Speaking of school-systems.....
Incorporating the best of both the capitalist and public worlds, schools should run as such:
Each school gets x amount of dollars per student. Students may go to whichever school they would like to within their designated district. Therefore, if school A is better than school B, more students will go to school A. With more students at school A, school A gets more money, allowing them to even further educate its students. Using this, we will be able to insert competition into a public facility.