degrees of belief help us quantify how much we believe some event A is more/less plausible than some event B. Let us take two statements: A Taylor gets Nobel Prize in Literature B Han shot first For instance, if we want to express “I think its more likely that Taylor gets the prize than Han shot first”:

axioms of degrees of belief universal comparability for two statements A, B, only three states can exist: A \succ B (A more likely) A \prec B (B more likely) A \sim B (equally likely) transitivity if A \succeq B and B \succeq C, then A \succeq C language of probability using this framework, we can then describe the events in terms of probability P(A) > P(B) \Leftrightarrow A \succ B P(A) = P(B) \Leftrightarrow A \sim B See also axiom of probability