In large balanced serial-dictatorship markets with independently random preferences, longer preference lists increase every student's probability of being matched to an acceptable school.
We have each of these flows fromπ¦π π toπ¦π+1 π forπ= 0,...,πβ 1and one from π¦πβ1 π toπ₯π
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Longer Lists Yield Better Matchings
In large balanced serial-dictatorship markets with independently random preferences, longer preference lists increase every student's probability of being matched to an acceptable school.