Substitutability (Utility Theory)

utility-theory

Definition

Substitutability (Utility Theory)

If an agent is indifferent between $A$ and $B$, then it is indifferent between two more complex lotteries that are the same except that $B$ is substituted for $A$:

$$A\sim B⟹[p,A;1-p,C]\sim [p,B;1-p,C]$$

This holds for preference $\succ$ instead of indifference $\sim$ as well.