The math you are using does not describe reality and rational people, since about Galileo anyway, have known better than to insist on broken models. First of a

The math you are using does not describe reality and rational people, since about Galileo anyway, have known better than to insist on broken models. First of all, it's a textbook exercise in topology to show that any rational decision process must have a utility function (at least for a countably infinite set of choices). Let me repeat the statement for utility functions. Suppose I have a 1% chance of being CEO and increasing my utility to U(CEO pay) - U(my pay). Suppose this increases to U(10x CEO pay) - U(my pay). It's simple arithmetic that 0.01 x U(10X CEO pay) + 0.99 x U(my pay) > 0.01 x U(CEO pay) + 0.99 x U(my pay). Rearranging the arithmetic, this is merely the statement that U(10X CEO pay) > U(CEO pay) - i.e. I'll be happier as a CEO with 10M than with 1M. Do you disagree with this statement?