I mean in a subjective interpretation, a probability function represents the beliefs of one person at one point in time. Equally, a (Jeffrey) utility function can represent the desires of one person at one particular point in time. As such it is a theory of what an agent believes and wants.
Decisions can come into play insofar individual actions can be described by propositions (“I do A”, “I do B”) and each of those propositions is equivalent to a disjunction of the form “I do A and X happens or I do A and not-X happens”, which is subject to the axioms. But decisions is not something which is baked into the theory, much like probability theory isn’t necessarily about urns and gambles.
I mean in a subjective interpretation, a probability function represents the beliefs of one person at one point in time. Equally, a (Jeffrey) utility function can represent the desires of one person at one particular point in time. As such it is a theory of what an agent believes and wants.
Decisions can come into play insofar individual actions can be described by propositions (“I do A”, “I do B”) and each of those propositions is equivalent to a disjunction of the form “I do A and X happens or I do A and not-X happens”, which is subject to the axioms. But decisions is not something which is baked into the theory, much like probability theory isn’t necessarily about urns and gambles.