Controlling Bayes and/or minimax risks under possibly different loss functions is formulated as a problem faced by two or more statisticians who must compromise and agree on the use of a single decision procedure. The theory characterizing solutions to Bayes compromise problems and minimax-Bayes compromise problems is presented. In a Bayes compromise problem, Bayes risks under different prior distributions and/or loss functions are minimized simultaneously. In a minimax-Bayes compromise problem, a Bayes risk under some loss function for a given prior distribution and a maximum risk under a possibly different loss function are minimized simultaneously.
"Controlling Risks under Different Loss Functions: The Compromise Decision Problem." Ann. Statist. 16 (4) 1594 - 1608, December, 1988. https://doi.org/10.1214/aos/1176351055