  Resettlement agencies have started to adopt data-driven algorithmic matching
to match refugees to locations using employment rate as a measure of utility.
Given a pool of refugees, data-driven algorithmic matching utilizes a
classifier to predict the probability that each refugee would find employment
at any given location. Then, it uses the predicted probabilities to estimate
the expected utility of all possible placement decisions. Finally, it finds the
placement decisions that maximize the predicted utility by solving a maximum
weight bipartite matching problem. In this work, we argue that, using existing
solutions, there may be pools of refugees for which data-driven algorithmic
matching is (counterfactually) harmful -- it would have achieved lower utility
than a given default policy used in the past, had it been used. Then, we
develop a post-processing algorithm that, given placement decisions made by a
default policy on a pool of refugees and their employment outcomes, solves an
inverse~matching problem to minimally modify the predictions made by a given
classifier. Under these modified predictions, the optimal matching policy that
maximizes predicted utility on the pool is guaranteed to be not harmful.
Further, we introduce a Transformer model that, given placement decisions made
by a default policy on multiple pools of refugees and their employment
outcomes, learns to modify the predictions made by a classifier so that the
optimal matching policy that maximizes predicted utility under the modified
predictions on an unseen pool of refugees is less likely to be harmful than
under the original predictions. Experiments on simulated resettlement processes
using synthetic refugee data created from a variety of publicly available data
suggest that our methodology may be effective in making algorithmic placement
decisions that are less likely to be harmful than existing solutions.
