Choosing Among Utility Functions: Guidance from Maximum Certain Equivalent Error

Although utility functions are a basic component of decision analysis, there are a variety of functional forms that can be used. For small decisions, the choice might not change the decision. But different utility functions can provide vastly different recommendations for large decisions. There are qualitative recommendations on which utility functional form to use. But there is no exact answer to how large uncertainties can be before modeling risk preferences or modeling risk preference as a function of wealth is required. By maximizing the certain equivalent error between different utility functions, this paper analyzes and provides guidance into how large uncertainties can become relative to a decision maker’s wealth before risk aversion should be modeled and when risk aversion needs to be modeled as a function of wealth.