prior probability

In honor of International Women’s Day (8 March 2020), I am posting Nelson Shanks’s oil-on-canvas portrait of Ruth Bader Ginsburg, Elena Kagan, Sandra Day O’Connor, and Sonia Sotomayor, the first four women to serve on the Supreme Court of the United States. More details about this elegant portrait are available here, via Politico.

Having now finished the first half of Cheryl Misak’s intellectual biography of Frank Ramsey (“A Sheer Excess of Powers”), I am especially struck by what Ramsey (pictured below) accomplished before reaching his 19th birthday. In particular, in the space of one month (January of 1922), Ramsey published a devastating critique of left-wing “social credit” proposals, akin to the “universal basic income” schemes of our times; he published a detailed review of John Maynard Keynes’s Treatise on Probability, a review that demolished Keynes’s approach to probability; and he not only translated Ludwig Wittgenstein’s now-famous Tractatus–which is considered to be one of the most important works of modern philosophy–his translation was approved by the demanding and ornery Wittgenstein himself!

Over a century ago, the legal giant Oliver Wendell Holmes invited us to look at the law through the lens of probability theory, or in Holmes’s own immortal words: “The prophecies of what the courts will do in fact, and nothing more pretentious, are what I mean by the law.” Ironically, few legal scholars have taken up Holmes’s intriguing invitation. During the last ten years (2011-2020), however, I authored the following papers in which I applied Bayesian probability to various aspects of law and culture:

1. A Bayesian Model of the Litigation Game (2011), in which I develop a Bayesian model of litigation.
2. Visualizing Probabilistic Proof (2013), in which I use Bayesian methods to solve the “blue bus problem” in evidence law.
3. Finding Santiago (2015), in which I focus on Hemingway’s hero in “The Old Man and the Sea” and explore the inner workings of the old man’s mind through a probabilistic or Bayesian lens.
4. Judge Hercules or Judge Bayes? (2016), in which I use Bayesian methods to solve Newcomb’s Problem.
5. Probabilistic Interpretation II: The Case of the Speluncean Explorers (2017), in which I examine Lon Fuller’s famous fictional case from a Bayesian perspective.
6. A Bayesian Analysis of the Hadley Rule (2019), one of the papers in this fine collection of essays, in which I examine the rule of Hadley v. Baxendale from a Bayesian perspective.
7. The Case for Bayesian Judges: Putting Posner and Vermeule into Practice (in press), in which I develop a simple Bayesian model of adjudication.

The formal paper pictured above consists of two succinct sentences and is the shortest-known paper published in a serious math journal; more details are available here. File under: proof by contradiction (hat tip: @pickover).