
  • Figure 3: Evolution of the institution's objective $\mathsf{Profit}(t)=\mathbf{E}[D_tY_t]-\lambda\cdot g(\Delta_t)$ for different levels of discrimination penalty $\lambda$.
  • Figure 4: Distribution of GPA across the two race groups in LSAC dataset
  • Figure 5: Impact of different penalty functions on disparity on LSAC dataset
  • ...and 5 more figures

Theorems & Definitions (26)

  • Definition 1
  • Theorem 1
  • Remark 1
  • Definition 2
  • Theorem 2
  • Definition 3
  • Theorem 3
  • Example 1
  • Theorem 4
  • Theorem 5
  • ...and 16 more