I will argue that when Keynes states that, in general, probabilities are not susceptible to numerical estimation, he is arguing that the probabilities, in general, can’t be represented by single number answers or point estimates. But they can be represented by intervals. Keynes’s general...

Frank P Ramsey’s critique of Keynes’s logical Theory of Probability, presented in 1925 and published in 1930, is so weak and poor that J M Keynes or Bertrand Russell could easily have refuted and decimated Ramsey’s claims in the space of one half of an hour to one hour at Keynes’s...

Keynes's initial, introductory presentation of his inexact measurement, approximation approach to interval valued probability occurred on pages 38-40 of chapter III of the A Treatise on Probability. Keynes used a simple diagram on page 38 to illustrate the non linear and non additive nature of...

Economists, working in the Heterodox schools of economics, have severely confused Keynes's interval valued probability–weight of the evidence approach to decision making from the A Treatise on Probability, that Keynes integrated into the General Theory by way of his definition of uncertainty...

Evidence shows that (i) people overweight low probabilities and underweight high probabilities, but (ii) ignore events of extremely low probability and treat extremely high probability events as certain. The main alternative decision theories, rank dependent utility (RDU) and cumulative prospect...

This paper discusses models of choice under imprecise objective probabilistic information featuring beliefs about beliefs -- second order beliefs. A new model, called Second Order Dual Expected Utility (SODEU) featuring non-additive second order beliefs is introduced, axiomatized and...

The psychological basis for rank-dependent probability weighting, and for an inverse-S probability weighting function (PWF) in particular, has often been questioned. I examine the existence and shape of the PWF in a model allowing for optimism/pessimism over probability distributions and for...

Two of the most well known regularities observed in preferences under risk and uncertainty are ambiguity aversion and the Allais paradox. We study the behav- ior of an agent who can display both tendencies simultaneously. We introduce a novel notion of preference for hedging that applies to both...

Stochastic independence has a complex status in probability theory. It is not part of the definition of a probability measure, but it is nonetheless an essential property for the mathematical development of this theory. Bayesian decision theorists such as Savage can be criticized for being...