Abstract
We provide a school choice model where the student priority orders are allowed not to be total. We introduce a class of algorithms each of which derive a student optimal stable matching once we have an initial stable matching. Since there is a method to derive a stable matching, we can derive a student optimal stable matching of this model. Moreover, any student optimal stable matchings that Pareto dominate the starting stable one are shown to be obtained via an algorithm within this class. For the problem of improving efficiency by allowing some priorities to be violated, the algorithms can also be applied, with a weaker assumption on the violations than in the previous study.
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