Let’s say someone is convicted of a crime for which the possible sentences are capital punishment and life in prison without possibility of parole. Under what circumstances does it make sense to execute them?
There’s the theoretical deterrent effect, although to the best of my knowledge reputable research overwhelmingly suggests that capital punishment provides no such deterrent. Executing someone demonstrates a belief that the person is either incapable or unworthy of rehabilitation or even being allowed to provide some value with the remainder of his or her life. It certainly demonstrates virtual certainty of guilt (though this appears to be at odds with the current reality of some portion of death row inmates).
Others? The desire to "send a message" is troubling absent a deterrent effect. Fear of escape or reoffending seems unlikely in the modern U.S. prison system. Preventing a leader from continuing to exert influence over an enemy outside organization is possible; at least in the case of John Gotti it seems like this was foiled, though it’s unclear if it was because of the nature of his incarceration or because his organization was crumbling on its own. Even if someone like Osama bin Laden were captured, it is at least theoretically possible to restrict contact with his allies, but regardless the percentage of death row inmates whose influence would be that powerful is tiny.
What’s left is vengeance, the desire to seek retribution on behalf of the victims and their survivors. It seems so common as to be a cliché, but whenever someone convicted of a horrible crime is spared the death penalty for life imprisonment, a victim’s relative is nearly always quoted as saying something about how unfair it is that the victim is dead but that the perpetrator survives.
If you’re a survivor of a victim, the goal of the retributive sentence is probably not strictly ending the life of the perpetrator, but to maximize the perpetrator’s suffering subject to the 8th Amendment’s highly subjective restrictions. This raises the question of whether a life sentence or a death sentence is a better fit. Differing beliefs about what happens to a person after death — on behalf of both the perpetrator and the victim’s survivors — influences this evaluation. So does a desire for martyrdom or a general feeling about being imprisoned for decades with no hope of release.
Of course, if you believe that it is not society’s role to exact vengeance on behalf of victims, what case is left for capital punishment?