 The last section provided an interval-valued utility representation of a person’s preferences over lotteries, on the assumption that lotteries are evaluated in terms of expected utility. Some might find this a bit quick. Why should we assume that people evaluate lotteries in terms of their expected utilities? The vNM theorem effectively shores up the gaps in reasoning by shifting attention back to the preference relation. In addition to Transitivity and Completeness, vNM introduce further principles governing rational preferences over lotteries, and show that an agent’s preferences can be represented as maximising expected utility whenever her preferences satisfy these principles.