THE UTILITY OF INFINITE MENUS

It is sometimes concluded from the St. Petersburg paradox that von Neumann-Morgenstern utility functions must be bounded. Some axiom systems for expected utility avoid this conclusion and allow for unbounded utility functions. This note goes a step further and constructs an axiom system which may yield a utility function that takes the value plus infinity. Such a utility function is potentially applicable in situations where 'blank checks' or 'infinite menus' are ranked along with other prospects.