A Separation of Utility and Beliefs Through Betting Consistency

For standard preferences under uncertainty, minimal requirements are proposed to identify cardinal utility and subjective, potentially nonadditive, beliefs. This is achieved through an application of betting consistency . This preference principle says that outcome midpoints derived from preferences over bets on an event are also midpoints when elicited from bets on a different event. This consistency requirement provides a simplified elicitation tool, while it also serves as a robustness test for utility measurements. An analyst can use betting consistency to identify a client’s cardinal utility index independent of the client’s beliefs. This follows from our simplified foundation for the biseparable utility model, the widely adopted framework for empirical measurements of utility under various sources of uncertainty. As a theoretical tool, betting consistency can be adopted to provide simple and intuitive foundations for new and for existing decision theories. For instance, an event-dependent version of betting consistency, if it is supplemented with Savage’s sure-thing principle or a version of that principle restricted to acts that satisfy Schmeidler’s comonotonicity property, delivers subjective expected utility or Choquet expected utility, as desired. We also demonstrate how models with specific nonadditive beliefs can easily be derived through bespoke formulations of betting consistency.