The Disparate Effects of Partial Information in Bayesian Strategic Learning

We study how partial information about scoring rules affects fairness in strategic learning settings. In strategic learning, a learner deploys a scoring rule, and agents respond strategically by modifying their features -- at some cost -- to improve their outcomes. However, in our work, agents do not observe the scoring rule directly; instead, they receive a noisy signal of said rule. We consider two different agent models: (i) naive agents, who take the noisy signal at face value, and (ii) Bayesian agents, who update a prior belief based on the signal. Our goal is to understand how disparities in outcomes arise between groups that differ in their costs of feature modification, and how these disparities vary with the level of transparency of the learner's rule. For naive agents, we show that utility disparities can grow unboundedly with noise, and that the group with lower costs can, perhaps counter-intuitively, be disproportionately harmed under limited transparency. In contrast, for Bayesian agents, disparities remain bounded. We provide a full characterization of disparities across groups as a function of the level of transparency and show that they can vary non-monotonically with noise; in particular, disparities are often minimized at intermediate levels of transparency. Finally, we extend our analysis to settings where groups differ not only in cost, but also in prior beliefs, and study how this asymmetry influences fairness.