Answer:
The #1 argument in favor of the death penalty is Retribution. In Debating the Death Penalty, Why the Death Penalty is Morally Permissible, by Louis P. Pojman goes into great detail in arguing for it and provides some other pro-arguments. He makes the distinction between retribution and revenge, revenge being emotional and having no upward limit. If you go to Wikipedia and search Capital Punishment Debate, there are sections on the arguments for the death penalty, and specifically a Retribution section with references to several articles you could read to get more in depth information.