# The Restricted Role of Caprice (Whim) in J M Keynes’s Interval Valued Theory of Probability in the A Treatise on Probability, General Theory, and in the Keynes-Townshend Correspondence of 1937–1938

18 Pages Posted: 29 May 2020

Date Written: May 2, 2020

### Abstract

Keynes recognized that there were a few cases where his rational analysis of decision making under conditions of uncertainty and risk using:

(a) interval valued probability in Parts II and III of the A Treatise on Probability,

(b) decision weights in Part IV of the A Treatise on Probability ,or

(c) safety first, based on the use of Chebyshev’s Inequality, in Part V of the A Treatise on Probability, would result in a stalemate.

Although Keynes introduced his concept of caprice to deal with this problem in Part I in chapter III on p.30 of the A Treatise on Probability, a complete understanding requires a mastery of his mathematical analysis in Chapter XV, where Keynes presented part of his mathematical analysis of his Boolean based theory of imprecise, indeterminate interval valued probability. Once the link between page 30 of Chapter III and Pages 160-163 of Chapter XV is understood, then Keynes’s use of caprice in the General Theory and the Keynes-Townshend correspondence can be seen to be an important, but small, part of his general decision theory of the A Treatise on Probability which he applied as a specific decision theory in economics in the General Theory and after.

**Keywords:** Caprice, Overlapping Interval Valued Probabilities, Upper-Lower Bounds

**JEL Classification:** B10, B12, B14, B16, B18, B20

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