So I agree with Gonzo, and here's my creative two cents.

There was an event of some kind (be it a natural disaster or WW3) and most of the worlds population and land masses were wiped out, reducing the entire population to just a couple thousand (or whatever). The survivors began to gather, and over the years were finally able to establish this city. However there was no set form of government, the people need to be ruled, therefore they created the District system, going by (at the time of origin) how much money you had (the more money you had, the less the number). Of course this didn't seem fair to those less fortunate, and therefore the ill/bitter feelings that say District 16 would have against District 3 people began, being handed down generation after generation. It would also explain how the cops were corrupt, they didn't give two shits about the legal system, they just knew that they were living better than those below them.

Sorry, got a bit long-winded there lol