# J. M. Keynes (D. Ellsberg) versus Ramsey (L. J. Savage –B. de Finetti): The Role of Interval Valued Probability and the Weight of the Evidence (Ambiguity)

33 Pages Posted: 29 Apr 2018

Date Written: April 11, 2018

### Abstract

It is mathematically impossible to integrate a concept like Keynes’s weight of the evidence variable, w, or Ellsberg’s rho, ρ, into a subjective theory of probability explicitly because of the definitions of probability given by de Finetti, Ramsey and Savage. The Ramsey –de Finetti–Savage definition of probability identifies the subjective estimate of probability itself to be the degree of confidence or doubt a decision maker has in the outcome. This directly conflicts with Keynes’s view that the degree of confidence can never have anything to do with the logical probability estimate, which is a degree of rational belief. The degree of confidence estimate that a decision maker has in his estimate of logical probability is entirely separate from the probability estimate. They are completely independent from each other as explicitly stated by Keynes in chapter 6 of the A Treatise on Probability.

The exact same type of analysis holds in the General Theory. The entire Liquidity Preference theory of the rate of interest erected by Keynes in the General Theory in chapters 13-17 is based on the definition of Liquidity Preference. Liquidity Preference is defined as a function of uncertainty. Uncertainty is then defined as a function of the weight of the evidence. Liquidity Preference is not a function of probability. Therefore, the confidence one has in one’s expectations of future outcomes, when the expectations are based on the estimated probabilities, is a conclusion that makes no sense in the subjective theories of Ramsey, de Finetti, Savage and of de Finetti and Savage. It is impossible to talk about the confidence one has in one’s probability estimate because the subjective probability estimate IS the decision maker’s degree of confidence.

Ellsberg’s attempt to convince Savage to change his mind about the nature of and concept of subjective probability, as defined by Savage, was thus doomed to failure from the very beginning. A new definition of subjective probability from Savage (de Finetti or Ramsey) would have been required in order to deal with Ellsberg’s concerns. Savage (de Finetti or Ramsey) would have been forced to abandon their own definition of what subjective probability meant.

It was impossible for Savage, de Finetti, Ramsey, or any advocate of the subjective theory of probability, to accept Ellsberg’s rho or Keynes’s w, as a measure of the confidence a decision maker has in his estimate of a probability, without completely changing their definition of what subjective probability means.

**Keywords:** Ellsberg, Savage, Keynes, interval valued probability, upper and lower probability, indeterminate and imprecise probability

**JEL Classification:** B10, B12, B14, B16, B20, B22

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