What was the benefit of using the lottery system

The benefit of using lottery system was to provide equal socially opportunities to all kids and parents.

Lottery system is also knows as “random allocation” that designates places using a ballot rather than proximity once a school is oversubscribed. This should give all parents an equal chance of success while reducing social selection fueled by wealthy families.

an informal structure in a bureaucracy would be something like so-called "office politics". where there's a formal structure set up for the organization, but then an informal subculture as well that has a way of organizing the bureaucracy further. this can be positive because it sets up an added degree of organization, albeit informal, within the bureaucracy.