Incentivizing Desirable Effort Profiles in Strategic Classification: The Role of Causality and Uncertainty

TL;DR

This paper investigates how to incentivize agents to invest effort in desirable features within strategic classification, considering causal feature structures and uncertainty, and provides conditions for optimal effort and classifier design.

Contribution

It introduces a framework analyzing agent effort in strategic classification with causal structures and uncertainty, deriving conditions for desirable behavior and tractability in special cases.

Findings

Agents focus on features favored by the principal under complete information.

Designing classifiers for desirable effort is generally non-convex, but tractable in special cases.

Uncertainty causes agents to prioritize features with higher expected importance and lower variance.

Abstract

We study strategic classification in binary decision-making settings where agents can modify their features in order to improve their classification outcomes. Importantly, our work considers the causal structure across different features, acknowledging that effort in a given feature may affect other features. The main goal of our work is to understand \emph{when and how much agent effort is invested towards desirable features}, and how this is influenced by the deployed classifier, the causal structure of the agent's features, their ability to modify them, and the information available to the agent about the classifier and the feature causal graph. In the complete information case, when agents know the classifier and the causal structure of the problem, we derive conditions ensuring that rational agents focus on features favored by the principal. We show that designing classifiers to induce desirable behavior is generally non-convex, though tractable in special cases. We also extend our analysis to settings where agents have incomplete information about the classifier or the causal graph. While optimal effort selection is again a non-convex problem under general uncertainty, we highlight special cases of partial uncertainty where this selection problem becomes tractable. Our results indicate that uncertainty drives agents to favor features with higher expected importance and lower variance, potentially misaligning with principal preferences. Finally, numerical experiments based on a cardiovascular disease risk study illustrate how to incentivize desirable modifications under uncertainty.