Performativity and Prospective Fairness

TL;DR

This work reframes algorithmic fairness as a policy problem by introducing prospective fairness, which asks whether deploying an algorithmically informed policy worsens context-relevant inequalities. It argues that static, training-time fairness criteria can be self-undermining when a policy changes decision-making and outcomes, and formalizes a method to predict post-deployment inequality from pre-deployment data given a specified decision rule. Under assumptions of Consistency, Unconfoundedness, No Unprecedented Decisions, Stable CATE, and No Feedback, the authors derive an identifiable expression for $P_{\text{post}}(Y=y|A=a)$ that combines pre-deployment outcome and covariate distributions with post-deployment decision rules. A toy model of a Public Employment Service demonstrates that different risk-based allocation policies can either ameliorate or exacerbate the gender reemployment gap, illustrating the practical value and risks of prospective fairness for policy design. The paper calls for further work to relax assumptions, incorporate dynamic causal modelling, and apply the framework to real administrative data to guide fair and effective labor-market interventions.

Abstract

Deploying an algorithmically informed policy is a significant intervention in the structure of society. As is increasingly acknowledged, predictive algorithms have performative effects: using them can shift the distribution of social outcomes away from the one on which the algorithms were trained. Algorithmic fairness research is usually motivated by the worry that these performative effects will exacerbate the structural inequalities that gave rise to the training data. However, standard retrospective fairness methodologies are ill-suited to predict these effects. They impose static fairness constraints that hold after the predictive algorithm is trained, but before it is deployed and, therefore, before performative effects have had a chance to kick in. However, satisfying static fairness criteria after training is not sufficient to avoid exacerbating inequality after deployment. Addressing the fundamental worry that motivates algorithmic fairness requires explicitly comparing the change in relevant structural inequalities before and after deployment. We propose a prospective methodology for estimating this post-deployment change from pre-deployment data and knowledge about the algorithmic policy. That requires a strategy for distinguishing between, and accounting for, different kinds of performative effects. In this paper, we focus on the algorithmic effect on the causally downstream outcome variable. Throughout, we are guided by an application from public administration: the use of algorithms to (1) predict who among the recently unemployed will stay unemployed for the long term and (2) targeting them with labor market programs. We illustrate our proposal by showing how to predict whether such policies will exacerbate gender inequalities in the labor market.

Figures (2)

• Figure 1: The left hand side shows the pre-deployment causal graph $G_{\text{pre}}$ inducing a joint probability distribution $P_{\text{pre}}$ over sensitive attributes $A$, features $X$, risk score $R$, decision $D$, and outcome variable $Y$. The risk score $R$ is the output of a learned function from $A$ and $X$. Since this graph represents the situation after training, but before deployment, there is no arrow from the risk score $R$ to the decision $D$. Retrospective fairness formulates constraints $\varphi(G_{\text{pre}}, P_{\text{pre}}, M)$ on the pre-deployment arrangement alone. The right-hand side represents the situation after the algorithmically informed policy has been deployed, with predictions $R$ now affecting decisions $D$. Prospective fairness requires comparing the consequences of intervening on the structure of $G_{\text{pre}}$ and moving to $G_{\text{post}}$. In other words, comparing $\varphi(G_{\text{pre}}, P_{\text{pre}}, M)$ with $\varphi(G_{\text{post}}, P_{\text{post}}, M)$.
• Figure 2: Data and Figure from the German PES arbeitsmarkt2022statistik. The risk of entering unemployment is estimated as the number of newly registered unemployed divided by the number of employees subject to social insurance contributions. The exit probability from unemployment is estimated as the number of registered unemployed who find a job in the primary labor market relative to the number of registered unemployed. Both time series are running annual averages from December 2012 to December 2022.

Theorems & Definitions (2)

• Theorem 1
• proof : Proof of Theorem $1$