Suppose that you have evidence of wrongdoing but it is not definitive evidence.  You are only 80% sure.  Suppose that if you were sure you would feel a certain level of moral outrage.  What fraction of that moral outrage should you feel when you are only 80% sure?

Surely it must be less than 100%.  The suspect stands before you and you know that he is either guilty or innocent.  Whatever level of outrage you feel, you are with 20% probability feeling morally outraged at someone who is innocent.

Is it 80%?  Is the level of moral outrage proportional to the probability of guilt?  This would lead to the absurd conclusion that, because we know somebody shot JFK, and we don’t know for sure who it is, and everybody around you is guilty with some probability, you feel a certain level of moral outrage toward everybody you meet.

Fortunately, there is a theory of crime and punishment that does not suffer from these paradoxes.  Punishment for suspicion of a crime is designed to create incentives for good behavior and this implies a precise relationship between the level of suspicion and the level of punishment.  And the relationship usually clashes with that of moral outrage.

For example, you can be certain that a crime was not committed and still insist on punishing.  For example, the best way to deter doping in sports might be to set such drastic penalties that nobody will ever use performance-enhancing drugs.  To enforce this we must use drug tests.  And when a drug test comes up positive, we know it was a false positive because we know that the penalty is so high that nobody would be doping.  But we must punish anyway because this is our deterrent.

The opposite is possible as well.  You can be quite certain that a crime was committed and let the suspect go free with no penalty.  For example, suppose there are two kinds of evidence suggestive of a crime.  There might be circumstantial evidence and there might be an eye-witness.  It may be an optimal deterrent to punish only in the event of an eye-witness and never when there is only circumstantial evidence, even very strong circumstantial evidence.  This would minimize type II errors (convicting the innocent in the event of circumstantial evidence) and would still be a sufficient deterrent if the penalty in the event of an eye-witness could be set high enough.

Ok, so we can escape the paradoxes of moral outrage.  Now that we have that settled, what I am trying to figure out is how these ideas extend so that I can escape the paradoxes of statistical voyeurism.