Let’s say we have a class of 30 kids. Twenty are white, ten are black. Five of the white kids are cut-ups. Five of the black kids are cut-ups. So what that means is that:
50% of the black kids are “criminal”, representing 50% of the problem element.
25% of the white kids are “criminal”, representing 50% of the problem element.
30% of the class is criminal.
As the teacher, you decide that you’re fed up with all these cut-ups. Because the black kids are the biggest source of the problem, you decide to kick them all out of your classroom. Get your black asses out of the classroom, black kids.
So now we’re left with twenty kids. Five of them are cut-ups. Now, only twenty-five percent of the class is the problem element. We can rest easy now.
BUT…
Let’s say in the classroom next door, I have a class of 30 kids. Twenty are white, ten are black. But only two of the black kids are cut-ups. Four of the white kids are cut-ups.
20% of the black kids are “criminal”, representing 30% of the problem element.
20% of the white kids are “criminal”, representing 70% of the problem element.
Overall, 20% of the class is criminal.
You decide to come to my class and kick out the black kids like you did in your classroom. Now we have twenty kids, 20% which is “criminal”. Status quo.
So yes, assuming that black criminals are disproportionately represented (as was the case in the first example) and that the criminals and non-criminals are independent entities*, then eliminating the entire black population will lower the proportion of criminals in the total population. But that diminishment will–heh–diminish as you approach proportional representation.
*This is a huge assumption to make. In the classroom example, you might be kicking out the classes’s biggest law enforcers: the tattle-tellers, the admirable role-models, the teacher’s pets (aren’t they the ones who always get to “take names”?), and the Protectors of the Underdogs (you know, the boy who beats up on the class bully every now and again). These individuals may keep the “problem element” in check. There’s no reason to believe that the “law enforcement element” must always be more evenly distributed than the “problem element.” Kick out the “do-gooders” along with the “bad doers” and who knows might happen to your class? Maybe the proportion of your bad apples will go from 20% to 30%?
Yeah, I’m over analyzing the question a LOT.