Long-Term Risks of Risk-Based Allocation

Algorithmic risk predictors are increasingly being used to inform resource allocation in healthcare and other high-stakes domains. Common in many such settings, the public decision maker delegates service provision to private organizations and compensates them according to each individual's predicted cost of service. We show that this common allocation mechanism can fail when organizations engage in \emph{favorable selection}, i.e., strategically choosing individuals whose actual costs are below the payment model predictions. Motivated by health insurance payments in the Medicare Advantage (MA) program, we provide a theoretical framework to study the interaction between a decision maker and a strategically selecting service provider. Our theoretical framework predicts two empirical patterns observed in Medicare Advantage that have become central concerns: enrollment in the private program expands, while government payments rise above the counterfactual cost of direct public provision. Guided by our theoretical framework, we then propose a reformed payment policy that is implementable under the government's data-access constraints. We prove that its equilibria eliminate overpayment while preserving profits for efficient organizations. We validate the framework in synthetic and semi-synthetic experiments that illustrate the advantages of our reformed policy, over the status quo.