TL;DR: students are not allowed to swap because (in the current system) that would enable strategizing. It encourages people to list popular schools rather than their preferred choices for the lottery, and then trade their popular spot for their true preferences afterwards.
The system has been designed to not allow strategizing, as strategy often backfires on the student, as well as it's argued that students from lower class backgrounds make more strategic mistakes.
A nitpick from me on the article though:
> Designing a lottery system to place students at the different schools is not just a mathematical optimization problem. Different design choices can have far-reaching effects. On whether everyone gets equal opportunities, for example.
It absolutely is. It's called game theory. And 'no strategizing' is a criterion you can optimize for.
This has close relations to the well-known stable marriage problem. The seminal paper on both these problems is Gale and Shapley, College Admissions and the Stability of Marriage.
The system has been designed to not allow strategizing, as strategy often backfires on the student, as well as it's argued that students from lower class backgrounds make more strategic mistakes.
A nitpick from me on the article though:
> Designing a lottery system to place students at the different schools is not just a mathematical optimization problem. Different design choices can have far-reaching effects. On whether everyone gets equal opportunities, for example.
It absolutely is. It's called game theory. And 'no strategizing' is a criterion you can optimize for.
This has close relations to the well-known stable marriage problem. The seminal paper on both these problems is Gale and Shapley, College Admissions and the Stability of Marriage.