A guard stands behind bars at the Adjustment Center during a media tour of California’s Death Row at San Quentin State Prison. (Stephen Lam/Reuters)

Since its 1976 ruling in Gregg v. Georgia, the Supreme Court has held that the death penalty is constitutional if reserved for the “worst of the worst” — those having committed the worst crimes, or with the least explanation for having done so. States are required to specify a range of eligible offenses, such as killing a police officer or torturing the victim, and to note relevant aggravating circumstances, such as a previous record of violent crime or, in Texas, to assess the “future dangerousness” of the inmate. All these “legally relevant” factors are supposed to change the odds of a given criminal receiving the ultimate punishment.

This year the justices will be assessing whether these aggravating circumstances have become too vague, potentially encompassing virtually all homicides, in Hidalgo v. Arizona, before they adjourn in June.

But what if some offenders are more likely to face the ultimate penalty not because the crime was especially heinous, but because they’re tried in a county that often imposes and then carries out the death penalty?

Are executions a self-reinforcing phenomenon?

One of us, Frank Baumgartner, along with other researchers, previously published an analysis showing that executions are extremely concentrated in just a few places. These “hot spots” are not the places with the highest numbers of homicides, as others have noted as well.

Of course, some states do not allow the death penalty, and each state differs in what rules it uses in deciding who’s eligible for the death penalty. States also differ dramatically in the likelihood of carrying out the death sentences their courts impose; some, like California and Pennsylvania, carry out only a tiny fraction of those that juries and judges impose. Others, like Texas, Oklahoma and Virginia, carry out a higher percentage. As a result, there is great reason to expect some variability in death sentencing and executions across states and counties.

But as we explain in a recent article, we find that the extreme concentration of executions across U.S. counties cannot be explained by random fluctuation. It can, however, be statistically explained with an event-dependence model. That is, each execution makes the next execution more likely. We looked at every execution in the United States since the creation of the modern death penalty system in 1976, paying attention to the county of the crime and the date of the execution.

Note that executions are carried out in centralized prison locations — for instance, all Texas executions are carried out in Huntsville — and many death sentences are later overturned on appeal. In our analysis, we link the county where the crime occurred and executions actually carried out.

We find that some counties, apparently, are just better at it than others; as they gain more experience with carrying out executions, each subsequent one comes faster. The longer counties go with no executions, the longer it takes to carry one out.

Carrying out executions, it appears, requires specialization and practice. Without specializing in it, few counties can do it. The more a county does it, however, the better it gets at doing it faster.

This would explain why Harris County, Tex., which includes most of Houston, has carried out 125 executions since 1976 — whereas the typical U.S. county has carried out none. The United States includes more than 3,000 counties; fewer than 500 have carried out any executions since 1976. And only 20 U.S. counties have carried out 10 or more executions in that time.

Many events are self-reinforcing, with each instance making the next more likely

Many researchers have noted that some phenomena — wealth, city size, website popularity — grow more concentrated because of some kind of self-reinforcing mechanism. The odds of the next event are correlated with the number of previous events. Random fluctuation just can’t achieve this kind of concentration.

Consider heart attacks: Any individual may have certain risk factors that make them more or less likely to have a heart attack. But an additional risk factor is whether the individual has had a previous attack. This weakens the heart, over and above whatever issues may have been present before. Two, three or four previous heart attacks increase the risk of the next one even more.

Self-reinforcing phenomena, or repeated events models, have been studied in many fields, from medical risk (heart attacks, strokes, hip replacements) and criminal justice (recidivism) to drug or alcohol treatment programs (relapse) — but never before, to our knowledge, to capital punishment.

Here’s how we did our research

We estimated the odds of a given county carrying out an execution, controlling for how many executions that same county had previously carried out, population size, homicides, poverty and relative share of nonwhite population. We used that last figure to evaluate something called “minority threat,” in which a county that is roughly 70 percent white is most likely to consider nonwhite residents especially threatening. Population size and “minority threat” are, indeed, significant in predicting use of the death penalty; that’s why we accounted for them. Crucially, our model also accounts for what we call state-level frailty — controlling for the legal differences from state to state. Of course, we only evaluated counties in states with the death penalty, and during the years when the death penalty was a legal option.

With all that accounted for, we found that the odds go up as the number of previous executions increases, as shown in the figure below.


Here’s what we found. After 18 months, counties with one prior execution have almost 2.5 times the odds of imposing the death penalty again as do counties with no prior executions. The odds increase ever-faster in counties that have carried out more executions. For the 58 U.S. counties that have carried out five or more executions, odds are almost five times greater that another execution stemming from a crime in that county will follow within the next 18 months. All this is in comparison to the vast majority of counties, which never carry out an execution.

Thus, counties separate out over time into two classes. The largest group are “never executors;” a smaller group develops highly localized habits of carrying out executions much more often than do other jurisdictions. Since our model controls for the number of homicides, racial dynamics, poverty, population size, and the characteristics of the state’s judicial system, these effects are over and above those factors.

The U.S. Supreme Court has never held that the number of previous executions in a county should be a relevant consideration in deciding who lives and who dies. According to the court, that should relate to the nature of the crime and the characteristics of the defendant.

A county’s history isn’t supposed to be an aggravating or mitigating factor in determining who gets death. But it is.

Read more:

Frank R. Baumgartner is the Richard J. Richardson Professor of Political Science at University of North Carolina at Chapel Hill. This research extends research he did with other collaborators published in a recent book, “Deadly Justice: A Statistical Portrait of the Death Penalty” (Oxford University Press, 2018).

Janet M. Box-Steffensmeier is the Vernal Riffe Professor of Political Science at Ohio State University and author, with Bradford S. Jones, of “Event History Modeling: A Guide for Social Scientists” (Cambridge University Press, 2004, 2012).

Benjamin W. Campbell is a PhD candidate in the department of political science at Ohio State University.