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Unfair Utilities and First Steps Towards Improving Them

Frederik Hytting Jørgensen, Sebastian Weichwald, Jonas Peters

TL;DR

The paper reframes algorithmic fairness by enforcing a fairness criterion on the utility function via value-of-information fairness (VoI-fairness), rather than constraining predictive policies. It defines VoI and $F$-VoI-fairness, provides graphical and structural criteria, and shows how to modify unfair utilities into VoI-fair ones that disincentivize inferring protected attributes. Through synthetic examples, college-admission simulations, and COMPAS data, it demonstrates practical procedures for constructing corresponding VoI-fair utilities and policies, including rejection-sampling-based estimation of the fair utility and its corresponding policy. The work argues that this utility-centric approach can avoid several shortcomings of existing notions like counterfactual fairness and equalized odds, while remaining computationally tractable and adaptable to real-world decision-making contexts. It also highlights the trade-offs and data-collection considerations necessary to achieve intuitively fair outcomes under VoI-fairness and points to future directions for deriving data-driven VoI-fair utilities.

Abstract

Many fairness criteria constrain the policy or choice of predictors, which can have unwanted consequences, in particular, when optimizing the policy under such constraints. Here, we advocate to instead focus on the utility function the policy is optimizing for. We define value of information fairness and propose to not use utility functions that violate this criterion. This principle suggests to modify these utility functions such that they satisfy value of information fairness. We describe how this can be done and discuss consequences for the corresponding optimal policies. We apply our framework to thought experiments and the COMPAS data. Focussing on the utility function provides better answers than existing fairness notions: We are not aware of any intuitively fair policy that is disallowed by value of information fairness, and when we find that value of information fairness recommends an intuitively unfair policy, no existing fairness notion finds an intuitively fair policy.

Unfair Utilities and First Steps Towards Improving Them

TL;DR

The paper reframes algorithmic fairness by enforcing a fairness criterion on the utility function via value-of-information fairness (VoI-fairness), rather than constraining predictive policies. It defines VoI and -VoI-fairness, provides graphical and structural criteria, and shows how to modify unfair utilities into VoI-fair ones that disincentivize inferring protected attributes. Through synthetic examples, college-admission simulations, and COMPAS data, it demonstrates practical procedures for constructing corresponding VoI-fair utilities and policies, including rejection-sampling-based estimation of the fair utility and its corresponding policy. The work argues that this utility-centric approach can avoid several shortcomings of existing notions like counterfactual fairness and equalized odds, while remaining computationally tractable and adaptable to real-world decision-making contexts. It also highlights the trade-offs and data-collection considerations necessary to achieve intuitively fair outcomes under VoI-fairness and points to future directions for deriving data-driven VoI-fair utilities.

Abstract

Many fairness criteria constrain the policy or choice of predictors, which can have unwanted consequences, in particular, when optimizing the policy under such constraints. Here, we advocate to instead focus on the utility function the policy is optimizing for. We define value of information fairness and propose to not use utility functions that violate this criterion. This principle suggests to modify these utility functions such that they satisfy value of information fairness. We describe how this can be done and discuss consequences for the corresponding optimal policies. We apply our framework to thought experiments and the COMPAS data. Focussing on the utility function provides better answers than existing fairness notions: We are not aware of any intuitively fair policy that is disallowed by value of information fairness, and when we find that value of information fairness recommends an intuitively unfair policy, no existing fairness notion finds an intuitively fair policy.
Paper Structure (49 sections, 3 theorems, 48 equations, 10 figures, 5 tables, 1 algorithm)

This paper contains 49 sections, 3 theorems, 48 equations, 10 figures, 5 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Motivation and methodology
  3. Structure of this work
  4. Setting and Notation
  5. Value of information fairness
  6. Value of information
  7. Value of information fairness
  8. Graphical criteria for value of information fairness
  9. A VoI-fair policy may need to be a non-constant function of S
  10. A VoI-fair policy may be considered intuitively unfair
  11. Improving utility functions
  12. An unfair utility function and a possible improvement
  13. Corresponding VoI-fair utility functions
  14. Relation to existing work
  15. Comparison with counterfactual fairness
  16. ...and 34 more sections

Key Result

Proposition 3.4

propgraphical1A DAG $\mathcal{G}$ over $(\text{\boldmath$X$}, D, U)$, where $U$ is a descendant of $D$ and $U$ has no children, admits VoI for $S\in \text{\boldmath$X$} \backslash \mathbf{DE}^D$ relative to $\text{\boldmath$M$}\subseteq \text{\boldmath$X$} \backslash (\mathbf{DE}^D\cup \{S\})$ if an propgraphical2Here, $\perp_{\mathcal{G}_{\mathbf{PA}^D:=\text{\boldmath$M$}}}$ denotes $d$-separati

Figures (10)

  • Figure 1: The graph contains utility node $U$ and decision node $D$. For making the decision only one feature is available, namely application material. We call this feature a usable decision input and denote it by $\text{\boldmath$O$}^D=\{A\}$. In this made up example, the graph admits value of information for parental leave relative to the essential feature $\text{\boldmath$F$} = \{Q\}$; that is, we could obtain a higher expected utility using both quality of work and parental leave rather than just quality of work (\ref{['def:voi']} and \ref{['prop: graphical']}). If parental leave has VoI relative to $\{Q\}$, we say that $U$ is not $\{Q\}$-VoI-fair (\ref{['def: VoI-fairness']}). \ref{['app: visual']} provides further visual explanation of these concepts.
  • Figure 2: This figure depicts the graph $\mathcal{G}$ induced by background model $\mathcal{C}$ and utility function $\upsilon$ from \ref{['ex: grade']} with $\text{\boldmath$O$}^D=\{\text{Grade}, S\}$. $\mathcal{G}$ does not admit VoI for $S$ relative to $\{\text{Abilities}\}$, so $U$ is $\{\text{Abilities}\}$-VoI-fair, but $\mathcal{G}$ does admit VoI for $S$ relative to $\{\text{Grade}\}$. Indeed, an $\{\text{Abilities}\}$-VoI-fair policy will use $S$ to obtain a better estimate of abilities.
  • Figure 3: Graph of \ref{['ex: hair']}, where $\text{\boldmath$O$}^D=\{\text{Hair length}\}$. If physical strength is an essential feature, a VoI-fair policy will be a policy that tries to infer physical strength based on hair length. Here, it seems impossible to make fair decisions. Even if it may seem repugnant to base decisions on hair length only, it is not clear that it is worse than a constant policy in $\Pi^{\emptyset}$.
  • Figure 4: This figure depicts the graph induced by $\mathcal{C}$ and $\upsilon$ from \ref{['ex: doctor VoI fair']}. The original utility function suggests optimizing for a quantity that contains a human bias, causing the utility function to not be $\{M\}$-VoI-fair. Using the concept of VoI-fairness (\ref{['def: VoI-fairness']}), we can identify this bias and adjust for it.
  • Figure 5: Possible approach for handling decision problems with protected attributes.
  • ...and 5 more figures

Theorems & Definitions (18)

  • Example 1.1: Predicting parental leave at hiring
  • Definition 3.1: Value of information, VoI
  • Definition 3.2: Value of information fairness
  • Definition 3.3: VoI-fair policy
  • Proposition 3.4: Graphical criterion for admitting VoI
  • Proposition 3.5: Graphical criterion for VoI-fairness
  • Corollary 3.6
  • Example 3.7: College admission based on grade and $S$
  • Example 3.8: Unfairness due to unavailability of relevant data
  • Example 4.1: Hiring medical staff
  • ...and 8 more