There is no death penalty in most counties and in the ones that have it there are many counties with very small populations and a small handful with mega cities like Dallas Texas in them.
(1) Crime scales with population.
(2) Death sentences scale with crime.
(3) Therefore, death sentences should scale with population.
(4) The U.S.'s geographic distribution results in very dense clustering such that only a handful of counties have a lot of population.
(5) Therefore, we would expect to see only a handful of counties account for the majority of death sentences.
However, this line from the abstract seems to make (2) unlikely:
> The number of death sentences in a given county in a given year is better predicted by that county’s previous experience in imposing death than by the number of homicides.
Thus, their argument is that something much deeper is going on than just population-level trends.
Now you're making me wonder if they controlled for elected judges.
Normalizing by population density might help, but only in a limited way, because huge concentrations of people create different effects than pretty sparsely populated areas.
The best predictor of death sentences is going to be whether or not you are in Texas.
> In the analyses below, we include only states allowing the death penalty in the year of analysis. Because we focus on the geographical variability in the use of the death penalty, we exclude the US military (which has sentenced 15 individuals to death since reestablishment in 1984, but carried out no executions) and the federal government (which has issued 79 death sentences since reinstatement in 1988, and carried out three executions).
And with this in mind, they still found that death sentences didn't correlate well with the homicide rate:
> The table also lists the rate of death sentences per 100 homicides and the rate of homicides per 100,000 population. If there was a direct link among these variables, we would expect some consistency here. But we see very little. In fact, the correlations are surprisingly low; in fact, the rate of death sentences per 100 homicides and the rate of homicides per 100,000 population correlate at -0.12. The counties with the highest raw numbers of death sentences listed in the table include not a single county that ranks in the top 100 with regards to death sentences per 100 homicides.
First, even the death penalty rate isn't approximately equal across the sample, so it's not just population. And second, they are saying that the death penalty rate doesn't even correlate well with the crime rate. And yet there are still a few outlier counties that have an abnormally high death penalty rate! That is what is unintuitive. I mean, sure, it makes some sense that some counties are more likely to issue the death penalty than others, even where it's legal, but it's a huge skew, and it's very different from saying "Texas has a lot of people."
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.