prior probability

Happy Boxing Day! You may have heard about the James Webb Space Telescope, which was launched 10 years behind schedule and cost almost $10 Billion USD to complete. (See this NY Times report, for example.) What you may not be aware of is that the Webb Telescope will not be in orbit around the Earth — it will orbit the Sun! (See image below; more details about the Webb Telescope’s solar orbit are available here, via NASA.) Also, the Webb Telescope is not the first spacecraft to orbit the Sun; that honor goes to Luna 1, which went into orbit around the Sun, between the orbits of Earth and Mars, on 4 January 1959. In any case, I am taking this opportunity to re-arrange and share the links of my previous blog posts on the possibility of allocating orbits in outer space using auctions:

1. In praise of Coase (again)
2. The tragedy of the outer space commons
3. The allocation of launch licenses
4. Launch Auctions and the Outer Space Treaty
5. Auctions for Outer Space

I will resume my epic, in-depth review of Nozick on Monday; in the meantime, all I want for Christmas is “Mariachi Show 2000” — check out their version of Jose Feliciano’s classic song “Feliz Navidad” — the best version I have ever heard!

To commemorate the holiday traditions of “Nochebuena” and Christmas I am posting this portrait of “The Virgin and Child with Saint Anne” by the Greek artist El Greco (b. 1541, d. 1614), who completed this work in the year 1600 in Toledo, Spain, where El Greco lived during the second half of his life. (This oil on canvas is now part of the art collection of the Wadsworth Atheneum Museum of Art in Hartford, Connecticut.) One of the things that I love about this work is that includes Saint Anne, the mother of the Virgin Mary and Jesus’ maternal grandmother.

Among other things, the holidays are a time when I finally get to catch up on my scholarly readings. Below, for example, is a listing of some of the sundry papers and books I am studying this season:

1. “Gametek: the math and science of gaming” by Geoffrey Engelstein.
2. “Where is my flying car?” by Josh Hall (cover pictured below).
3. “Games: agency as art” by C. Thi Nguyen.
4. “Do you have to reply to this paper?” by Saul Smilansky.
5. “Moral theory and anomaly” by Tom Sorrell.
6. “Measuring the accuracy of diagnostic systems” by John A. Swets.
7. “Extreme entrepreneurship” by Adam J. Sulkowski.

I still have one more piece of unfinished business before I resume my in-depth review of Robert Nozick’s magnum opus Anarchy, State, and Utopia, and that is “Grounding Legal Proof” — a paper on the “epistemology of evidence law” authored by Michael S. Pardo, a law professor at Georgetown. (Hat tip to my colleague and friend Larry Solum, who also teaches at Georgetown, for bringing Pardo’s thought-provoking paper to my attention last summer.) Specifically, how do we prove a fact in a legal case?

By way of example, consider the case of Muckler v. Buchl, 276 Minn. 490 (1967), available here, which Pardo mentions in the introduction to his paper. In that case, a 55-year-old woman fell down a flight of stairs at an apartment building and died four months later as a result of the injuries she suffered during the fall. Her husband brought a wrongful-death lawsuit against the landlord, and during the trial of this case, a witness testified that the stairs were dimly lit, but this witness did not actually see the plaintiff’s fall. Is there sufficient evidence for the jury to find, by a preponderance of evidence (the standard of proof in civil cases), that the woman’s fall was caused by the lack of lighting?

In summary, Professor Pardo provides a good overview of the two main academic schools of thought regarding how to approach questions like these — he describes probabilistic approaches to evidence as well as story-telling or “explanatory” accounts — but he is on more shaky ground (pun intended!) when he concludes that explanatory theories of evidence law are better than probabilistic ones. Why? Because Pardo’s basic “probability-versus-explanation” dichotomy presents us with a false choice! In reality, all evidence is probabilistic — even the definition of relevant evidence in the modern rules of evidence expresses the test of legal relevance in probabilistic terms — and as the great Frank Ramsey (pictured below), along with Bruno de Finetti, showed us almost 100 years ago, the truth-value of a disputed fact can always be expressed in terms of the fact-finder’s subjective “degree of belief” or credence. (FYI: I explain Ramsey’s ideas more fully here.)

To return to the tort case mentioned above, whether the evidence supports the conclusion that the woman’s fall was due to poor lighting is ultimately nothing more than a probabilistic guess based on the testimony presented in the case and one’s common sense. Or to borrow Professor Pardo’s own preferred jargon, whether an explanation of the evidence in a case is “plausible” or not — or whether that explanation is more believable than a competing story — depends on one’s subjective probability of that particular story being true. Why evidence scholars would choose to gratuitously reject this key insight is beyond me. Perhaps “probability-phobia” is to blame? Whatever the reason, if there is one area of law that stands to benefit the most from Ramsey and de Finetti’s insights it is the law of the evidence.

PS: I will return to the topic of evidence law and subjective probability after I complete my review of Nozick.