I did a similar paper on this subject and here is another point to include if you wish.  

Criminals are punished so that they can be turned around and be re-entered into the community for good cause.(why else punish them other than to make good use of them)  The death penalty does not achieve this goal.  There is much more that could be added to this but I don't want to write the paper for you, just get you some brain storming ideas.