Choice without beliefs

We provide an axiomatic foundation for decision making in a complex environment. We do not assume that the decision maker has complete structural knowledge of the environment. Instead the agent knows the set of actions he can take, he formulates preferences directly on the actions, and chooses according to these preferences. On the basis of experience he modifies these preferences according to a systematic procedure. Our axioms are imposed on this procedure, rather than directly on the choice itself. The axioms consist of a group of natural structural restrictions and a group of independence axioms. Our main result is an axiomatic foundation for a set of simple adaptive learning procedures that include the replicator dynamic.