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Another way to look at it is from the perspective of efficiency:

- What type of punishment hinders the convict to commit the crime again? - What type of punishment deters criminals of committing this crime?

Death penalty certainly meets the first criterion, but cost to society for type I errors are disproportionate. After having spent 20 years behind bars with proper preparation for re-entry, convicts are different people and can function as normal citizens. Think of your 20-year old self and the person you are at 40.

Second, threat of prison or worse does not deter murder, quite unlike tax fraud where threat of prison works well as deterrent.

That said, death penalty merely speaks to our archaic desire to take revenge, but is neither rational nor does it meet the standards of societies that commit themselves to humanist ideals.