In the case of the exponential family of distributions it is well known that the use of a prior distribution belonging to the natural conjugate family substantially simplifies the analysis whilst often being realistic in applications. The present paper explores the related idea of a conjugate family of utilities, and generally the notion of choosing a utility structure that is suitably "matched" to the probability structure and, at the same time, realistic in application.
"A Class of Utility Functions." Ann. Statist. 4 (1) 1 - 10, January, 1976. https://doi.org/10.1214/aos/1176343343