Equitable stable matchings under modular assessment

An important feature of matching markets is that there typically exist many stable matchings. These matchings have a remarkable orderliness property in two-sided markets. They form a lattice according to the group preferences of one side that is opposite to the group preferences of the other side. The two extremal matchings, optimal for one side pessimal for the other, bear extreme inequity. Nonetheless, research and applications in the area mostly involved the extremal matchings and much less so the "middle"of the stable matchings where inequity may be resolved. This is partly because the optimal stable matching has proved very useful in applications on account of its algorithmic properties. It is also because the "middle"has proved challenging definitionally as well as computationally