Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Algorithmic Fairness and Social Welfare

Annie Liang, Jay Lu

TL;DR

The paper investigates the relationship between algorithmic fairness (group-based, statistical definitions) and social-welfare fairness (veil-of-ignorance approach). It demonstrates a fundamental mismatch via a simple two-group example, showing that optimal rules under Equalized Odds can starkly differ from a utilitarian or Rawlsian welfare objective. It then proposes a general nesting framework that subsumes both approaches by introducing a fairness-unfairness penalty $h(P)$ or a concave transform $\phi$, enabling analysis of trade-offs between accuracy and fairness under either objective. This framework clarifies the normative commitments behind different fairness criteria and offers a basis for designing new, justified fairness notions with practical implications for high-stakes decisions.

Abstract

Algorithms are increasingly used to guide high-stakes decisions about individuals. Consequently, substantial interest has developed around defining and measuring the ``fairness'' of these algorithms. These definitions of fair algorithms share two features: First, they prioritize the role of a pre-defined group identity (e.g., race or gender) by focusing on how the algorithm's impact differs systematically across groups. Second, they are statistical in nature; for example, comparing false positive rates, or assessing whether group identity is independent of the decision (where both are viewed as random variables). These notions are facially distinct from a social welfare approach to fairness, in particular one based on ``veil of ignorance'' thought experiments in which individuals choose how to structure society prior to the realization of their social identity. In this paper, we seek to understand and organize the relationship between these different approaches to fairness. Can the optimization criteria proposed in the algorithmic fairness literature also be motivated as the choices of someone from behind the veil of ignorance? If not, what properties distinguish either approach to fairness?

Algorithmic Fairness and Social Welfare

TL;DR

The paper investigates the relationship between algorithmic fairness (group-based, statistical definitions) and social-welfare fairness (veil-of-ignorance approach). It demonstrates a fundamental mismatch via a simple two-group example, showing that optimal rules under Equalized Odds can starkly differ from a utilitarian or Rawlsian welfare objective. It then proposes a general nesting framework that subsumes both approaches by introducing a fairness-unfairness penalty or a concave transform , enabling analysis of trade-offs between accuracy and fairness under either objective. This framework clarifies the normative commitments behind different fairness criteria and offers a basis for designing new, justified fairness notions with practical implications for high-stakes decisions.

Abstract

Algorithms are increasingly used to guide high-stakes decisions about individuals. Consequently, substantial interest has developed around defining and measuring the ``fairness'' of these algorithms. These definitions of fair algorithms share two features: First, they prioritize the role of a pre-defined group identity (e.g., race or gender) by focusing on how the algorithm's impact differs systematically across groups. Second, they are statistical in nature; for example, comparing false positive rates, or assessing whether group identity is independent of the decision (where both are viewed as random variables). These notions are facially distinct from a social welfare approach to fairness, in particular one based on ``veil of ignorance'' thought experiments in which individuals choose how to structure society prior to the realization of their social identity. In this paper, we seek to understand and organize the relationship between these different approaches to fairness. Can the optimization criteria proposed in the algorithmic fairness literature also be motivated as the choices of someone from behind the veil of ignorance? If not, what properties distinguish either approach to fairness?
Paper Structure (5 sections, 1 theorem, 12 equations)

This paper contains 5 sections, 1 theorem, 12 equations.

Table of Contents

  1. Setup
  2. Fair Algorithms
  3. Social Welfare Approach
  4. Comparing the Two Approaches
  5. A More General Framework

Key Result

Proposition 1

Any constrained optimization choice rule is not a social welfare choice rule, and vice versa, i.e. $\mathcal{C}_{co} \cap \mathcal{C}_{sw} = \emptyset$

Theorems & Definitions (8)

  • Definition 1: Equalized Odds
  • Definition 2: Equality of False Negatives
  • Definition 3: Equality of False Positives
  • Definition 4: Statistical Parity
  • Example 1
  • Claim 1
  • Definition 5
  • Proposition 1