prior probability

Below are links to some free mathematics textbooks/lecture notes: (hat tips: @pickover, @LunesDes, and @ParamSiddh)

• Donna Kirk, Contemporary Mathematics (2026)
• W. W. Sawyer, A Path to Modern Mathematics (1966)
• C. H. Taubes, Probability, Statistics, and Linear Algebra (2010)

Bonus link: See also my 2015 paper “Finding Santiago“, where I trace the biographical origins of the legendary protagonist of Ernest Hemingway’s timeless novella The Old Man and the Sea.

Are prediction markets (PMs) immoral or dangerous? What about retrodiction markets? What would Adam Smith or F. A. Hayek say? In alphabetical order (by author), below are some anti-PM links:

1. Saahil Desai, Polymarket is going to get someone killed, The Atlantic (7 March 2026)
2. Aisha Down, ‘Abhorrent’: the inside story of the Polymarket gamblers betting millions on war, The Guardian (11 April 2026)
3. Eleanor Harmsworth and Matthew Field, You can now gamble on war, death and destruction. Some people never lose, The Telegraph (7 March 2026)
4. Augustin Lebron, Predicting our own demise, Reducible Errors (17 August 2025)
5. Nitish Pahwa, The legalized gambling industry is collapsing in on itself, Slate (25 August 2025)
6. Bonus link: @TomJrSr, Replies to anti-prediction market claims

For further reference, here is an overview of how prediction markets work.

More generally, is “good faith” more like a rule (e.g. a speed limit or “no smoking” sign), or is it more like a standard (e.g. “fair use” or “be careful”)? Or does the meaning of good faith depend on purely subjective or idiosyncratic factors (e.g. “I know it when I see it”)? My favorite paper thus far at this year’s ALSB (Academy of Legal Studies in Business) conference in Minneapolis has been “Statutory Good Faith and its Continuum of Definitions, Rules, and Standards” by my colleague and friend David Orozco (Florida State), who presents several competing definitions of “good faith” along a sliding-scale or continuum.

Evolvable AI or “eAI” refers to artificial intelligence systems that can autonomously create copies of themselves, pass on heritable traits, and undergo some form of natural selection, e.g. random mutation, recombination, and survival of the fittest. Some AI researchers claim that eAI poses a serious threat to humanity. See Victor Müller, et al., Evolvable AI: Threats of a new major transition in evolution, PNAS (20 April 2026)? Others dispute that claim. See, for example, Maarten Boudry, Domesticated, not feral: Why evolvable AI is not yet a Darwinian threat, PNAS (2 July 2026)? So, who’s right? And if it’s too soon to say who’s right, then what?

Is it possible to tame the A.I. beast in higher ed? I am a college professor who sees the handwriting on the wall: it’s only a matter of time before university administrators begin using “A.I. tools” to replace costly faculty. Although resistance is probably futile at this stage, some law school faculties in the U.S. are now starting to fight back by restricting the use of new technologies like “generative A.I.” in the classroom. (See here, for example.) Is this a lost cause or the start of a counter-revolution in higher ed?

I have returned from my travels in Costa Rica (family vacation) and North Texas (among other highlights, my daughter Adys and I saw the semi-final match between France and Spain at Dallas Stadium) to attend the annual conference of the Academy of Legal Studies in Business (ALSB). This year, the ALSB will take place at “The Depot”, a historic hotel and former train station (pictured below) in the Mill District of downtown Minneapolis, where I will be staying until the end of this week (July 20-23).

I will therefore resume — and conclude! — my multi-part review of Adam Smith’s 1784 pamphlet, Additions and Corrections to the First and Second Editions of Dr. Adam Smith’s Inquiry into the Nature and Causes of the Wealth of Nations, next week (July 27-31). In the meantime, I will be meeting with friends and colleagues as well as presenting two of my forthcoming papers at the ALSB: “Buchanan v. Samuels: The Cedar Rust Case Redux” (on Tuesday, July 21) and “Stoic Capitalism? Adam Smith versus Marcus Aurelius” (on Wednesday, July 22).

Does it get any better than this? La Furia Roja vs. La Albiceleste! Lamine Yamal vs. Lionel Messi Messi! To celebrate today’s historic World Cup championship match between Spain and Argentina, I am posting this Spanish language remix of K’NAAN’s “Wavin’ Flag” featuring David Bisbal.

Thus far this past week (see here, here, here, here, and here), we have done a deep dive into paragraphs 1 to 53 of Part #12 of the pamphlet “Additions and Corrections to the First and Second Editions of Dr. Adam Smith’s Inquiry into the Nature and Causes of the Wealth of Nations” (Smith 1784, pp. 23-46). But I have saved the best for last: the closing paragraph of Part #12 (paragraph 54). It is here, in this concluding paragraph to Part #12 of his 1784 pamphlet, that Adam Smith pulls back the green curtain, so to speak — like Dorothy’s dog Toto in The Wizard of Oz — to reveal the true villains of his story:

“It cannot be very difficult to determine who have been the contrivers of this whole mercantile system; not the consumers, we may believe, whose interest has been entirely neglected; but the producers, whose interest has been so carefully attended to; and among this latter class our merchants and manufacturers have been by far the principal architects. In the mercantile regulations, which have been taken notice of in this chapter, the interest of our manufacturers has been most peculiarly attended to; and the interest, not so much of the consumers, as that of some other sets of producers, has been sacrificed to it.” (Smith 1784, p. 47)

On this note, compare the “Big Tech” firms of today, such as Apple, Google, Meta/Facebook, Microsoft, and OpenAI, to the evil economic “contrivers” of Smith’s day. Plus ça change, plus c’est la même chose!

But how is such a small group of nefarious “contrivers” — past and present — able to manipulate the legal system to put their private economic and legal interests ahead of those of the great majority of the public: consumers? Whatever happened to the consequentialist notion of “the greatest good for the greatest number”?

As it happens, Adam Smith anticipates Mancur Olson’s Logic of Collective Action by two centuries. Buried deep in his discussion of the wool market in England (see paragraph 34 on pp. 38-39 of Smith’s 1784 pamphlet), the Scottish scholar compares and contrasts cattle ranchers and sheep farmers (“graziers”) on the one hand with the manufacturers of leather and woollen goods on the other:

“Graziers separated from one another, and dispersed through all the different corners of
the country, cannot, without great difficulty, combine together for the purpose either of imposing monopolies upon their fellow citizens, or of exempting themselves from such as may have been imposed upon them by other people. Manufacturers of all kinds, collected together in numerous bodies in all great cities, easily can.” (Smith 1784, p. 38)

In other words, there is a market for political and legal favors just like there is a market for ordinary goods like wool, leather, and meat. Large and diffuse majorities — whether they be cattle ranchers, sheep farmers, or consumers — are unable to effectively band together to lobby the government to protect their interests because they are spatially dispersed across the country. (Implicit in the passage above is what Mancur Olson makes explicit: when a group is large and dispersed, the benefits to any individual member of the group of lobbying the government are small relative to the costs of banding together.) Small and geographically-concentrated groups, by contrast, are another story. They can more easily organize and band together than large and diffuse majorities can because the financial rewards for them are large. Simply put, the costs of banding together for small and concentrated groups are worth it.

Nota bene: I will be taking next week off, but starting on Monday, 27 July, I will turn my attention to the last separate substantive section of Smith’s 1784 pamphlet: Part #13.