Market Design for Distributional Objectives in (Re)assignment: An Application to Improve the Distribution of Teachers in Schools

Centralized (re)assignment of workers to jobs is increasingly common in public and private sectors. These markets often suffer from distributional problems. To alleviate these, we propose two new strategy-proof (re)assignment mechanisms. While they both improve individual and distributional welfare over the status quo, one achieves two-sided efficiency and the other achieves a novel fairness property. We quantify the performance of these mechanisms in teacher (re)assignment where unequal distribution of experienced teachers in schools is a widespread concern. Using French data, we show that our efficient mechanism reduces the teacher experience gap across regions more effectively than benchmarks, including the current mechanism, while also effectively increasing teacher welfare. As an interesting finding, while our fairness-based mechanism is very effective in reducing teacher experience gap, it prevents the mobility of tenured teachers, which is a detrimental teacher welfare indicator.