Student Optimal Stable Matching – AER 2009. Not transparent that they are choosing an arbitrary one to compare to. TTC is justified envy minimal. Here are two possible meanings: So this feels pretty meaningless. Theorem. [In one-to-one markets,] TTC is justified envy minimal in the class of Pareto efficient and strategy-proof mechanisms. Many other mechanisms could satisfy this property, and they could have much less envy than TTC “on average”. There is some value to the empirical statistics. But the theory, I see as fairly meaningless. Theorem 2: with uniformly random preferences, random priority TTC produces less justified envy than RSD. (Equivalent in terms of student outcomes, but not priorities). Table 1: RSD, TTC, and Student Proposing DA are nearly equivalent in New Orleans and Boston in terms of student outcomes, but not in terms of justified envy. (Somewhat surprising that student-proposing DA isn’t meaningfully worse for students – they mention that this is not true in NYC, as shown in prior work. What explains the difference?) Other somewhat interesting finding (mostly from appendix): in Leshno large market limit, TTC has significantly less justified envy than RSD (short cycles persist). In AKL large market limit, TTC is essentially equivalent to RSD in terms of justified envy (this is the message of the new paper). Really comes down to, “how likely are short cycles”? Stop assuming long lists! Either type of large market limit can be useful.
Summary of 5 person TTC paper (not directly relevant to this post)
Separate future post: different types of limits