Dynamic Envy-Free Permanency in Child Welfare Systems [link]
Abstract: Caseworkers in foster care systems seek to place waiting children in the most suitable homes. Furthermore, social work guidelines prioritize heterogeneous attributes of children and homes when deliberating placements. We use insights from market design and dynamic matching to characterize a class of dynamically envy-free mechanisms that incentivize expedient placements when children and homes arrive to the market over time and homes may accept or decline placements. The mechanisms have robustness against justified envy and costly patience. We analyze strategic incentives and efficiency properties of dynamic envy-freeness. Finally, we conduct empirical simulations that affirm that our mechanisms drastically increase placements and reduce waiting costs while maintaining robustness to prediction error versus a naive mechanism that always sequentially runs Deferred Acceptance. Practitioners can implement our mechanisms through assigning priority to child-home matches or through existing match recommendation systems.
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.