It’s far from obvious that the death penalty has a deterrent effect. Some of the data even suggest the possibility that instead of a deterrent effect, capital punishment has a brutalization effect (because it sends out the normative message that violent retaliation is the normal response to ill-treatment and that the sanctity of life is a naive moral ideal). States with high numbers of executions tend to have high levels of violent crime and murder.
Anyway, let’s be generous and admit that there may or may not be a deterrent effect. According to me, as long as this question is open, deterrence can’t be used as a justification for capital punishment. Of course, proponents of capital punishment keep looking for the effect because it would be the only widely acceptable justification of this type of punishment. (I argued here that even if the deterrent effect exists, it doesn’t justify the death penalty because deterrence is inherently immoral).
One of the most silly “findings” I’ve ever seen is here. This “study” claims to show that every execution results in 18 fewer murders. However, the authors failed to note that, if this were true, and the U.S. would execute today all the approx. 3.300 inmates on death row, there would be no more murders in the U.S. (there are between 15.000 and 20.000 homicides in the U.S. annually). That can’t possibly be true. A nice study, I have to say.
(Pointed out to me by this paper).