What is Keynes's theory on probability?

Answer 1

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This answer is very simple .Keynes's theory is a non additive,non numerical , .interval valued approach.It was extended by Keynes to cover decision weights in chapter 26.It also covers additive,numerical, probability if the weight,w,defined on the unit interval [0,1],equals 1.It can easily deal with ordinal probability by the use of standard conditional probability.

Answer 2

Keynes's theory is based on the work of George Boole.Boole demonstrated that the probability calculus would fail unless the weight of the evidence,Keynes's w, or Johnson's worth of the evidence,also denoted by w,where w ,in both definitions is defined on the unit interval between 0 and 1 was equal to 1.Boole's Famous Challenge problem demonstrated that if w were less than 1,then the probabilities would have to be intervals.Thus, modern theories of probability and statistics must assume that the weight or worth of the evidence must always equal 1.Uncertainty ,in Keynes's system, is handled by interval estimates.This is the case where w < 1.If w= 0,no probabilities can be estimated.If w=1,point estimates can be specified.However, two cases will exist,one for linear probability preferences and one for nonlinear probability preferences.'