A Dynamic Matching Framework for Faster Child Adoptions [link]
Abstract: Caseworkers in foster care systems match waiting children to adoptive homes. We use dynamic matching market design to characterize a class of mechanisms that incentivize expedient matches that homes can accept or decline. We design mechanisms satisfying fairness and limited strategy-proofness. They also avoid costly patience. Our empirically-based simulations suggest the mechanisms could increase adoptions by at least 25% versus the status quo. A naive dynamic extension of Deferred Acceptance does not attain these benefits. Our mechanisms sidestep direct preference elicitation by predicting preferences, and they are robust to prediction error.
Matching Design with Algorithms and Applications to Foster Care [link]
Abstract: We study the problem of an organization that matches agents to objects where agents have preference rankings over objects and the organization uses algorithms to construct a ranking over objects on behalf of each agent. Our new framework carries the interpretation that the organization and its agents may be misaligned in pursuing some underlying matching goal. We design matching mechanisms that integrate agent decision-making and the algorithm by avoiding matches that are unanimously disagreeable between the two parties. Our mechanisms also satisfy restricted efficiency properties. Subsequently, we prove that no unanimous mechanism is strategy-proof but that ours can be non-obviously manipulable. We generalize our framework to allow for any preference aggregation rules and extend the famed Gibbard-Satterthwaite Theorem to our setting. We apply our framework to place foster children in foster homes to maximize welfare. Using a machine learning model that predicts child welfare in placements and a (planned) novel lab-in-the-field eliciting real caseworkers' preferences, we empirically demonstrate that there are important match-specific welfare gains that our mechanisms extract that are not realized under the status quo.