# Essays on Risk and Uncertainty: Comparing J. M. Keynes and the Von Mises Brothers, Richard and Ludwig, on Probability and Decision Theory

36 Pages Posted: 20 Nov 2016

Date Written: November 18, 2016

### Abstract

Richard von Mises set forth a Limiting Frequency approach to probability for use primarily in physics and some areas of biology, chemistry and engineering. Emphasis was placed on the existence of series or sequences of events that resulted from a known generating mechanism. The series consisted of repeated, homogeneous events that were identical to each other, except for their particular place selection in an infinite series. This conception of probability is extremely limited and can play only a very limited role in liberal arts, social science, behavioral science, and especially in economics, business, and finance.

Ludwig von Mises conception was that there were two different concepts of probability. First, there was a class concept of probability that was basically a version of a limiting frequency interpretation of probability. He had a second conception that he called case probability. Case probability was supposed to deal with unique events. It essentially is a subjective degree of belief approach that allows one to calculate no more than an ordinal relationship. Ludwig Von Mises is thus not a Bayesian Subjectivist. His dual approach to probability is reminiscent of Rudolf Carnap, although it is greatly underdeveloped technically when compared to Carnap.

J. M. Keynes’s conception of probability is a logical theory of probability built on G. Boole’s earlier logical theory of probability. Keynes’s theory deals with the degree of rational belief one should believe and act on. It is not “a” or “the” degree of belief used by Subjectivists. It was a relative concept, which means that all probabilities are conditional probabilities. There is an objective probability relation that holds between a given body of evidence, the premises, E, and a conclusion or hypothesis, H. Thus, P (H/E) =α. The objective probability relation measures the degree of similarity (dissimilarity) that exists between the evidence, E (premises), and the conclusion or Hypothesis, H.

There are many severe and numerous errors in Richard Von Mises book, Probability, Statistics and Truth, regarding Keynes’s logical theory of probability that will be identified and corrected in this paper. Neither of the Von Mises brothers understood Keynes’s interval valued approach to probability or had any clear cut understanding of the concept of weight or decision weights like Keynes’s conventional coefficient in chapter 26 of the A Treatise on Probability, although such an approach appears out of nowhere in Probability, Statistics and Truth in Lecture 4.

Ludwig von Mises’s conception of case probability has no developed concept of the weight of the evidence underlying it. Its identification of probability as being ordinal probability would be too weak from Keynes’s point of view to help an entrepreneur in making decisions related to his revenues and costs and the question of whether he should invest in fixed capital now or wait to do so at some time in the future (liquidity preference and user cost of capital issues).

**Keywords:** Principle of Indifference,Keynes, Laplace,a priori probability,interval valued probability

**JEL Classification:** B10,B12,B20,B22

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