Is the death penalty an acceptable punishment? Is it moral? Is it prudential? I will take a pragmatic position, arguing that the death penalty is an instrumental and symbolic act for maintaining order and harmony. Morality, that which appeals to a higher good, is typically codified by societal conventions and expectations. Arguing whether the death penalty is moral would require appealing to what is traditionally acceptable, or asking whether it benefits society in some way. In this case the question of the death penalty is a pragmatic one.
A society based on liberalism is characterized by the mutual collaboration of free and equal individuals working towards certain ends, with the most general end being the growth and flourishing of all of its constituent citizens. This is a feature of life more generally. Laws are created to preserve order and to ensure that this collaboration occurs justly, where liberty and equality are preserved for all. Why do we use the death penalty? This form of punishment is reserved for those who undermine the harmonious order, order that is instantiated to ensure the well-being of society, and is used for punishing the most heinous of crimes, most typically those committed by individuals who murder.
I argue that the death penalty is justifiable on moral and prudential grounds, that the authority established in the formation of the government, in which all citizens tacitly consent to, has ultimate power to exercise its interpretation of the law in order to justify punishments. Speaking broadly, this authority is derived not from its power to exercise rule, but because of the constitutional document which established it and the tacit consent of its citizens to exist under the rule of this document.