Is this thing good for state and social stability?

Although it should be used extremely sparingly, death should exist as a penalty for some crimes in some circumstances.

Death is already a punishment the state can use on you, in the sense that it has the power and, if it gives itself it, the right to employ lethal force against you. When we speak of the death penalty, the only thing we are really talking about is one of many circumstances in which an authority exercises its right to kill you.

If you are a threat the state deems unacceptable to it or you present an imminent threat of killing others (hot pursuit), the authority in the land gives himself the option to kill you. So, why is this power not extended to other situations where the ruling authority might require your death for the safety of innumerable others and the protection of society? The answer is that liberal absolutes dictate the law, in the case of the UK, and these absolutes cannot adjust to changes in society and the behaviour of the citizen.

Capital punishment as a moderating influence

The killing of a defenceless captive by an authority, an execution, may be justifiable if the alternative is known to involve a greater degree of unrest, suffering and death. Some crimes are so severe, for example, that not executing the perpetrators encourages acts of vigilantism that cannot be contained.

Take, for example, those who are found guilty of sexual assaults on children. The perceived inadequacy of the punishment for that offence has given rise to vigilantes who actively hunt such offenders, as well as legions who, with modern social media, may be prepared to falsely accuse and shame individuals who are merely suspected. Happening because of the perceived inadequacy of the legal authorities, this can push the falsely accused into undue distress or even suicide in larger numbers than the potential executions that would be required to calm the situation. As such, failure to kill the perpetrator presents a continuous risk to the lives of others even if the perpetrator is detained. In contrast, a state in which those guilty of this crime are executed would not experience as much vigilantism and distress, and things could be handled always in a more orderly way.

On the inevitable innocent victims

One could argue that an innocent suspect's death may also placate society and avert deeper tragedy under some circumstances, and that my argument above is therefore absurd because it would encourage random executions when the state feels they will placate the crowd. The killing of innocents is yet another thing destabilising to the social order, and therefore bad for the same reason as leaving alive those who have been confirmed to have monstrous guilt.

Even when applied sparingly, the death penalty will sometimes take innocent lives, but it can be used in such a way that it results in fewer innocent lost lives than the chaos of never applying it. It is likely that the number of executions that are truly necessary for the reasons outlined above is extremely low, but capital punishment should still be available to a ruling power in the same way that lethal force is to be employed in situations of immediate peril.