Death Penalty
So we have a discussion asking how many innocents is it okay for the state to execute to keep the guilty from escaping prison and killing innocents. Even phrased that way I believe the answer is none.
The two possible killings are not of the same character. For the state to choose someone to die with the acknowledgment that there is a chance the person is innocent degrades trust in the system of laws that maintains societies (irregardless of whether that system is perfect.) It is bad enough when the populace has the idea that they can be taken off the street and put in jail for crimes they did not commit, but if the risk is elevated to death, the populace begins to consider that an unacceptable personal risk.
If the average citizen considers the risk of being randomly killed by the state to be at all significant, over successive generations trust in and support of law is reduced, the rendering of aid to those charged with enforcing law is also reduced. The police take on an (even more) adversarial role. If/when this occurs it become mores difficult to find and charge those actually guilty of crimes, which will cause more innocents to die.
In an imperfect system there is a juggling of priorities. If there is chance that you are sentencing an innocent man, you must show more mercy than if there was no chance of the person being innocent. To make the punishment of citizens innocent or guilty apparently capricious and irreversible is to invite resistance from the innocent populace.
People will accept some level of danger from lunatics to keep that level of danger from becoming institutionalized into the justice system. You can institutionalize the mercy or deal with the resistance.
–Zafkiel