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Morris H. DeGroot, Stephen E. Fienberg, The Comparison and Evaluation of Forecasters, Journal of the Royal Statistical Society. Series D (The Statistician), Vol. 32, No. 1/2, Proceedings of the 1982 I.O.S. Annual Conference on Practical Bayesian Statistics (Mar. - Jun., 1983), pp. 12-22
DeGroot et al. (Tue,) studied this question.