Performative Validity of Recourse Explanations

TL;DR

The paper investigates how recourse explanations can paradoxically invalidate themselves through performative effects: when applicants act on recommendations, the data distribution and decision boundary shift after model retraining. It formalizes performative recourse using causal models, defines performative validity, and identifies two mechanisms that can cause invalidity—actions influenced by effect variables and actions that intervene on effects. The authors compare three recourse methods (CE, CR, ICR) and show theoretically and empirically that CE and CR often lose validity while ICR remains robust across a broad class of data-generating processes. The results suggest practitioners should favor recourse that acts only on causal variables to ensure stable, valid guidance for applicants and to avoid costly, ineffective interventions.

Abstract

When applicants get rejected by an algorithmic decision system, recourse explanations provide actionable suggestions for how to change their input features to get a positive evaluation. A crucial yet overlooked phenomenon is that recourse explanations are performative: When many applicants act according to their recommendations, their collective behavior may change statistical regularities in the data and, once the model is refitted, also the decision boundary. Consequently, the recourse algorithm may render its own recommendations invalid, such that applicants who make the effort of implementing their recommendations may be rejected again when they reapply. In this work, we formally characterize the conditions under which recourse explanations remain valid under performativity. A key finding is that recourse actions may become invalid if they are influenced by or if they intervene on non-causal variables. Based on our analysis, we caution against the use of standard counterfactual explanations and causal recourse methods, and instead advocate for recourse methods that recommend actions exclusively on causal variables.

Figures (3)

• Figure 1: Simplified causal graph of features used to predict if applicants should be invited for a software engineering (SE) job interview.
• Figure 2: Causal graphs. In each graph, we color open paths between action $\mathcolor{actioncolor}{A}$ and post-recourse target $\mathcolor{targetvarcolor}{Y^p}$ given post-recourse observations $X^p$ via the incoming and outgoing edges, and highlight the decisive edges $X_E \rightarrow \mathcolor{actioncolor}{A}$ and $\mathcolor{actioncolor}{A} \rightarrow X_E^p$ using thicker arrows. (a): We illustrate the relationships between the target $Y$ and its causes $X_C$, its direct effects $X_E$, and its spouses $X_S$, as well as their relationships with their post-recourse counterparts $\mathcolor{targetvarcolor}{Y^p}, X^p$. In general, the pre- and post-recourse variables are connected both via the action $\mathcolor{actioncolor}{A}$ and the unobserved causal influences $U, U^p$ (Section \ref{['subsec:causal-model-shift']}), and there are open paths via $X_E \rightarrow \mathcolor{actioncolor}{A}$ and $\mathcolor{actioncolor}{A} \rightarrow X_E^p$ (Theorem \ref{['thm:two-sources']}). (b): The causal graph for Example \ref{['ex:interventions-depend-on-effects-problematic']}, where $X_C=D$ indicates having a master's degree and $X_E=G$ indicates the GitHub activity. Since only interventions on causes are suggested, only the path via $G \rightarrow \mathcolor{actioncolor}{A}$ is open. (c): The causal graph for Example \ref{['ex:interventions-effects-problematic']}, where $X_C=R$ is the general risk score and $X_E=M$ indicates the mood. Since the unobserved causal influences are resampled, only the path via $\mathcolor{actioncolor}{A} \rightarrow M^p$ is open.
• Figure 3: Experimental results.(Q1, left): The pointwise differences between pre- and post-recourse conditional distribution aggregated using the mean, the lines indicate the range. All values are averages over $10$ runs. (Q2, right): The difference in acceptance rate (refit minus original), average ($\bullet$) and standard deviation (lines) over $10$ runs. While CE and CR lead to unfavorable shifts and performative invalidity, ICR is performatively valid in all settings.

Theorems & Definitions (32)

• Definition 4.1: Performative Validity
• Proposition 5.0: Uninformative actions imply performative validity
• Theorem 5.1: Two Sources of Invalidity
• proof
• Example 5.1: Interventions that are influenced by effects may cause performative invalidity
• Proposition 5.1: Assumption \ref{['asmp:noise']} restores performative validity
• Theorem 5.2: Assumption \ref{['asmp:func-form']} restores performative validity.
• Example 5.2: Interventions on effects cause performative invalidity
• Corollary 5.2
• Definition A.1: $d$-separation