It’s possible to view utility functions just like probability functions (“probability distributions”), namely as rational restrictions on a subjective state of mind at a particular point in time. Utilities can describe desires, just as probabilities can describe beliefs. That doesn’t cover multi-agent rationality, or diachronic changes over time, but that isn’t much different from probability theory. (Richard Jeffrey’s axiomatization of utility theory is expressed for such a “subjective Bayesian” purpose, but unfortunately it isn’t well known.)
It’s possible to view utility functions just like probability functions (“probability distributions”), namely as rational restrictions on a subjective state of mind at a particular point in time. Utilities can describe desires, just as probabilities can describe beliefs. That doesn’t cover multi-agent rationality, or diachronic changes over time, but that isn’t much different from probability theory. (Richard Jeffrey’s axiomatization of utility theory is expressed for such a “subjective Bayesian” purpose, but unfortunately it isn’t well known.)