Well... it actually is a bit complicated. I think what you’ve said regarding low income groups perfect illustrates the confusion between probability and prejudice. The probability than a low income individual is a criminal is much higher than a wealthy one. Prejudice, however, would be disallowing poor people access to public places because they are more likely to be a mugger. It is also fair to say that correlation is not causation; meaning that it may be that low income leads to crime, or that crime leads to low income, or that neither condition leads to the other. Low income and crime, however, do overlap considerably.
As far as I’m concerned, public policy should be governed by statistics and probabilities. Meaning, people respond to the incentives they understand. Harsh penalties for crimes absolutely deter criminal behavior, and public policy should reflect that. On the other hand, people will [nearly] always act according to their best interests; but those can be hard to predict for those outside of the situation. For example how many people here, regardless of the penalty, would steal food to keep their children alive? I’m willing to bet nearly anyone. On the other hand, if stealing a quad meant 20 yrs in jail it’s unlikely anyone would risk it, especially since, given the potential cost (20years in jail) you would actually be more likely to be caught.
My point is this; the conservative platform of harsh penalties for crime absolutely are based on real statistics and incentives. They are often implemented badly, but the thinking behind them is sound.