Vermont Abduction Case

My wife shared this story with me last night. I can't imagine what the friends and family are suffering through right now. If the charges brought against the uncle and step-father are true, I can only hope that the death penalty will be brought against those involved. As Mankiw quipped the other day, whether capital punishment is a viable deterrent is still empirically up in the air. But it does deal with the recidivism problem. Since the girl was presumably murdered, the recent Supreme Court ruling disallowing capital punishment to be used in child rape cases isn't relevant.

Which brings me to a separate observation. David Friedman points out in Law's Order the danger in prescribing the death penalty for child-rape, or rape of any kind for that matter. With a flat punishment penalty for both murder and rape, a rapist faces an incentive to murder the victim after the rape is finished. The calculus seems straightforward. The marginal cost of keeping the victim alive is equal to probability of conviction (due to her role as forensic evidence in his apprehension later) multiplied by his own subjective valuation of his presently discounted life, since he'll die from the death penalty if he's captured. The marginal cost of murdering her is the probability of conviction multiplied by his own subjective valuation of his presently discounted life. Presumably, the probability of conviction is lower if the victim is dead than alive, and so rationally he is inclined to murder the victim after the rape is completed so as to minimize the probability of apprehension.

But with an escalating fine wherein rape is fined lower than murder, we increase the probability of the victim surviving the ordeal. Unless I'm missing something unique about child-rape, my intuition is that banning the use of capital punishment for child rapists will increase the probability of a child surviving a rape. But, it may also increase the probability of a child being raped at all, if in fact it takes something as severe as the death penalty to deter the marginal offender in the first place. But that is an empirical question ultimately, as what I have heard about pedophilia is that it is a criminal pathology that centers around a propensity for violence, selfishness, and extremely myopic preferences. That does not sound to me like the kind of person who will be realistically considering the price effects due to capital punishment, but again, I may be wrong. We would need to determine which is more important to us to know how to answer this. More child rapes with a higher proportion surviving, or fewer child rapes but with a lower proportion surviving. I don't know the answer to this, and such questions feel almost impossible to answer.