A Pragmatic Defense of Blackstone's Ratio

i think it works

The Problem

Blackstone’s Ratio is the preposition that:

It is better that ten guilty persons escape than that one innocent suffer.

Benjamin Franklin would increase the ratio to 100:1. I suppose that radicalism was in style. Ol’ Ben didn’t want appear a square, so he squared the ratio. Medieval rabbi Maimonides would go even further. Cubing Blackstone’s ratio to 1000:1 because of Jewish physics. Whatever ratio you go by, there is a widespread consensus across many legal systems that there should be a presumption of innocence. That guilt must be ptoven “beyond a reasonable doubt”.

From a utilitarian this kind of seems to hard to justify. Putting a criminal in jail prevents about 7 crimes ( = felonies ) a year. Can we really say that the freedom of one man is worth more than 70 felonies? What about 700? If it is, how do we justify imprisoning a guilty man for 7? Maybe the guilty man’s freedom is worth less than the guilty man’s, but is it 10, 100, 1000 times less worthy of consideration? It may not surprise you that among the ratio’s earliest critics was Jeremy Bentham.

Daniel Epps¹ provides additional reasons to be skeptical. He argues that if you take into account the dynamic effects, Blackstone’s ratio comes out looking even worse. It may not even help innocent offenders. Furthermore, that in the original context of the principle all felonies carried capital punishment, and that the ratio was supposed to apply to capital punishments only. But he notes that even in olden days, justifications for the principle were sparse.

At this point perhaps, you just appeal to deontology. Fair enough. My own ethical intuitions are mostly consequentialist, but I do not follow consequentialism down a cliff. But let me offer a purely consequentialist justification anyway. If only for the die-hard consequentialists in the back.

Interlude, Adams’ Case.

Before we turn to my argument in favor of the ratio, let us first give one of the founders a chance to make his. So here is John Adams making a case for the presumption of innocence in a 1770 trial:

We find, in the rules laid down by the greatest English Judges, who have been the brightest of mankind; We are to look upon it as more beneficial, that many guilty persons should escape unpunished, than one innocent person should suffer. The reason is, because it’s of more importance to community, that innocence should be protected, than it is, that guilt should be punished; for guilt and crimes are so frequent in the world, that all of them cannot be punished; and many times they happen in such a manner, that it is not of much consequence to the public, whether they are punished or not. But when innocence itself, is brought to the bar and condemned, especially to die, the subject will exclaim, it is immaterial to me, whether I behave well or ill; for virtue itself, is no security. And if such a sentiment as this, should take place in the mind of the subject, there would be an end to all security what so ever.

Even before stumbling across this, I often thought a justification like this might work. Most people don’t understand probability intuitively. Much less so the type of person that might commit a crime. If your legal system convicts 40% of murderers and 1% of non-murderers, a rational agent would still not murder unless he thinks 39% chance of execution is worth it (the standard penalty in Adam’s time). But most people don’t think like that. They would perceive it as “if you do crime, you might be punished. If you don’t, you still might get punished”. Putting it like that, your would be criminal is hardly deterred. If you want to deter you could create a system where “if you do crime, you will be punished. If you don’t, you might get punished”. As Adams points out though, that’s impossible. So instead “if you do crime, you might be punished. If you don’t, you won’t get punished” is the one we try for.

There is a lot to like here, but I don’t think it quite works. It is too reliant on a particular idea of behavioral economics, and only works to the extent that particular model holds water. I want to ground my arguments a little bit more.

The Solution?

I hope you passed Wiskunde D, because it is time to talk probabilities.

Suppose there is a disease that affects 2% of the population. Suppose further that you have a 95% accurate test for that same disease. You test someone, and they come out positive. What is the chance they actually have the disease?

If you answered ~28%. Congrats! You probably saw some science video/read some blog about this elsewhere, or you just guessed where this is going from context. But what you probably didn’t do is work it out from first principles². This counterintuitive result may be referred to as the base rate fallacy. Most people would fall for it, even when the probabilities are given. But when they serve on a jury, and the sort of evidence don’t have very good numbers assigned to them, they are bound to be even more confused.

Consider the context in which Blackstone himself introduces his ratio.

Fourthly, all presumptive evidence of felony should be admitted cautiously, for the law holds that it is better that ten guilty persons escape than that one innocent suffer. And Sir Matthew Hale in particular lays down two rules most prudent and necessary to be observed: 1. Never to convict a man for stealing the goods of a person unknown, merely because he will give no account how he came by them, unless an actual felony be proved of such goods; and, 2. Never to convict any person of murder or manslaughter till at least the body be found dead; on account of two instances he mentions where persons were executed for the murder of others who were then alive but missing.

Consider that most things people own are not stolen (in the order of 98%). Yet the fact that a person cannot explain how an object came into his possession is strong evidence that it might be stolen. Still, you should not convict. Blackstone grounds that in his ratio. We can can ground that in Bayes’ theorem, through the base rate fallacy. Perhaps Blackstone and his colleagues are morally lucky. Perhaps they intuitively grasped that there is a insufficient with the amount of evidence in this example, but just couldn’t figure out what the underlying principle is. Either way, their trepidation was warranted.

But should we still apply Blackstone’s method today, when we understand the underlying maths? Can’t we just explain the base rate fallacy to the jury, so that they can apply it directly? I really doubt that would work. Even if you can actually get the jury to understand the fallacy in between all the other shit that they are required to remember from jury instructions, there is no way you can get them to apply it correctly. Some legal systems have trial by judge, rather than jury.

I am less certain whether to replace presumption of innocence with base rate eduction in case of trial by judges. Most lawyers are terminal worcels, Blackstone himself could have figured the probability. His book came out several years after Bayes’ book on probability, but he did not apply it. On the other hand, I expect lawyers to be selected for general IQ and things like the LSAT plausibly tests shape rotation skills. But that is America, I don’t know how mathematically capable judges might be in countries that actually douse trial by judge.

1. Epps, Daniel. "The consequences of error in criminal justice." Harv. L. Rev. 128 (2014): 1065.

2. P(true positive) = 2% * 95% = 1.9%
P(false positive) = 98% * 5% = 4.9%
P(true positive|positive) = 1.9% / (1.9% + 4.9%) = ~28%