The Model Selection Curse

A statistician takes an action on behalf of an agent, based on the agent's self-reported personal data and a sample involving other people. The action that he takes is an estimated function of the agent's report. The estimation procedure involves model selection. We ask the following question: Is truth-telling optimal for the agent given the statistician's procedure? We analyze this question in the context of a simple example that highlights the role of model selection. We suggest that our simple exercise may have implications for the broader issue of human interaction with machine learning algorithms.