Learning Classifiers That Induce Markets

When learning is used to inform decisions about humans, such as for loans, hiring, or admissions, this can incentivize users to strategically modify their features, at a cost, to obtain positive predictions. The common assumption is that the function governing costs is exogenous, fixed, and predetermined. We challenge this assumption, and assert that costs emerge as a result of deploying a classifier. Our idea is simple: when users seek positive predictions, this creates demand for important features; and if features are available for purchase, then a market will form, and competition will give rise to prices. We extend the strategic classification framework to support this notion, and study learning in a setting where a classifier can induce a market for features. We present an analysis of the learning task, devise an algorithm for computing market prices, propose a differentiable learning framework, and conduct experiments to explore our novel setting and approach.

Learning is increasingly being used to inform decisions about people—such as loan approval, hiring, or university admissions. This makes people more likely to modify their profile or update their application in a way which they believe will improve outcomes for them. A key point is that such changes are typically costly, and people will invest the time, effort, and money only if doing so is cost-effective for them. So far the assumption has been that these costs are fixed, predetermined, and known to the designer of the learning algorithm. We challenge this view: rather than assuming costs simply "exist", we argue that they arise as a result of how the system makes decisions about individuals. When this holds, the choice of decision rule can determine costs; in other words, it will create a market. One example is university admissions: if the importance of SAT scores in the decision rule changes (say relative to GPA scores), then this can impact the price of prep courses and private tutoring. Our paper studies learning in a setting where learned decision rules give rise to markets for the attributes that the decision rule uses. We expect prices to be high for attributes that are important, and low for those that are not. This gives the algorithm flexibility in trading-off performance and market behavior. We study such market behavior and how it interacts with learning. We also propose an algorithm for learning in a way that anticipates market formation, and demonstrate our approach on real data with simulated behavior.