prior probability

What is the best way to describe or visualize the law? As I mentioned in a previous blog post, it was the legal historian F. W. Maitland (1898, p. 13) who first compared law to a “seamless web” (see here). His 1898 essay A Prologue to a History of English Law begins with the following timeless sentence: “Such is the unity of all history that any one who endeavors to tell a piece of it must feel that his first sentence tears a seamless web.” But Maitland’s metaphor is not the only one out there. I came across two additional visualizations of law this weekend when I was reading a 2022 chapter on Law and Society in Eighteenth Century Scottish Thought by Peter Stein: the law as a large flowing river like the Nile (Stein 2022, p. 158) and the law as an ancient castle (ibid., p. 165).

The river Nile metaphor appears in Lord Kames’ Historical Law-Tracts (Kames 1758, pp. ix-x), which was first published in Edinburgh in 1758 and is available here for your reference. By way of background, Henry Home, Lord Kames (1696–1782), was an influential Scottish judge, a prolific man of letters, and one of Adam Smith’s early patrons, and his Historical Law-Tracts is considered one of the earliest contributions of the Scottish Enlightenment. In the preface to this historical work, Lord Kames compares law to the river Nile, and he also compares a student of law to a sailor crossing the Delta, who “loses his way among the numberless branches of the Egyptian river”:

“I have often amused myself with a fanciful resemblance of law to the river Nile. When we enter upon the municipal law of any country in its present state, we resemble a traveller, who, crossing the Delta, loses his way among the numberless branches of the Egyptian river. But when we begin at the source, and follow the current of law, it is in that case no less easy and agreeable; and all its relations and dependencies are traced with no greater difficulty than are the many streams into which that magnificent river is divided before it is lost in the sea.”

For its part, the ancient castle metaphor appears in Volume 1 of the Memoirs of the Life of Sir Walter Scott (Lockhart 1837, pp. 58–59), which is available here. Among other things, Walter Scott (1771–1832) was a Scottish historian, novelist, and playwright, and in his memoirs he acknowledges David Hume, Baron Hume of Ninewells as the source of this metaphor. Baron Hume was the philosopher David Hume’s nephew(!) and the Professor of Scots Law at the University of Edinburgh from 1786 to 1822. According to Scott, who attended Baron Hume’s law lectures in person and copied out his lecture notes twice in his own hand, it was Hume who first described law as an “ancient castle, partly entire, partly ruinous, partly dilapidated, patched and altered during the succession of ages by a thousand additions and combinations ….” Sir Walter Scott also uses this castle metaphor to describe Baron Hume’s teaching style and Hume’s intellectual contribution to the study of Scottish law:

“[My] Scotch Law lectures were those of Mr. David Hume [the nephew of the famous philosopher], who still continues to occupy that situation with as much honor to himself as advantage to his country. I copied over his lectures twice with my own hand, from notes taken in the class; and when I have had occasion to consult them, I can never sufficiently admire the penetration and clearness of conception which were necessary to the arrangement of the fabric of law, formed originally under the strictest influence of feudal principles, and innovated, altered, and broken in upon by the change of times, of habits, and of manners, until it resembles some ancient castle, partly entire, partly ruinous, partly dilapidated, patched and altered during the succession of ages by a thousand additions and combinations, yet still exhibiting, with the marks of its antiquity, symptoms of the skill and wisdom of its founders, and capable of being analyzed and made the subject of a methodical plan by an architect who can understand the various styles of the different ages in which it was subjected to alteration. Such an architect has Mr. Hume been to the law of Scotland, neither wandering into fanciful and abstruse disquisitions, which are the more proper subject of the antiquary, nor satisfied with presenting to his pupils a dry and undigested detail of the laws in their present state, but combining the past state of our legal enactments with the present, and tracing clearly and judiciously the changes which took place, and the causes which led to them.”

In addition to these three metaphors, ChatGPT regurgitated several others (see screenshot below). So, which metaphor do you like best?

P.S.: Aside from ChatGPT, below the fold is a bibliography of the scholarly works I have cited in this blog post:

That is the title of this excellent essay published in 1876, the first page of which is pictured below, by the great English essayist Walter Bagehot. (I serendipitously stumbled upon this work via the late David Winch.) Although this text is relatively short — just 40 paragraphs spanning across 25 pages — it is full of so many original insights that I have decided to write up a paragraph-by-paragraph review of Bagehot’s beautiful essay, starting next week. Stay tuned!

The greatest of all time? Yes, as a lifelong baseball fan, Shohei Ohtani has my vote!

Inspired by the ideas of Robin Hanson (see, by way of example, the video below on prediction markets), I have proposed the creation of a “truth market” in order to counteract the spread of false information on the Internet, and in my previous two posts this week (see here and here), I have compared and contrasted my proposed truth market with prediction markets, described how a decentralized truth market would work in practice, and explained why such a market could dispense with two features of prediction markets: closing dates and trusted arbiters. In summary, truth markets allow people to trade belief contracts (i.e. to bet on their beliefs about past events, such as conspiracy theories, fake news, etc.), but unlike a traditional prediction market, my truth market would remain open indefinitely and would not have any final arbiters.

Today, I will address a different concern or possible objection to my proposed truth market: the likelihood of market manipulation, either by government officials who have access to secret information or to media insiders who, in turn, have access to those officials. Fortuitously, the market manipulation or “insider trading” argument is the easiest objection to refute. Why? Because from a global or information perspective, insider trading is actually a good thing! Insider trading might be morally wrong (using secret information to make a profit) or not (what’s wrong with making a profit?), but either way insider trading makes markets more efficient and more liquid. In the case of a truth market, any attempt by government or media insiders to manipulate the market would soon be reflected in the prices of the belief contracts. Alert traders would quickly spot any unusual or unexpected changes in the market price of a belief contract and seize the opportunity presented by any distortion in the price. My slogan therefore is: the more market manipulation, the better!

In my previous post I described how a “truth market” could be used to counteract the spread of false information on the Internet. To the point, my proposed truth market would operate like a betting market but would remain open indefinitely and would not have any final arbiters. That is, unlike a traditional prediction market, where participants trade carefully-worded “event contracts” and have to agree ahead of time to a trusted arbiter to decide whether the event being bet on has occurred or not by a specified date, my truth market would allow people to trade “belief contracts”, would eschew external arbiters, and would remain open indefinitely.

As it happens, my truth market paper underwent peer review earlier this year, and both of my reviewers objected to the open-ended nature of my market (no close date) as well as to the lack of final resolution (no arbiters). The objection boils down to this: without a final arbiter or “some trusted person” (to quote one of my reviewers) or other “disciplining function” (to quote the other) to resolve on some certain date the belief contracts being bet on, how could we determine whether the truth market was working or not, i.e. whether the price of a belief contract reflected the underlying truth or truth-value of the proposition being bet on?

In reply, I would ask: Why can’t the market as a whole be the arbiter? The whole point of a truth market is to allow people to bet on their beliefs about past events, but when those past events are contested or disputed, there is often no way of knowing with any degree of certainty what the truth is. This key epistemological observation is especially true in the realm of conspiracy theories and fake news. Was there a conspiracy to assassinate JFK? Did Jeffrey Epstein really kill himself? Did COVID-19 originate in the Wuhan Institute of Virology? Simply put: in each of these cases, no trusted person or institution is available to decide the truth of the matter in controversy.

A decentralized truth market, by contrast, would provide people with a creative way of generating new information about conspiracy theories and measuring the truth-values of such theories. Bettors who think the price of a belief contract in “Proposition X” will increase (where Prop X is the lone gunman theory, the Wuhan lab-leak theory, or any other popular conspiracy theory) will keep their existing belief contract holdings in Prop X or buy more belief contracts in Prop X. In the alternative, a bettor will sell his existing belief contracts or refuse to buy such contracts if he thinks the price will fall. Either way, with a sufficient number of bettors the market price of a belief contract will track belief or non-belief in the conspiracy theory being bet on with no necessary final resolution. As long as there is yet-to-be-discovered evidence that may be convincing to some bettors, at least some subset of belief contracts should move toward resolution without the need for a trusted arbiter.

To sum up, we don’t need trusted arbiters to tells us whether a given conspiracy theory is true or not, and in any case no such arbiters exist in the real world. But by keeping truth markets open indefinitely, the market price of any given belief contract will itself be the arbiter of the truth of Prop X! How? Because markets and prices reflect dispersed or global information and rapidly adjust to changing conditions, a fundamental observation that goes back to “The Use of Knowledge in Society” by F. A. Hayek (pictured below, left), and markets are more likely to lead to the production of new information in the first place, an idea that can be traced to Ludwig von Mises’ classic treatise Human Action.

Note: I will address an additional objection to my truth market proposal in my next post: the possibility of market manipulation or “insider trading” — either by government officials who have access to secret information or to media insiders who, in turn, have access to those officials.

Earlier this year I posted a short white paper on SSRN (see here) in which I proposed the creation of a “truth market” to counteract the spread of false information on the Internet, and in a previous post, I identified three potential problems with my truth market proposal based on feedback I have received from the peer-review process and from other colleagues. Today, I will address the first and most fundamental of these three objections: how would my proposed market work in practice?

Simply put, my truth market would look like an existing prediction market such as Kalshi or PredictIt (see also the infogram pictured below) but with one major modification or tweak. First off, what is a prediction market? Broadly speaking, a prediction market is a market where people can trade “event contracts” that are tied to the outcome of an unknown future event. (By way of example: “Will Donald Trump be indicted before the end of this week?“) My tweak or modification, however, is to replace prospective event contracts with retrospective belief contracts.

My proposed truth market would thus operate like an ordinary betting market — but instead of placing bets on the outcome of future events (like an upcoming football match or basketball game), participants would trade belief contracts in which people would be able to place wagers on their beliefs about past events, such as conspiracy theories, fake news, and the like. Bettors could opt out at any time, pocketing their winnings if the current price of their belief contracts are above what they paid for them or taking a loss at the current price.

The main difference between a standard prediction market and my proposed truth market is that traditional betting markets must close by a specified date. My truth market, by contrast, would remain open indefinitely and would not have any final arbiters. Both the open-ended nature of my truth market (no close date) and its lack of formal resolution (no arbiters) are the most novel and unorthodox features of my proposal — and the most criticized. I will therefore address these concerns in my next two posts.

On this day (20 March) in 2003, the United States and Britain, along with Australia and Poland, led a full-scale and illegal war of aggression against their former ally Iraq. Alas, 20 years later none of the public officials who instigated the Iraq war have yet to be charged by the International Criminal Court in The Hague. More details about this gross miscarriage of international justice are available here.