And every single student who want to go to the public school in Tribecca have to have an address there to be zoned for it. If you want to talk about selection bias thats your case not a lottery.

Plenty of kids in Harlem goes to Success Academy. Most of the kids in Williamsburg comes from fairly low-income families. That was the very premise of the school and why it's popular.

Watch the documentary The Lottery on Netflix it's quite illuminating.