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In that case I don't see what your objections to the penalty are. 1) we could do the killing humanely if we wanted to (interesting that we don't)
And if we sometimes killed an innocent person it would still be for the good of greater society overall.
We should not use the death penalty because 1) Our system cannot administer it fairly (i.e., those with resources can sometimes, literally, get away with murder), and 2) sometimes the "innocent" are mistakenly executed.
I do not agree that, mistakenly, executing innocent persons promotes the greater good of society.