The death penalty fulfills a preventive function, but it is also very clearly a form of revenge. It is an especially severe form of punishment because it is so final. The human life is ended and the executed person is deprived of the opportunity to change, to restore the harm done or compensate for it.
We can more easily avenge an injury than requite a kindness; on this account, because there is less difficulty in getting the better of the wicked than in making one's self equal with the good.
Why seeketh thou revenge, O man! with what purpose is it that thou pursuest it? Thinkest thou to pain thine adversary by it? Know that thou thyself feelest its greatest torments.
I don't think you should support the death penalty to seek revenge. I don't think that's right. I think the reason to support the death penalty is because it saves other people's lives.
Teller contended, not implausibly, that hydrogen bombs keep the peace, or at least prevent thermonuclear war, because the consequences of warfare between nuclear powers are now too dangerous. We haven't had a nuclear war yet, have we? But all such arguments assume that the nuclear-armed nations are and always will be, without exception, rational actors, and that bouts of anger and revenge and madness will never overtake their leaders (or military and secret police officers in charge of nuclear weapons). In the century of Hitler and Stalin, this seems ingenuous.
Therein lies the defect of revenge: it's all in the anticipation; the thing itself is a pain, not a pleasure; at least the pain is the biggest end of it.