Libertarian perspectives on capital punishment
Most libertarians believe that the capital punishment (death penalty) is an extreme exertion of state power and is of little use in a free society, while it is of great use to a tyrannical government. Proponents of capital punishment believe that such punishment may be justified as a deterrent to particularly atrocious crimes (although it is the case in the United States that states with the death penalty have higher murder rates than ones which don't[1]) and as a means of keeping dangerous individuals permanently incapacitated. Furthermore, if people commit crimes, they may sacrifice their rights; if the legal system is legitimate, perhaps capital punishment is justified.
Some libertarians, including anarcho-capitalists, believe that penal justice in general should not exist. On this view, all penalties, including capital punishment, should be abolished. Others that support it, do so on self-defense or retributive justice grounds.
There is also the fundamental problem of the possibility of error, or even outright framing of the accused. To this effect, lack of trust in government to make decisions (including life-and-death decisions) competently or for the best motives may confound the issue.
In any case, to anarcho-capitalists, making judges, police officers, and other law enforcement personnel just as responsible for their acts as any citizen, with no privilege or special right or exemption, will prevent abuse of force in general, and of deadly force in particular. Walter Block went so far as to say, "We have seen that in the libertarian philosophy, the death penalty is justified for those whose crimes rise to a sufficient degree of severity. Surely, there are heads of state whose evil deeds many times eclipse such a level. Thus, it would altogether be justified to end their lives by violence."[2]