Mathematical Justice Initiative
Preface
So if you're reading this, you likely know I'm a pretty big fan of math. And while I think math is no replacement for character and integrity, I personally think it can be used to help "solve" problems where character and integrity come into question. "Solve" being in quotes as these are issues of the heart so to speak. Fair warning, you may find this controversial.
And on that note, I'm going to try to give all the technical details that would allow this to be reproduced. Those details can be found in the dedicated demo pages and will list more of the nitty gritty details behind the creation of the demos. I built this in such a way that it should auto-update so if you find something that seems to be flawed, please let me know so I can get it fixed for future iterations.
With that out of the way, let's get our hands nerdy with some math.
Capital Punishment
The Problem
Until recently, if you asked me what I thought about the death penalty, I think I would have said something like, it's certainly not fun to think about, but certain evils warrant death. And in general I still agree with that. If I didn't, I don't know how I'd justify any war ever. That said, recent events have pushed me further than I was pushing myself to understand the racial tension that remains in the United States today.
After giving up on the audiobook version of Just Mercy due to distracting turbulence on my plane, I did eventually watch the film adaptation this May. Since then, I've gone back and listened to the full audiobook as well as to the audiobook of The Sun Does Shine. Just Mercy is written by Bryan Stevenson, a Black, Harvard-educated lawyer who runs a non-profit, Equal Justice Initiative, that provides legal representation largely for those unable to afford adequate representation. While not exclusively representing death row inmates, the primary stories in the aforementioned audiobooks are about wrongly/wrongfully -convicted Black men on Alabama's death row who were represented by Bryan.
Anyway, I don't want to spoil those stories as I highly recommend taking a look at them. But they did force me to think about the racial injustice involved and how it should actually be pretty simple to detect that mathematically. Side note: I realize racial injustice expands beyond death row, but that which is present in capital punishment seems the most grievous and also the most easily accessible from a data perspective. So that's what I set out to analyze.
Diagnosing the Problem
My approach was mostly inspired by a statistical method called hypothesis testing. Instead of boring you with my own written explanation as I had planned, you can take a look at a real educator's fun little explanatory video on the topic if you'd like.
Without re-explaining what you may have just watched, I have an example more fitting of my approach. Let's say I give you a bag saying it contains 100 marbles with 20 being yellow and 80 being red. You then reach in and blindly grab a handful of marbles. If that handful included 15 yellow marbles and 0 red marbles, you might suspect I was lying/confused/incorrect about the actual distribution of marbles in the bag. It seems unlikely that you would have randomly removed that distribution of marbles if what I said was accurate.
This provides a good analogy for what I'm doing. The marble colors correspond to race/ethnicity, the bag of marbles to a state's population, and the handful of marbles to death row inmates in that state. Just like the marble example, we can get probabilities that we'd see a certain sample given the distribution of the whole. Now if you see a sufficiently unlikely sample, you might reject what you've been told about the whole. OR you could also reject that the sampling method was truly random. So if you see where this is going, you might be saying, "hey, who ever claimed that putting people on death row was supposed to be like randomly pulling marbles out of a bag." For what it's worth, that's actually a rather solid argument, but I want to address that later.
So for now, if we assume that it should be like the marble example and that our data is relatively accurate, then we can get a sense of how not random death row "sampling" is. This takes the form of an "accusation" on what I like to call the "fishiness meter" to the right of the map below. I'm trying to use weaker language because I'm basically doing 600 separate tests here. And if you do 600 of these tests, you shouldn't be surprised to find one thing with a 1/600 chance of happening just by coincidence rather than by some sort of misconduct. But if you're seeing many similarly improbable occurrences, they probably aren't all coincidences. So please don't send me this wonderful and relevant xkcd comic that was just too long to directly throw in this article.
And so with just a little more ado, below is the demo I created (full version viewable on the dedicated demo page). For each race/ethnicity, there are three different views. The first uses the actual population of the entire state which serves as something of a control. If everybody in the state was on death row, there'd be no ground to stand on when claiming racial injustice there. Additionally, there is a view for the distribution of death row inmates executed since 1977 and a separate view for current death row inmates. Then there are two things I want you to look at on each view. The fishiness meter shows the likelihood of such a distribution and the size of each pie chart shows the liberal usage of the death penalty.
IF VIEWING ON A PHONE, PLEASE TURN PHONE LANDSCAPE
Note that the liberal usage of the death penalty is not factored in to the "accusation" on the fishiness meter. I note this because I think both are important to consider. My initial approach somewhat unintentionally accounted for both in the "accusation." This was due to me dampening accusations where there wasn't enough data to meet the requirements for the less computationally intensive approach I was using. That approach required a normal distribution that often would not have been representative of the data. So instead I bought millions of marbles and ran some tests. Okay, I didn't actually buy the marbles, but I did run simulations akin to the marble example.
By running simulations, I no longer feel the statistical need to dampen accusations where previous requirements weren't quite met. This also allows us to get better results for minority minorities - having to dampen accusations due to having too small a representation was always going to affect smaller minorities more and make it impossible to detect any fishiness directed at them.
I note all this though because I think it's fair to consider both the liberal usage of the death penalty and the likelihood of such a distribution. If the death penalty is disproportionately affecting one group in two states, I see the state that actually employs the death penalty more as the more urgent problem.
So while you can't see it as easily now that I've revised my approach, I was surprised to see how much the former Confederate States stood out as some of the most seemingly problematic. Relative to other states, these states tend to more liberally employ the death penalty. And in general, they seem to disproportionately affect Black people. Perhaps this isn't surprising to most, but to me this seems like pretty decent evidence that the effects of slavery are not gone. (Yes, I know, correlation does not imply causation, but please note that correlation also doesn't imply a lack of causation.) To be honest, I expected to see all of the states appearing to be equally problematic in how they're impacting the Black population. And to note, I think outside of death row, incarceration rates would actually show that, according to Sentencing Project's data. But the former Confederate States being noticeably distinct in this data was a shock to me.
So after seeing how the above visualization panned out, I wanted to get a better sense of any trends that may or may not exist here. Ideally, I wanted to see the US trending toward what I believe to be a more fair distribution. So I created a second visualization (with it's own interactive dedicated demo page). The concise version here compares the proportion of Black people on death row to that of the whole country over time. As much as I would have loved to end on a "hey, at least we're getting better" sort of note, I don't think that's quite what I'm seeing here. We may not be getting worse, but it does seem like there's still plenty of work to be done.
Now before getting to the solution, I promised to address the assumption that death rows should be like marbles randomly picked from a bag. I think that is a fair assumption to question. Using that same assumption, I'd have to argue to either put more women on death row or fewer men. And I don't plan on making that argument because I do believe there are some general differences in different groups of people. However, I still think a marble-like distribution should be our aim when it comes to race and ethnicity. The reason being that historically white men have held most of the positions of power in the US. If there was an injustice based on gender, I would expect it to be to the benefit of men - which is not what we see. If there was an injustice based on race/ethnicity, I would expect it to benefit white people - which is something we see here.
The Solution
So initially I claimed that I thought mathematics could be used to help solve problems where character and integrity come into question. And so far I've only actually identified the problem. What's the solution then? Bryan Stevenson would argue against the death penalty altogether. I wouldn't say I'm terribly opposed to that seeing what I see here. However, there are some less drastic options I see as well. The first fairly simple option is some sort of Affirmative Action for death row. Executions and/or death row sentencings could be forced to conform to the actual ethnic/racial distribution of the state involved.
I have another more complex option as well. This one I think generalizes better to situations outside of just capital punishment. Essentially the idea is to incentivize states to operate with ethnic/racial fairness. A portion of federal funding could be divvied up such that states that statistically appear fair get more than states that don't. You may be able to argue that that would have a negative effect on the states that could perhaps use the money to become more fair. My proposal to address that would be to still provide that funding EXCEPT direct it to the marginalized community(ies) themselves instead of the institutions hurting them. And if that sounds dangerously socialist, note that in this framework there's this nice loophole that avoids it altogether called: stop acting racist. Not to mention wouldn't it be fairly capitalistic to make states try to earn their federal funding?
Conclusion
So the takeaway isn't supposed to be, "Wow, Brandon fixed racism!" There's a lot involved here that I'm not an expert in, namely politics. But I do like to think I'm half decent - nay, two whole fourths decent - at math. I think math and data should be part of the conversations. I want to advocate for transparency in the relevant arenas, but it's hard to advocate for more transparent data when it doesn't feel like we're getting anywhere with the data we do have.
Anyway, let's go back one last time to the claim that I think math can help solve problems where character and integrity are concerned. This is just one problem. And it's super political. So clearly I'm full of it and only see math as a way to manipulate people into agreeing with my politics, right? Glad you asked. I am, in fact, actually quite strange, and I enjoy contemplating mathematical solutions to problems regardless of whether I think they'll impact me and regardless of whether there's any sort political controversy involved. If you don't believe me, or even if you do, you may want to check out a separate blog post about how I think freelancer's should be paid that I wrote in conjunction with this one because it aims to make a similar point. That is, that perhaps math can help us solve for more than just x.