[jcims]

I would probably qualify (3) with 'in counties that choose to implement it' which would make your model (which I agree with) fit the observations in the abstract.

I wouldn't think most counties decide to implement the death penalty based on number or types of crime (aside from 100 year outliers) as 'life in prison without possibility of parole' is also satisfactory in most cases. I would wager that the first execution in most counties occur after a specific election rather than a specific crime.