Typically, we do not look at the death penalty as a balance between the rights of society and the political system. It is more common to look at it as a balance between the rights of society and those of the individual.
Society (defined as all the people living in a country) has a right to live and to be safe from criminal acts. The death penalty can be seen as supporting this right. This is a valid argument if we believe that the death penalty deters and/or prevents murders. In this view, the death penalty upholds the rights of society by making it less likely that people will be murdered.
The political system, however, does not really have interests of its own. It only exists to reflect the will of the people. Because of this, we see that politicians in the US tend to support the death penalty. We do not have a situation where society wants the death penalty while the government resists or vice versa. Therefore, there does not seem to be a need to balance society against the political system when considering the death penalty.
By contrast, there may well be a need to balance society against individual rights. The individual murderer who is sentence to death is not really helped by the death penalty. He would be better served by a system that would rehabilitate him, if possible. Therefore, the death penalty is more of a balance between individual rights and the needs of society.