The 5 Branches of Philosophy
Initiation Of Force
Necessity Of Government
Rule Of Law
Separation of Powers
Checks and Balances
Right To Bear Arms
Trial By Jury
Financing A Government
The Death Penalty
There are two aspects of the question: Should the state have a death penalty? The first is ethical: "Is it moral to execute guilty criminals?" The second is epistemological: "What should be the burden of proof for capital cases?" In order to support the Death Penalty, it must be moral to execute criminals and the burden of proof must specified and always met.
Morality of Executions
Once a man has initiated force against an innocent person, he has in effect declared that he does not live by the principle of individual rights. He does not wish to live among men as a rational being, but as a predator, to the detriment and destruction of all those around. Rights stem from man's nature as a rational being, and a man living irrationally has no rights. It is not only prudent for a society to destroy such a harmful animal, but it is an act of justice: treating a person according to how they act.
There is a concept in justice called proportionality which states basically that the reaction should fit the action, (the punishment should fit the crime or the reward should fit the act.) The justification for proportionality is outside the scope of this article, but it's worth noting that without proportionality, death would be an appropriate punishment for all who initiate force. Taking proportionality into account, the premeditated murder of an innocent by a criminal justly deserves the premeditated execution by the state of that criminal. A lack justice would encourage citizens to take justice into their own hands.
Necessary Burden of Proof - The Epistemological Argument
The above moral justification for the death penalty in certain situations assumes absolute certainty regarding the facts. The problem is that in real-life, despite overwhelming evidence, juries sometimes make mistakes. The punishment of a criminal is prudence, but the punishment of an innocent is a tragedy. How much are we willing to risk the life of an innocent for the punishment of a criminal? If an innocent man is unjustly imprisoned, he can be set free later when new evidence is discovered, but there is no recovering from an incorrect execution.
It is tempting to side with either the moral argument, or the epistemological argument. Both have an appeal. It is right to punish criminals, and in some cases the death penalty is appropriate. If the court system isn't capable of doing this, people will take the burden on themselves. They will make sure justice is dealt. This undermines the objective nature of the courts. On the other hand, to kill even a single innocent man is reprehensible. Most people try to pick one argument, while neglecting the other.
This is untenable, though, and will lead to unintended consequences. If there is no death penalty via the courts, people will take justice into their own hands. This has the disadvantage of eliminating an objective standard of proof. The likely result will be that more innocent people will die than if there was confidence in the courts.
On the other hand, if there is a death penalty, and people believe it is being used too loosely, they will avoid convicting people, or they will obstruct justice. The courts will seem to be an arbitrary threat, and the people will fight against them in several ways. Already we see calls for jury nullification in certain cases believed to have a racial bias. This would have still further consequences, though. As people begin to understand that certain criminals will be released due to their race, they will be less likely to trust the courts, having similar problems as officially rejecting the death penalty.
The answer isn't obvious, which is why so many people disagree on the topic. Ultimately, the courts must be trusted to enact justice. This means no artificial restrictions, such as the prevention of the death penalty. If the restrictions are too high, confidence in the courts will be lost, undermining their purpose. In cases of the death penalty, the burden of proof must be higher than normal though. It must be clear that death is final. The risk of killing an innocent man must be weighed heavily. The burden of proof is higher, but it must be objective and possible. A burden that can't be met is the same as eliminating the death penalty.