Capital punishment is usually defended on the basis of a theory of deterrence or retribution, but another common argument is incapacitation: killing criminals guarantees that they cannot commit further crimes. It’s likely that this argument plays an important role in many decisions to impose capital punishment, since members of juries may fear, mistakenly, that life imprisonment without parole actually means something like “on average 10 years in prison” (see here).
The obvious counter-argument is that life imprisonment, when it really means “life”, is equally incapacitating. True, say the proponents of capital punishment, but criminals may kill when in prison. In particular, they may kill fellow inmates. OK, so let’s do a thought experiment. Imagine that we don’t use the death penalty for murder, but incarcerate murderers for life, together with only fellow murderers. The only killing they can do is of their fellow incarcerated murderers.
Would that kind of killing be objectionable to proponents of capital punishment? I think it shouldn’t be, since the victims of this kind of killing would also have been killed under a regime of capital punishment. Maybe opponents would object that this system doesn’t treat all murderers the same: some get killed, others not. However, I fail to see what difference it makes to a murderer if she is killed by fellow inmates rather than by the state, or if she is killed while others aren’t. She’ll be dead, and in no position to complain about others being still alive. (And don’t tell me murder by the state is preferable because it’s more “humane”). Moreover, our existing regimes of capital punishment don’t manage to kill all murderers either. And finally, non-murderers can also kill while in prison. Should we execute them preemptively?
For opponents of capital punishment, it does make a huge difference whether murderers are killed by the state or by their colleagues: murder by the state means the instrumentalization of human beings, whereas murders between inmates are regrettable and to be avoided, but not more or less than murders in general.
More on capital punishment here.