prior probability

Note: This is my first blog post in a month-long series on the basics of Bayesian probability theory.

It’s the “1st of tha month,” so as promised let’s begin my series of Bayesian blog posts, and let me start by stating “what Bayes is not.” It is not a magic conjurer, Delphic oracle, or “veritable sorcerer.” [1] That is, it is not a method for eliminating uncertainty. Instead, Bayesian probability is a method for measuring our level of uncertainty. [2] Put another way, the Bayesian approach to legal and moral judgements is not just a method of drawing inferences from observations or evidence presented; it is also a method of testing the strength or weakness of such inferences. This insight is extremely relevant to law and legal processes. Although Bayesian reasoning cannot replace human intuition or judgement or decide for us the ultimate guilt or innocence of a defendant, we can nevertheless use Bayesian methods to measure or evaluate the strength of a party’s evidence, whether it be evidence of guilt or evidence of innocence. As a result, Bayesian methods may not only be used offensively by a moving party (plaintiff or prosecutor) to measure the strength of his case; such methods can also be used defensively by a defendant to test or challenge the strength of the moving party’s case. (In my next post, I will show how legal trials are like bets.)

[1] People v. Collins, 438 P.2d 33, 33 (1968).

[2] See, e.g., Colin Howson &Peter Urbach, Bayesian Reasoning in Science, 350 Nature 371, 372 (1991) (Bayesian reasoning is a method of “characterizing a scientific conclusion about a hypothesis as a statement of its probability”); Stephen Fienberg & Mark Schervish, The Relevance of Bayesian Inference for the Presentation of Statistical Evidence and for Legal Decisionmaking, 66 Boston University Law Review 771, 773 (1986) (“Bayesian probability theory … provide[s] both a framework forquantifying uncertainty and methods for revising uncertainty measures in the light of acquired evidence”).

This blog is called “prior probability,” which refers to a special idea in the world of Bayesian probability theory, the idea of a “prior”: one’s personal or subjective belief/probability estimate of an event, before any data is collected or observed. I have long been fascinated with this concept and with Bayesian probability generally. Specifically, where do we get our priors from, and why are most people so reluctant to update their priors? Also, why is Bayesian reasoning so special, and why are Bayesian methods worth studying? These last two questions are especially poignant and relevant in my case. After all, what do Bayes or priors have to do with law, let alone ethics, my two areas of study? As it happens, I have written a number of scholarly essays, book reviews, blog posts, and law journal articles, just to name a few, on this subject:

1. A Bayesian Model of the Litigation Game, European Journal of Legal Studies (2011).
2. The Turing Test and the Legal Process, Information & Communications Technology Law (2012).
3. Visualizing Probabilistic Proof, Washington University Jurisprudence Review (2014).
4. Why Don’t Juries Try ‘Range Voting’?, Criminal Law Bulletin (2015).
5. Bayesian Manipulation of Litigation Outcomes, unpublished manuscript (2016).
6. The Case for Bayesian Judges, Journal of Legal Metrics (2019).
7. Bayesian Verdicts, Journal of Brief Ideas (2020).
8. Weyl Versus Ramsey: A Bayesian Voting Primer, unpublished manuscript (2020).
9. Frank Ramsey’s Contributions to Probability and Legal Theory, work in progress.

But truth be told, only a handful of individuals have ever read any of my scholarly papers. Also, hardly anyone, especially in such non-mathematical fields like law and ethics, wants to take the time to figure out the meaning of technical formulas or solve equations, so beginning on Monday, March 1st–and for the entire month of March–I will be returning to my Bayesian roots, so to speak, and will be blogging about first Bayesian principles and explaining their relevance to law and ethics. (I will, however, in honor of my hero, the good Reverend Thomas Bayes, be taking Sundays off.)

Background: The geometry problem pictured below, which popped up in my Twitter feed, was originally assigned on a seven-year-old’s math homework. For my part, I thought at first that the answer had to be “false,” but after seeing some of the replies in this fascinating thread, a thread which contains many deep mathematical insights, I have changed my answer to “true”!

I agree with the sentiment of my colleague Andrew Fleischman (@ASFleischman), who tweeted the following rhetorical question: “… I wonder how vaccine rollout would have gone if it was just first come, first serve[?]” The answer, of course, is pretty clear: the people who really wanted the vaccines would have received them first. Most of the replies to Fleischman’s tweet, however, are clueless. (At the very least, young ladies won’t have to pretend to be grannies to get a vaccine! See here.)

The Lego image pictured below is from Dr Abigail Graham (@abby_fecit), an archaeology-minded historian and Romanophile. Her article is titled: “Reconstructing the Past: Lego Colosseum & 8 reasons why Lego is great training for an archaeologist.” Source: https://bit.ly/37xiwt2

That is the title of this classic paper by Steven Lubar, which was published in 1992 in Volume 15 of The Journal of American Culture. What other arcane or obsolete physical objects are deserving of having their cultural histories told? (hat tip: chad wellmon, @cwellmon)

Which one?! My “bitcoin prior” is that Bitcoin is insanely-overvalued, that it’s a purely speculative “bubble” akin to the South Sea Bubble of 1720 or the even more famous episode of Tulip mania in 17th-Century Amsterdam. Now that I see this “map of bitcoin forks” (pictured below), in which direction should I update my bitcoin prior? As an aside, I wrote about the taxation of Bitcoin here, and here is a bonus Bitcoin video (starring Remy): https://youtube.com/watch?v=UG7zLhEWanc

I am considering adding a new “Taxonomy Tuesdays” section as a regular feature on this blog. In the meantime, enjoy …

This tongue-in-cheek taxonomy is across three dimensions: cartoon avatar, leisure-time activity, and footwear. What other dimensions might be important, e.g. latest-book read, type of car, etc.?

Probably–after all, Rawls’ “reflective equilibrium” concept is pure philosophical nonsense, and the inferences he draws from his “original position/veil of ignorance” thought-experiment are unsound. (If you disagree, ask John Harsanyi.) Nevertheless, in honor of what would’ve been Rawls’ 100th birthday (21 Feb. 2021), the Boston Review just published ten new essays to commemorate the occasion. Also, my colleague Larry Solum honors the late Rawls here.