Death sentences and race-ethnicity biases

When data shows that Black Lives literaly Mattered less

Jean-Matthieu Schertzer

8 minute read

This article addresses a very serious topic in our post-slavery, post-colonisation and post-segregation world. How is it that, while laws explicitly condemn disparate treatments or outcomes1, there are still clear differences? These differences move part of the public opinion - and that should move everyone by the way because this problem is not going to resolve only with minorities.

This post will expose and explain a situation where Black Lives Mattered less. In Oklahoma, from 1990 to 2012, 143 offenders were sentenced to death. In 2017, Pierce et al.2 collected and analyzed the homicide data (4668 offenders) and the death sentences. It shows that there are several race/ethnicity effects involved in the death sentences outcomes. The paper contains all details. Terminology used (“nonwhite”, “race”) comes from the paper. I don’t like the “nonwhite” term, but I cannot easily replace it each time with Black, Hispanic, Native American and Asian. I will stick to it in this post.

If you are in a hurry, go and see the conclusions.


1. Educated guess about the best/worst odds for death sentences?

Although the topic is very serious, I would like to know your first thoughts on what the potential biases could be. Assume that there is an offender3, judged for a “willful (non-negligent) killing”. We don’t know anything about him.

What would decrease the probability that he is sentenced to death?

  1. Less sentence to death if the offender is white.
  2. Less sentence to death if the victim is not white.
  3. It’s about the same odds, justice system is fair, isn’t it?
  4. Your question is biased (please say how, it’s interesting).

What do you think? You can put your answer in the comments below.


2. From homicide offenders to death sentences, an apparent equality of outcomes

Let’s go back to Oklahoma, where authors have compiled homicides3 and death sentences4 for the 1990-2012 period .

An overview by race/ethnicity gives us a first glimpse of the story:

  • Homicide Rate (HR = HO/POP): Nonwhite people are clearly over-represented among homicide offenders3. Although any prevention/mitigation strategy to reduce homicides should take it into account, we will follow the article and focus on death sentences rates, as it is at the heart of Justice system and not upstream.
  • Death Sentences Rate (DSR = DS/HO): DSR are very similar for white vs nonwhite homicide offenders (3.2% vs 3.0%).

The equality of DSR (Death Sentences Rate) is a central notion of fairness here and we will compute it along multiple dimensions. DSR is defined as the number of Death Sentences divided by number of Homicide Offenders.

Equality of outcomes means that similar homicides (under similar degree of felony circumstances) should lead to similar Death Sentences Rates (DSR).

So, DSR looks similar whatever the race/ethnicity of the offender. Has the full story being told for Oklahoma? No, it has not, there is far more.


3. Death sentence rates by race/ethnicity of victim tells an other story

An other perspective is to consider the race/ethnicity of the victim and not of its offender. It is, literally speaking, the ideas behind the “Black Lives Matter” motto.


The conclusion is striking: a white victim doubles (2.05 = 3.9%/1.9%) the odds of being sentenced to death, vs a nonwhite victim.

However, are there other strong DSR disparities that should be considered before concluding that these differences of outcomes are discriminatory.


4. There is also a strong gender-of-victim effect

An other victim characteristic should be considered: the gender. It has actually a large effect: DSR for female victims is 7.2% vs 1.6% for male victims. In other words, a female victim multiply the odds by 4.5 (= 7.2%/1.6%) of being sentenced to death, vs male victims.

How do the 2 effects (race/ethnicity and gender of victims) combine? We could argue here that maybe there are more women among white victims, which would explain why the DSR of white victims is higher. In that scenario, there would potentially be no discriminatory effect (assuming that it is ok to condemn more seriously when the victim is female).

When we compute crossed race-gender Death Sentences Rates, this hypothetical scenario disappears:

There is no Simpson-like distortion effect: there is a clear white vs nonwhite spread of DSR both for female and male. The more striking effect is for male victims: a white victim multiply the odds by 2.9 (= 2.3%/0.8%) of being sentenced to death, vs nonwhite victims.

Let’s consider potential other factors before wrapping it up.


5. Other effects: felony circumstances aggravators

Before jumping from previous analyses to conclusion of discriminatory effects regarding the race/ethnicity of the victim, we need to think and test for possible confounding factors.

The first in mind is the degree of felony circumstances of the homicides. 3 degrees of felony circumstances aggravators5 are taken into accounts and they have the strongest link with the DSR. Their DSRs are 1.7% (for no aggravator), 6.2% (1 aggravator) and 30.2% (for the few cases with 2 aggravators).


6. A “causal” interaction graph to sum it up

To account for possible confounding effects and to reason ceteris paribus, authors have run a logistic regression with all previously mentioned variables. I encourage you to go and see the results in the paper (Table 11). But for simplicity, I have translated it into a “causal graph”6 while reporting the regression coefficients as direction and intensity on arrows (+/-) pointing to DSR. The last arrow from Offender Race to Victim Race accounts for the observation that White offender kills mostly white victims and reversely.

The picture becomes clearer, the Death Sentence Rate is:

  • mostly driven by the severity of the crime (odds multiplied by 13 between worst and best cases)
  • then driven by the gender of the victim (odds are multiplied roughly by 5 for female victims)
  • thirdly driven by the race/ethnicity of the victim (odds are multiplied roughly by 1.8 for white victims. But note that among men only, the white vs nonwhite odds is 3.2).
  • finally weakly driven by the offender race/ethnicity (odds are multiplied by about 1.3 for nonwhite offender).

7. Conclusion about potential race/ethnicity fairness issues

  1. The direct discrimination (through offender race) is “relatively” small compared to other effects. It is so small that the authors of the paper conclude that there is no evidence supporting this direct effect. However, the logistic regression suggests that there still is a small effect, but not very significant.
    Imagine a case with a nonwhite offender with a Death Sentence Rate of 2%. Being white would decrease its DSR to 1.5% (odds divided by 1.3).
  2. There is a clear “Black lives matter less” effect, which is even stronger among men. Imagine a white-man-victim case with a Death Sentence Rate of 2%. In same conditions, the DSR drops to 0.6% (odds divided by 3.2 for men) with a nonwhite man victim.

Note that these 2 effects are partially cancelling in general. We mentioned that the typical cases are white offenders killing white victims and nonwhite offenders killing nonwhite victims. In those cases, the 2 effects partially cancels themselves, so the DSR are similar. However, in the less frequent “cross-race” homicides the effects adds up and lead to significant differences in DSR.

So, to answer our first question, given a homicide offender and we don’t know more about him:

  • Answer 1 (Less sentence to death if the offender is white) would reduce the odds by 23% (1-1/1.3)
  • Answer 2 (Less sentence to death if the victim is not white) would reduce the odds by 44% (1-1/1.8) in general, and by 69% if the victim is a man.

Answer 2 was correct:

The victim race/ethnicity effect (Killers of a white victim are punished more severely) is stronger than the offender race/ethnicity effect (Nonwhite offenders are punished more severely).

Note that this statement is drawn from analyses of the 1990-2012 death sentences in Oklahoma.

More generally, note that there are overwhelming evidence of discriminatory effects in the criminal-justice system in the US. These two Washington Post articles by Radley Balko are listing a lot of them.



  1. In the US, there are legally protected classes in lots of domains. See the Fairness in Machine Learning 2017 Tutorial by Solon Barocas and Moritz Hardt for more details. ↩︎

  2. Pierce, G. L., Radelet, M. L., & Sharp, S. (2017). Race and death sentencing for Oklahoma homicides committed between 1990 and 2012. J. Crim. L. & Criminology, 107, 733. ↩︎

  3. Homicide offenders are people involved in murders and non-negligent manslaughters, defined as “the willful (non-negligent) killing of one human being by another”. It excludes deaths caused by negligence, attempts to kill, assaults to kill, suicides, and accidental deaths. ↩︎

  4. Death sentences are all people sentenced to death (death penalty) between 199O and 2012 in Oklahoma.
    ↩︎

  5. 3 degrees of felony circumstances aggravators:
    1. The base case, 2. Either multiple victim homicide or homicide with additional felony circumstances, 3. Both multiple victim homicide and homicide with additional felony circumstances. ↩︎

  6. Read the Book of WHY, by J. Pearl and D. Mckenzie, if causality questions are troubling you. ↩︎

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