> Your assertion that trade always implies that both parties are better off is just wrong
I have never made such an assertion, I've only said that in this specific instance free trade would have made both parties come out better off (which is indisputable -- both students would then be in their preferred school!), and that the judge's rationalization for forbidding students to swap their lottery results can be extrapolated as an anti-free trade argument.
We can discuss whether free trade always leads to better outcomes if you want, but that is not the point I am making in this thread. But in this instance it clearly does.
On the other hand you never explain WHY you think what I'm saying is wrong. You mentioned local optima, but the exchange pushes the end result towards the global optimum! What does exchange have to be "aware of all the interested parties involved"? If it is consensual and mutually beneficial to the parties involved, why do other parties even matter?
You said my premise doesn't hold, but you never explained why do you think so. I can't accept that just because you say so.
Explain to me what is wrong in this reasoning:
1) We got each other's preferred school;
2) We swap schools;
3) Now two students are happier than they were before; the rest remains the same as they were.
4) Repeat this process for more pairs of students and each time two people will emerge happier than they were before the exchange.
How does that not lead to a better global outcome?