Author: Garrett M. Petersen

Louis XIV Lives On

When calico printed cloth was introduced to Europe, the French government banned it. They employed gestapo-style tactics to stamp out the new innovation. Here’s Murray Rothbard’s summary of the fiasco, from his excellent An Austrian Perspective on the History of Economic Thought (vol. 1, p. 219):

The new cloth, printed calicoes, began to be imported from India in the 1660s, and became highly popular, useful for an inexpensive mass market, as well as for high fashion. As a result, calico printing was launched in France. By the 1680s, the indignant woollen, cloth, silk and linen industries all complained to the state of ‘unfair competition’ by the highly popular upstart. The printed colours were readily outcompeting the older cloths. And so the French state responded in 1686 by total prohibition of printed calicoes: their import or their domestic production. In 1700, the French government went all the way: an absolute ban on every aspect of calicoes including their use in consumption. Government spies had a hysterical field day: ‘peering into coaches and private houses and reporting that the governess of the Marquis de Cormoy had been seen at her window clothed in calico of a white background with big red flowers, almost new, or that the wife of a lemonade-seller had been seen in her shop in a casquin of calico’. Literally thousands of Frenchmen died in the calico struggles, either being executed for wearing calicoes or in armed raids against calico-users.

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Mises, Probability, and the Two Envelopes Problem

In Human Action, Mises distinguishes between what he calls “class probability” and “case probability.” He defines class probability as such:

Class probability means: We know or assume to know, with regard to the problem concerned, everything about the behavior of a whole class of events or phenomena; but about the actual singular events or phenomena we know nothing but that they are elements of this class.

This is the ordinary sort of probability. We reach into an urn containing seven red balls and two white balls, so the probability of choosing a red ball is 7:2. We can say this because we have knowledge about the class of balls in the urn. Mises distinguishes this from case probability:

Case probability means: We know, with regard to a particular event, some of the factors which determine its outcome; but there are other determining factors about which we know nothing.

Mises goes on to criticize the tendency to conflate case probability with class probability.  To say that a political candidate’s odds of winning an election are 9:1 is a meaningless statement; there is no class of ten elections of which nine result in the candidate’s victory. At best, it is a faulty analogy.

There is a famous math problem that demonstrates the error in applying the reasoning of class probability to case probability: the Ali Baba problem (also known as the two envelopes problem).

Two men, Ali and Baba, are presented with a problem. Ali is given an envelope containing a certain amount of money. There are two other envelopes, one with half the original amount and one with double the original amount. A fair coin is flipped to select which envelope to give to Baba.

Ali reasons that his expected payoff is increased by switching envelopes with Baba. If X is the amount in Ali’s envelope, he gets 2X with probability one half and 1/2X with probability one half, so his expected value from switching is 2X*1/2+1/2X*1/2=5/4X. But herein lies the (apparent) paradox: Baba concludes by the same reasoning that he can also get a larger expected return by switching. How can this be?

The answer is that Baba has made an error; he has wrongly applied the logic of class probability to a problem of case probability. Baba’s envelope was drawn from a class of envelopes with known properties: specifically, there were two envelopes, one of which contained four times the amount of money in the other. Ali, in making the calculation above, uses his knowledge about the class of envelopes from which Baba’s envelope was drawn. For Baba to apply the same reasoning to Ali’s envelope is incorrect; although we are uncertain about the amount in Ali’s envelope, we cannot treat it as if it were drawn from a known class (double Baba’s envelope or half Baba’s envelope).

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Mises, Probability, and the Two Envelopes Problem

In Human Action, Mises distinguishes between what he calls “class probability” and “case probability.” He defines class probability as such:

Class probability means: We know or assume to know, with regard to the problem concerned, everything about the behavior of a whole class of events or phenomena; but about the actual singular events or phenomena we know nothing but that they are elements of this class.

This is the ordinary sort of probability. We reach into an urn containing seven red balls and two white balls, so the probability of choosing a red ball is 7:2. We can say this because we have knowledge about the class of balls in the urn. Mises distinguishes this from case probability:

Case probability means: We know, with regard to a particular event, some of the factors which determine its outcome; but there are other determining factors about which we know nothing.

(more…)

The post Mises, Probability, and the Two Envelopes Problem appeared first on The Economics Detective.