In certain episodes of Voyager and DS9, we learn about the existence of the New Zealand Penal Settlement on Earth. But at multiple times during DS9, Sisko and others wax on about how Earth is a paradise: no crime, no hunger, no war, no needs unmet, etc. Indeed, several episodes of DS9 are dedicated to exploring how lax the security on Earth is, with a complete absence of personnel that can deal with violence, because they are so used to being in such a paradise.

So why, then, is there a penal colony on a crime-free paradise world?