> In 1970 the proportion of Americans behind bars was below one in 400, compared with today’s one in 100. Since then, the voters, alarmed at a surge in violent crime, have demanded fiercer sentences. Politicians have obliged. New laws have removed from judges much of their discretion to set a sentence that takes full account of the circumstances of the offence. Since no politician wants to be tarred as soft on crime, such laws, mandating minimum sentences, are seldom softened. On the contrary, they tend to get harder.
On top of that, you also have an entrenched set of special interests who benefit from the status quo (police unions, prison guard unions, private prisons, etc.), so the pressure on politicians is from two sides.
So how do you "solve" a problem that special interests, along with a sizable majority of the voting population, have no interest whatsoever in solving?
Without a massive culture shift, you don't.
First: since you go to prison after the crime, the inmate population size should be a trailing indicator of the crime rate. More serious crimes affect the prison population for a long period, since their sentences are longer.
Second: take a look at these graphs, and how dramatically they shoot up around 1965:
http://www.wolframalpha.com/input/?i=murder+USA