Suppose two students have identical rankings and end up with the same school. If one of them manages to trade (e.g. because they quickly manage to find someone

Suppose two students have identical rankings and end up with the same school. If one of them manages to trade (e.g. because they quickly manage to find someone that wants to trade with them), they have an advantage over the other student who is stuck with their lottery result. This is the unfairness the article talks about (besides the strategizing argument). Perhaps this can be remedied by automatic trading and another lottery, determining the order in which people get to trade, but that still doesn't solve the problem with strategic choices.