The death penalty was declared unconstitutional in the landmark 1972 Furman v. Georgia case largely because of how arbitrary it was. You could commit a murder in one place and get a maximum of life in prison, while in other places the exact same crime would have you be put to death (of course, it was later declared constitutional again after nothing had changed, but we decided we missed killing people).
Looking back at the past five years, it seems that death sentences are just as arbitrary as ever. In fact, over that span, a mere 10% of counties in the entire nation have been responsible for 100% of death sentences meted out.
Seeing it graphically only highlights the disparity:
Regardless of how you feel about capital punishment, you've got to be hard pressed to find a way this type of clearly unequal justice does not fall under the label of arbitrary...