## Tuesday, November 29, 2011

### Michael Emmett Brady on Keynes’s Probability Theory in Mises and Rothbard

A quick post. There are some interesting reviews here by Michael Emmett Brady on Mises and Rothbard’s understanding of Keynes’ work on probability theory:

“Rothbard’s Many Errors about Keynes and Probability,” http://www.amazon.com/gp/richpub/syltguides/fullview/R83TIX8MB95QW
These bear careful reading, especially the second on Rothbard.

A sample:
‘Rothbard has made at least 10 errors in the space of 5 short paragraphs. The first 4 errors occur in Rothbard’s claim that “Keynes’s Treatise championed the classical a priori theory of probability, where probability fractions are deduced purely by logic and have nothing to do with empirical reality.” First, Keynes’s logical theory of probability is based on George Boole’s 1854 The Laws of Thought. It has nothing to do with the Classical theory of Laplace, whose Principle of Non Sufficient Reason Keynes decimated in the A Treatise on Probability in chapter 4. Second, all of Keynes’s probabilities are conditional. Third, the hypothesis, h, is always related to empirical evidence, e. Thus, a probability is always of the form P(h/e). Fourth, the claim that the “probability fractions are deduced purely by logic and have nothing to do with empirical reality” is simply bizarre as Keynes’s probabilities, in general, are intervals and are not sharp or point probabilities (fractions) except in the limiting case where the weight of the evidence, w, = or approaches 1. The condition that w = 1 or approaches 1 only occurs in the physical and biological sciences. Fifth, the probability relation is not deduced. It is perceived by the decision maker based on intuition, analogy and pattern recognition. …. Eighth, the claim that “… Keynes’s a priori theory was demolished by Richard von Mises (1951) in his 1920s work, ‘Probability, Statistics, and Truth’ is a bad joke. Richard von Mises incorrectly identifies Keynes as a subjectivist and committed the fatal error of overlooking Keynes’s requirement that all probabilities require that w > 0. Richard von Mises claim that Keynes specified probabilities for the case where w = 0 means that he never read the book he claimed to be discussing. Nineth, Rothbard’s claim that “Mises demonstrated that the probability fraction can be meaningfully used only when it embodies an empirically derived law of entities which are homogeneous, random, and indefinitely repeatable” had already been done by Keynes in chapters 8 and 33 of the TP. Keynes would have added the terms uniform and stable as he did in his debate with Tinbergen in 1939–40 in the Economic Journal. Ninth, the claim that “probability theory can only be applied to events which, in human life, are confined to those like the lottery or the roulette wheel” is only correct if one is using mathematical probability. Keynes includes interval probability as the main way in which people use probability. … Rothbard’s scholarship can only be characterized as pathetic.’
“Rothbard’s Many Errors about Keynes and Probability,” http://www.amazon.com/gp/richpub/syltguides/fullview/R83TIX8MB95QW
Comments are welcome: I have no hesitation in saying that the finer, technical points of probability theory are not my area.

1. I started off sitting down to read Minsky's John Maynard Keynes. However, a short ways in it dawned on me that I'd probably be able to appreciate his take on Keynes' General Theory more if I had read it first. So I started in on that instead.

Then I came across Brady talking about how everyone misinterprets Keynes because they haven't read his Treatise on Probability, and they misinterpret that because they haven't read Boole's Laws of Thought.

So now to get back to Minsky's short book, I've got three long ones sitting ahead of me. I hope that covers it all, but with my luck I'll probably also need to read Bayes or something.

I see Brady has a couple of books. By any chance, does anyone know if one of them neatly traces, summarizes and synthesizes this sequence in a single volume? Because it seems to me that to do so would actually be a pretty handy contribution.

2. @Anonymous: Whilst I haven't read his books, Dr. Brady has recommended that people turn to his articles on the SSRN instead of the books he has written. If you want a good article by Dr. Brady on the Boole/Keynes connection, read this article.

http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1546726

@Lord Keynes: Speaking of probability, have you read this review by Michael Emmett Brady? It criticizes Michal Kalecki's theory and use of probabiity theory.

http://www.amazon.com/review/RSC9MH6RF7ZZ0

3. Fifth, the probability relation is not deduced. It is perceived by the decision maker based on intuition, analogy and pattern recognition.

That means it is deduced.

Empirical probabilities are based not on intuition or analogies, but rather on performing a random experiment over and over again, and observing the relative occurrences of each possible outcome and assigning a percentage statistic to each one.

Intuition and analogies are an a priori category of propositions.

Richard von Mises incorrectly identifies Keynes as a subjectivist

Keynes was a subjectivist.

and committed the fatal error of overlooking Keynes’s requirement that all probabilities require that w > 0.

Utter rubbish.

"We could, if we liked, define a conventional coefficient c of weight and risk, such as c = 2pw/(1+q)(1+w), where w measures the "weight", which is equal to unity when p = l and w = l, and to zero when y = 0 or w = 0, and has an intermediate value in other cases."

"But if doubts as to the sufficiency of the conception of "mathematical expectation" be sustained, it is not likely that the solution will lie, as D'Alembert suggests, and as has been exemplified above, in the discovery of some more complicated function of the probability wherewith to compound the proposed good. The judgment of goodness and the judgment of probability both involve somewhere an element of direct apprehension, and both are quantitative." - pgs 315-316, "Treatise on Probability."

In other words, Keynes considered w = 0, and while his model leaves the resulting probability to complete ambiguity, i.e. c = 0, he nevertheless claimed, as Richard Von Mises noted correctly, that Keynes believed that when there are any doubts, such as c = 0, Keynes suggested going ahead and use "good judgment" and assign a quantitative number anyway. Keynes said that the answer is not found through a more rigorous mathematical formulation.

Brady probably just looked at Keynes' formulation, saw that when w = 0, then c = 0, and then thought "that means Keynes requires w > 0 to determine probability." Brady seemed to have failed to read the very next paragraph where Keynes said when the mathematics are doubtful, go ahead and assign a probability anyway. That was R. Von Mises' criticism, and it is a valid one.

4. "Empirical probabilities are based not on intuition or analogies, but rather on performing a random experiment over and over again, and observing the relative occurrences of each possible outcome and assigning a percentage statistic to each one"

That is called induction (or inductive reasoning), not deduction.

5. "Empirical probabilities are based not on intuition or analogies, but rather on performing a random experiment over and over again, and observing the relative occurrences of each possible outcome and assigning a percentage statistic to each one"

That is called induction (or inductive reasoning), not deduction

Please try to keep up. I wasn't claiming that empirical probabilities are a form of deduction. I said that empirical probabilities are NOT deduction.

Empirical induction is precisely what Keynes was not espousing, as Rothbard showed, in intuition and analogies in forming probability estimates. That's the criticism, and by what you just said, you agree with Rothbard!

It's like you confused yourself into refuting yourself.

6. "I wasn't claiming that empirical probabilities are a form of deduction."

Oh, jeez, "Major_Freedom" - I should have known.

7. "I wasn't claiming that empirical probabilities are a form of deduction. I said that empirical probabilities are NOT deduction."

You did nothing of the sort. Your statement:

"Intuition and analogies are an a priori category of propositions."

8. No, Keynes was not a subjectivist. It was Richard von Mises's mistake to consider him a subjectivist, when his theory was clearly described by others as a "logical relationist" theory of probability. I own a Phoenix Books re-print, and it clearly considers J.M. Keynes to be of the logical tradition.

9. "I wasn't claiming that empirical probabilities are a form of deduction. I said that empirical probabilities are NOT deduction."

You did nothing of the sort. Your statement:

"Intuition and analogies are an a priori category of propositions."

You are hopelessly confused.

That statement is consistent with the statement that empirical probabilities are not deduction.

Intuition and analogies are not empirical categories of thought.

You're right. Probabilities is something you don't understand.

10. Blue Aurora:

"No, Keynes was not a subjectivist. It was Richard von Mises's mistake to consider him a subjectivist, when his theory was clearly described by others as a "logical relationist" theory of probability. I own a Phoenix Books re-print, and it clearly considers J.M. Keynes to be of the logical tradition."

No, Keynes was a subjectivist. It was R. Von Mises' correct identification.

Keynes' claiming that his theory is "logical relationist" is no more proof than Popper's theory is rationalist on account of him calling himself a critical rationalist.

You can't go by just names. You have to go by arguments and meanings. What Keynes argued was subjectivist.

11. He was not subjectivist. Concepts like the "weight of evidence" imply some consideration of objectivity. Going by the same logic, just because von Mises labelled Keynes a "subjectivist" doesn't mean he's correct either.

Keynes was basically providing a precursor to imprecise probability. Theodore Hailperin, a mathematician who has written on Keynes, confirms that Keynes was building upon Boole, and was not of the subjectivist tradition. Brady has cited Hailperin in this paper, and goes onto argue that Keynes was in fact, an early logical empiricist in another.

http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1546726

http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1920578

12. Yes, he was a subjectivist.

His concept of "weight of evidence" was not limited to objective empirical observations. He said that when mathematics is lacking, that one should use "sound judgment" based on intuition, and analogy. That is subjectivism.

13. I will wander into this fray, with the observation that David seems to miss the point of Keynes' work, and does so with the self-certainty so characteristic of those who often miss the point. To quote David:
"Fifth [citing Brady's eminently sound critiques], the probability relation is not deduced. It is perceived by the decision maker based on intuition, analogy and pattern recognition.".... "That means [writes David] it is deduced."

Hello?

David then goes on to assert - and this is precisely the immobilized mindset Keynes sought to move beyond, that "Empirical probabilities are based not on intuition or analogies, but rather on performing a random experiment over and over again, and observing the relative occurrences of each possible outcome and assigning a percentage statistic to each one."

Not what is at issue for Keynes! This shows his failure to understand what Keynes is talking about.

However, it is late, and I have no objective of getting into a catfight with David - only to assert that he misses the point.

14. Thanks for pointing that out, gfwt.