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Assessing Group Fairness with Social Welfare Optimization

Violet Chen, J. N. Hooker, Derek Leben

TL;DR

This paper investigates how a welfare-economic lens can illuminate group fairness in AI by linking parity metrics to the alpha-fairness social welfare function $W_{\alpha}(\mathbf{u})$. By formulating a constrained selection problem and deriving a greedy solution based on the welfare differential $\Delta_i(\alpha)$, it analyzes how demographic parity, equalized odds, and predictive rate parity arise (or fail to) under different $\alpha$ and group-utility structures. The authors show that demographic parity can align with alpha-fairness for certain parameters, while equalized odds and predictive rate parity often require accuracy-maximizing or highly specific conditions, respectively; predictive rate parity tends to have limited usefulness except in particular regimes. Overall, the work demonstrates that optimization theory offers a principled way to justify or critique parity definitions and informs the practical choice of fairness criteria in AI systems, with avenues for extending to alternative SWFs and broader welfare objectives.

Abstract

Statistical parity metrics have been widely studied and endorsed in the AI community as a means of achieving fairness, but they suffer from at least two weaknesses. They disregard the actual welfare consequences of decisions and may therefore fail to achieve the kind of fairness that is desired for disadvantaged groups. In addition, they are often incompatible with each other, and there is no convincing justification for selecting one rather than another. This paper explores whether a broader conception of social justice, based on optimizing a social welfare function (SWF), can be useful for assessing various definitions of parity. We focus on the well-known alpha fairness SWF, which has been defended by axiomatic and bargaining arguments over a period of 70 years. We analyze the optimal solution and show that it can justify demographic parity or equalized odds under certain conditions, but frequently requires a departure from these types of parity. In addition, we find that predictive rate parity is of limited usefulness. These results suggest that optimization theory can shed light on the intensely discussed question of how to achieve group fairness in AI.

Assessing Group Fairness with Social Welfare Optimization

TL;DR

This paper investigates how a welfare-economic lens can illuminate group fairness in AI by linking parity metrics to the alpha-fairness social welfare function . By formulating a constrained selection problem and deriving a greedy solution based on the welfare differential , it analyzes how demographic parity, equalized odds, and predictive rate parity arise (or fail to) under different and group-utility structures. The authors show that demographic parity can align with alpha-fairness for certain parameters, while equalized odds and predictive rate parity often require accuracy-maximizing or highly specific conditions, respectively; predictive rate parity tends to have limited usefulness except in particular regimes. Overall, the work demonstrates that optimization theory offers a principled way to justify or critique parity definitions and informs the practical choice of fairness criteria in AI systems, with avenues for extending to alternative SWFs and broader welfare objectives.

Abstract

Statistical parity metrics have been widely studied and endorsed in the AI community as a means of achieving fairness, but they suffer from at least two weaknesses. They disregard the actual welfare consequences of decisions and may therefore fail to achieve the kind of fairness that is desired for disadvantaged groups. In addition, they are often incompatible with each other, and there is no convincing justification for selecting one rather than another. This paper explores whether a broader conception of social justice, based on optimizing a social welfare function (SWF), can be useful for assessing various definitions of parity. We focus on the well-known alpha fairness SWF, which has been defended by axiomatic and bargaining arguments over a period of 70 years. We analyze the optimal solution and show that it can justify demographic parity or equalized odds under certain conditions, but frequently requires a departure from these types of parity. In addition, we find that predictive rate parity is of limited usefulness. These results suggest that optimization theory can shed light on the intensely discussed question of how to achieve group fairness in AI.
Paper Structure (8 sections, 5 theorems, 17 equations, 9 figures)

This paper contains 8 sections, 5 theorems, 17 equations, 9 figures.

Table of Contents

  1. Introduction
  2. Related Work
  3. The Basic Model
  4. Modeling Protected and Nonprotected Groups
  5. Demographic Parity
  6. Equalized Odds
  7. Predictive Rate Parity
  8. Conclusion

Key Result

theorem 1

If $\Delta_{\pi_1}(\alpha)\geq \cdots\geq\Delta_{\pi_n}(\alpha)$, where $\pi_1,\ldots,\pi_n$ is a permutation of $1,\ldots,n$, then one can maximize $W_{\alpha}(\bm{x})$ subject to $\sum_{i=1}^n x_i = m$ by setting $x_i=1$ for $i=\pi_1,\ldots,\pi_m$, and $x_i=0$ for $i=\pi_{m+1},\ldots,\pi_n$.

Figures (9)

  • Figure 1: Cases (a), (b), and (c) in the proof of Theorem \ref{['th:alpha']}
  • Figure 2: Alpha fair selection rates, assuming overall selection rate of 0.25
  • Figure 3: Alpha fair selection rates, assuming overall selection rate of 0.6
  • Figure 4: Alpha fair selection rates, assuming overall selection rate of 0.8
  • Figure 5: Values of alpha that achieve demographic parity
  • ...and 4 more figures

Theorems & Definitions (8)

  • theorem 1
  • theorem 2
  • proof
  • theorem 3
  • proof
  • theorem 4
  • proof
  • theorem 5