Thank you for your comment.Unfortunately, Kolmogorov's axiom system assumes linearity and additivity. His precise or point estimate approach to probability gives correct answers only in those fields where the weight of the evidence, w, equals, approximates, or approaches 1 in the limit. It is in many of the areas of physics, chemistry, biology ,and engineering where the weight of the evidence is close to 1,where w, the weight of the evidence ,is defined on the unit interval between 0 and 1.w=1 means you are able to define a sample space of all possible outcomes before you begin your experiment or analysis.
Keynes's approach is based on Boole's indeterminate approach to probability and uses intervals, not point estimates ,because in many instances, especially in social science, liberal arts , economics, business, finance , and public policy, there is substantial missing evidence that will never be available to the decision maker when he must make a choice. Boole's system, Keynes's version, and Hailperin's 1986 linear programming approach ,would treat Kolmogorov's approach as a special case where w=1.