But you can have a probability distribution of utility functions. Now that is true only in certain circumstances, but there is a simple model in which you can make a very nice probabilistic statement.
If the state of the world consists of a vector of N real variables, and a utility function is another vector, with the utility being the dot product (meaning all utility functions are linear in those variables), and the expected value of each coefficient is 0
then expected utility can be expressed as the covariance of this vector, and rational behavior maximizes that covariance. So that’s something.
But you can have a probability distribution of utility functions. Now that is true only in certain circumstances, but there is a simple model in which you can make a very nice probabilistic statement.
If the state of the world consists of a vector of N real variables, and a utility function is another vector, with the utility being the dot product (meaning all utility functions are linear in those variables), and the expected value of each coefficient is 0
then expected utility can be expressed as the covariance of this vector, and rational behavior maximizes that covariance. So that’s something.