If criminals are rational, crime is deterred by large expected punishments, which are the product of the fine or the sentence if convicted and the probability of being caught and convicted. Thus, one can raise the expected value of the punishment by raising either the penalty or the odds of capture and conviction. Is the following argument logical?
"I propose executing one spammer per year. That way, even if we don't catch and convict many, the penalty will have substantial deterrent effect. Because the cost of executing them is much less than the cost of catching them, it is cost effective to increase the punishment rather than the odds of capture and conviction."
Explain your answer taking into account attitudes toward risk.