Collective Reasoning in Performative Prediction
Haiqing Zhu, Tijana Zrnic, Celestine Mendler-Dünner
Modern predictive models can learn complex statistical patterns and personalize predictions to individual users. While minimizing a notion of risk for the learner, the consequences of these predictions might not always equally align with the interests of the users they concern.As a way to contest predictive systems, users might act strategically in order to achieve favorable outcomes. While past work has studied strategic user behavior in learning systems, the focus has largely been on individual strategies: users respond to the system without consideration of the other users' utilities and actions.In this paper, we study the consequences of collective reasoning in predictive systems. First, we formalize level-$k$ thinking, a concept from behavioral economics, and analyze how more sophisticated levels of strategic thought influence learning dynamics and equilibrium outcomes. Then, by contrasting the resulting equilibria with those achievable through coordinated actions we characterize the benefits and trade-offs of collective reasoning. A key quantity in our analysis is a new notion of alignment between the learner's and the population's utilities. Together with extensive simulations, our novel concepts and results, bridge between strategic classification and collective action, two widely studied, but so far disjoint subfields of machine learning.