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It is a deterrent of heinous and violent crimes that could be committed in the future by other citizens (deterrent)
There are some crimes for which the death penalty is the only just punishment (retribution)
What is the purpose of the death penalty?
It costs more to imprison someone for life
The death penalty prevents the perpetrator from committing further violent crimes (a dead murderer can't murder again)
The risk of administering the death penalty unjustly outweighs any potential gain from its administration (poorly administered)