Here's a recent paper that (among other things) considers using the top trading cycles algorithm for matching refugees to sponsors (under a special program for Ukraine), to satisfy the location preferences of refugees.
Optimizing Sponsored Humanitarian Parole by Fatemeh Farajzadeh, Ryan B. Killea, Alexander Teytelboym, Andrew C. Trapp, working paper, 2023
Abstract: The United States has introduced a special humanitarian parole process for Ukrainian citizens in response to Russia’s 2022 invasion of Ukraine. To qualify for parole, Ukrainian applicants must have a sponsor in the United States. In collaboration with HIAS, a refugee resettlement agency involved in the parole process, we deployed RUTH (Refugees Uniting Through HIAS), a novel algorithmic matching system that is driven by the relocation preferences of refugees and the priorities of US sponsors. RUTH adapts Thakral [2016] Multiple-Waitlist Procedure (MWP) that combines the main First-In/First-Out (FIFO) queue with location specific FIFO queues in order to effectively manage the preferences of refugees and the supply of community sponsors. In addition to refugee preferences and sponsor priorities, RUTH incorporates various feasibility considerations such as community capacity, religious, and medical needs. The adapted mechanism is envy-free, efficient and strategy-proof for refugees. Our analysis reveals that refugee preferences over locations are diverse, even controlling for observables, by demonstrating the difficulty of solving a much simpler problem than modeling preferences directly from observables. We use our data for two counterfactual simulations. First, we consider the effects of increased waiting times for refugees on the quality of their matches. We find that with a periodic Top Trading Cycles algorithm, increasing period length from 24 days to 80 days, improves average rank of a refugee’s match from 3.20 to 2.44. On the other hand, using the available preference data RUTH achieved an average rank of 4.07 with a waiting time of 20 days. Second, we estimate the arrival rates of sponsors in each location that would be consistent with a long-run steady state. We find that more desirable locations (in terms of refugee preferences) require the highest arrival rates suggesting that preferences might be a useful indicator for investments in sponsorship capacity. Our study highlights the potential for preference-based algorithms such as RUTH to improve the efficiency and fairness of other rapidly-deployed humanitarian parole processes.
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