Before revision: In decision theory, the von Neumann–Morgenstern (VNM) utility theorem shows that , under certain axioms of rational behavior, a decision-maker faced with risky (probabilistic) outcomes of different choices will behave as if they are maximizing the expected value of some function defined over the potential outcomes at some specified point in the future .
After revision: In decision theory, the von Neumann–Morgenstern (VNM) utility theorem showing that rational choice under uncertainty the preferences requires decisions that take the form of maximizing the expected value of some cardinal utility function .