> This creates a strictly worse outcome for that school year, since only students who would mutually benefit from a trade would trade, and students who did noth

> This creates a strictly worse outcome for that school year, since only students who would mutually benefit from a trade would trade, and students who did nothing or could not trade would remain unchanged. That's true. My understanding is that they did that for two reasons. The first was that a property of this particular algorithm is that mutually beneficial swaps are only possible if there is a third student placed at a third school who would also prefer one of the two being swapped, but whose school is not desirable, so he doesn't have a choice, which was deemed unfair (I don't know how I feel about this argument). The second was that allowing trades for this school year would encourage strategizing in the following years, which would lead to worse outcomes over time. These two things were addressed when they changed the lottery system once again.