I would argue that the death penalty removes any chance that the individual will murder again, thus providing a benefit to society.
As we all know, even "life without chance of parole" doesn't mean that any more. If they are alive, the likelihood that they will be released gets greater with each passing year. Recividism rates (particularly among violent criminals) are pretty high. Better to execute the murderer than give him a chance to kill again.
Sure, eliminating the criminal has some advantages, but it also cheapens life, which not so obviously seen, is the problem underlying the issue.IMO.
This is the answer that I came up with after much wrestling with the subject.
To some, it may seem too simple.
But answers to complex social problems, usually are, as I have discovered