About Subjective Probability

The main purpose of this note is to study Anscombe and Aumann’s [1963] definition of subjective probability and their contributions to decision theory. We emphasize their main ideas, and we revise the framework that they proposed and which became one of the most used in axiomatizations in decision theory. We also develop a new framework to derive subjective probabilities based on the Cartesian product of two sets. We show how two simple axioms allow us to define a subjective probability on a state space of primary interest, given an auxiliary set endowed with an objective probability.