## In Defense of the "Quants"

That the article should take this critical position is completely unsurprising, given the orthodox Austrian perspective on probability theory that Mr. Sanchez utilizes 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 of "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]

Mr. Sanchez's article offers an excellent
illustration of just how question-begging and banal Ludwig von Mises's
distinction between "class" and "case" probability really is. In the first place, Mr. Sanchez's article is
concerned to determine 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 to this question
that Mr. Sanchez arrives at, citing Ludwig von Mises's famous distinction
between "class" and "case" probability, 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 Mr.
Sanchez, and nothing more.

A closer inspection of Ludwig von Mises's
distinction between "class" and "case" probability, however, reveals that Mr.
Sanchez's claim is baldly question begging.
Ludwig von Mises's distinction between "class" and "case" probability 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. Mr. 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 Mr. Sanchez and Ludwig
von 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 Ludwig von Mises
and Mr. 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 Mr. Sanchez
goes far beyond that, following the lead of Ludwig von Mises, and claims that *no*
numerical probabilities can ever be applied to singular economic events. This sweeping claim is not justifiable based
upon the argument that he has provided.

Neither Ludwig von Mises nor Mr. Sanchez provide us a reason, for example, 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 why it would be inappropriate for the "Quants" to employ some other non-frequentist method for generating numerical probabilities.[5] On the contrary, they simply condemn the entire application of numerical probability to the economic world, simply based on the banal observation that no relative frequencies can be calculated in that realm.

The root of the problem here is that neither Ludwig von Mises nor Mr. 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 that he is that something will or will not occur. This is just as true of the economic world as the natural world.

Both Ludwig von Mises and Mr. 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 Mr. 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 sciences of human action.

In fact, because both Ludwig von Mises and Mr. 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 alter 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 Ludwig von Mises's theory of probability, such as it is,[8] it does not justify the wholesale condemnation of the application of probability in the sciences of human action.

[1] Daniel James Sanchez, "What Mises
can Teach the Quants," *Mises
Daily***,**
Friday, June 10, 2011

[2] The relative frequency
method for calculating probabilities, (which was first developed by John Venn
in the 19^{th} century, but was popularized by Ludwig von Mises's
brother, Richard von Mises in the 20^{th} century), involves calculating the relative frequency
at which a certain type of event occurs in repeated trials. If a coin is flipped ten 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 comes up by the total number
of tosses. For a more thoroughgoing
technical explanation of the relative frequency method, see page 23 of Robert
A. Crovelli's "An
Analysis of the Basic Concepts in Applied Mathematics. For a more complete critique of the relative
frequency method, see Mark R. Crovelli, "On the
Possibility of Assigning Probabilities to Singular Events: Or, Probability is
Subjective, Too!" Libertarian Papers 1, 26 (2009).

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

[4] For a succinct discussion of the "classical approach" to generating numerical probabilities, see page 23 of Robert A. Crovelli's "An Analysis of the Basic Concepts in Applied Mathematics"

[5] For an explication of the
"subjective approach" to generating numerical probabilities, see Ibid, *loc.
cit*.

[6] For an elaboration of this claim with regard to Ludwig von Mises, see Mark R. 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 Mark R. Crovelli "Why the Definition of Probability Matters,"
** Mises Daily,**
Wednesday, January 26, 2011.

[8] See Crovelli (2010) for an argument that Ludwig von Mises did not truly develop a full-blown theory or definition of probability.

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