# Mises Daily Articles

## In Defense of the "Quants"

Daniel James Sanchez's recent article offers a fascinating analysis of the use of probability and mathematical modeling in the financial markets.1 He is highly critical of the use of probability and mathematical modeling for the purpose of predicting future economic conditions or future prices in the market.

That the article should take this critical position is completely unsurprising, given the orthodox Austrian perspective on probability theory that Mr. Sanchez uses to make his argument. Unfortunately, the article's sweeping criticism of the use of probability theory for the purposes of predicting future economic conditions does not hold up under closer inspection.

Mr. Sanchez bases his criticism of the use of probabilistic methods in the economic sphere primarily on Ludwig von Mises's famous distinction between so-called "class" and "case" probability. Mises held that numerical probabilities can legitimately be assigned to classes of events and phenomena, whereas singular cases are not open to any type of numerical probabilistic evaluation. Mises based his claim on the observation that the relative-frequency method for generating numerical probabilities can only be utilized for "repeatable" events or phenomena.[2]

This claim may seem completely unobjectionable to Austrians who have become accustomed to Mises's famous distinction, and it may appear to have profound methodological and epistemological implications, but in reality the claim is quite banal and question-begging, as I have attempted to demonstrate elsewhere.[3]

Sanchez's article offers an excellent illustration of just how banal and question-begging Mises's distinction between class and case probability really is. In the first place, Sanchez's article is concerned with determining whether it is epistemologically and methodologically justifiable to assign numerical probabilities to singular and complicated economic events, as was increasingly done by the "quants" over the past two decades. The answer Sanchez arrives at, citing Mises's famous distinction, is that it was *not* legitimate for the quants to assign numerical probabilities to these events, because they lacked the necessary "class knowledge" to do so. They were "gambling," according to Sanchez, and nothing more.

A closer inspection of Mises's distinction between class and case probability, however, reveals that Sanchez's claim is baldly questionable. Mises's distinction is simply a distinction between those situations in which a relative frequency can be calculated and those situations where it is not possible to calculate a relative frequency. Sanchez recognizes as much when he writes that "the most important thing to note about this distinction is that class probability has to do with *frequency*, and case probability does *not*."

This means that both Sanchez and Mises are assuming from the outset that probabilities are *always* and *necessarily* relative frequencies. And the only justification they provide for believing that probabilities are always relative frequencies is that certain situations are amenable to the frequentist method (i.e., class probability), while others are not (i.e., case probability). In other words, they are assuming the very thing they are attempting to prove. They are assuming that numerical probabilities must be relative frequencies in the process of trying to prove that numerical probability cannot be applied to singular cases, such as singular economic events. This is a textbook case of begging the question.

It would be one thing for Mises and Sanchez to pick out and criticize certain instances where the relative-frequency method for generating numerical probabilities was being misapplied. I am certain that there were many quants who misapplied the relative-frequency method over the past two decades, for example. But Sanchez goes far beyond that, following Mises's lead, and claims that *no* numerical probabilities can ever be applied to singular economic events. This sweeping claim is not justifiable based on the argument that he has provided.

Neither Mises nor Sanchez provide us a reason, for example, as to why it would be epistemologically or methodologically inappropriate for the quants to employ "classical" or "combinatorial" methods for generating numerical probabilities for economic events.4 Nor do they provide us with a reason as to why it would be inappropriate for them to employ some other nonfrequentist method for generating numerical probabilities.[5] On the contrary, Mises and Sanchez simply condemn the entire application of numerical probability to the economic world, simply based on the hackneyed observation that no relative frequencies can be calculated in that realm.

The root of the problem here is that neither Mises nor Sanchez makes an attempt to define probability.6 They start from the observation that relative frequencies can be calculated in some instances while they cannot be calculated in others, as if this were a definition of probability in itself. Recognizing that uncertainty plays a role in both the study of human beings and natural phenomena, they admit that "judgment" and "psychological insight" play a critical role in predicting the future state of the human world, but they nevertheless persist in completely condemning the use of a numerical scale to measure that uncertainty.

This bizarre condemnation of the use of a numerical scale to measure man's uncertainty, "judgment" and "psychological insight" could be completely eliminated were they to adopt a subjective definition for probability. A subjective definition for probability simply asserts that, in a world where every event has a cause of some sort, a numerical probability is simply a measure of some man's (or some men's) uncertainty about what will or will not occur.7 There is thus no reason why man cannot use a numerical scale to describe how certain or uncertain he is that something will or will not occur. This is just as true of the economic world as the natural world.

Both Mises and Sanchez appear to be extremely concerned that the use of probability theory in the realm of economic forecasting will lead to a concomitant neglect of the relevant thymological and praxeological insights that truly matter for making accurate economic forecasts. While this is a valid concern in general, and Sanchez rightly points out that this was a primary failing of the quants, it does not justify ejecting the entire corpus of probability theory from the study of human action.

In fact, because both Mises and Sanchez conceive of probability as a frequency alone, they unintentionally ascribe more gravity to frequentist probabilities than they deserve. If probabilities are conceived as nothing more than measures of human uncertainty, as the subjective approach demands, then there exists ample room to criticize all sorts of probabilistic methods and applications from a praxeological perspective.

If, on the other hand, one conceives of probabilities as "objective" relative frequencies, and thereby ascribes more epistemological weight to them than they deserve because they are supposedly "objective," one unintentionally bolsters the case of dogmatic positivists and empiricists, like many of the quants, who worship at the altar of these supposedly "objective" methods. The adoption of a subjective definition puts the methods and the probabilities they generate on the shaky "subjective" epistemological foundation that they deserve.

In conclusion, while Mr. Sanchez's article is both fascinating and valuable in terms of outlining Mises's theory of probability, such as it is,8 it does not justify the wholesale condemnation of the application of probability to the study of human action.

[2] The relative-frequency method for calculating probabilities, first developed by John Venn in the 19th century, and popularized by Mises's brother, Richard von Mises, in the 20th century, involves calculating the relative frequency at which a certain type of event occurs in repeated trials. If a coin is flipped 100 times, for example, the relative-frequency method for calculating the probability of flipping a head would be to divide the number of times a head is tossed by the total number of tosses. For a more thoroughgoing, technical explanation of the relative frequency method, see Robert A. Crovelli, "An Analysis of the Basic Concepts in Applied Mathematics," p. 23.

[3] Mark R. Crovelli, "A Challenge to Ludwig von Mises's Theory of Probability," *Libertarian Papers* 2, 23 (2010).

[5] For an explication of the "subjective approach" to generating numerical probabilities, see "Analysis of the Basic Concepts," p. 23.

- 1. Daniel James Sanchez, "What Mises can Teach the Quants,"
*Mises Daily*, Friday, June 10, 2011. - 4. For a succinct discussion of the "classical approach" to generating numerical probabilities, see Robert A. Crovelli, "Analysis of the Basic Concepts," p. 23.
- 6. For an elaboration of this claim with regard to Mises, see Crovelli, "On the Possibility of Assigning Probabilities to Singular Events: Or, Probability is Subjective, Too!"
*Libertarian Papers*1, 26 (2009). - 7. For more on the subjective definition of probability, see Crovelli (2009) and Crovelli, "Why the Definition of Probability Matters."
- 8. See Crovelli (2010) for an argument that Mises did not truly develop a full-blown theory or definition of probability.