Fifty-six countries retain death penalty capital punishment, 103 countries have completely abolished it. The U.S. is one of the few advanced countries to retain it Federally and in 31 States. The process for administering the punishment is occasionally brutal – many Citizens terminate their animals’ lives with greater compassion. (In fact, it would be far more humane to authorize Veterinarians, who are more skilled in this field and not bound by a doctor’s hippocratic oath, to administer the death penalty, if it did not raise aesthetic resistance.) Also, the finality of death leaves no remedy if innocence is determined later. On the other hand, vengeance is a valid human emotional expectation, and some Citizens would prefer death over life in prison. There currently appear to be under 40 executions per year. It also appears that the cost of getting, imprisoning, and administering a death penalty is greater than life in prison.
Thus, it appears that there are no clear decision-making criteria other than personal preference to reserve extreme punishment for some classes of crime. The Supreme Court struck down the Death Penalty from 1972 to 1976 when it was reinstated (Furman v. Georgia). Congress is wary about taking up the issue. As of October 1, 2016, there were 2,902 death row inmates in the United States, and 20 were executed in 2016. The number of death row inmates changes daily with new convictions, appellate decisions, sentence commutations, deaths (through execution or otherwise), and exonerations (Wikipedia).
The use of an Advisory Initiative would give the People general guidance on the appropriate action to be taken without trampling State rights.