Proponents of capital punishment (like myself) usually argue their case according to the ideals of justice. They often include in their presentation also the critical need of a society to uphold the sanctity of human life; i.e., if murdering an innocent doesn't deserve the ultimate punishment, what signal does that send to the whole culture about the value of a human being?
Related to this second argument is today's Dennis Prager column which includes yet another persuasive element in the case for capital punishment -- sheer pragmatics.