Multi-Bayesian Statistical Decision Theory

SUMMARY A solution is proposed to the problem of finding ajoint decision procedure for a group of n persons. It is any Pareto optimal solution which maximizes the generalized Nash product over the set of jointly achievable utility n-vectors. This result was originally proposed in the theory of bargaining but is readily adapted to the statistical context. The individuals involved need not have identical utility functions or identical prior (posterior) distributions. The solution may be a non-randomized rule but is randomized when the individual opinions or preferences are sufficiently diverse. Applications to hypothesis testing and estimation are included.