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Compatibility of De Groot’s method of finding a consensus with the Bayes rule. (Spanish. English summary) Zbl 0731.62035

Summary: M. H. De Groot’s [J. Am. Stat. Assoc. 69, 118-121 (1974; Zbl 0282.92011)] simple method of reaching a consensus when several decision makers have different prior opinions expressed in terms of p.m.’s is shown to be compatible with the Bayes rule when sample information is included as an aid into decision making. It is proven that updating the priors of the different d.m.’s by means of Bayes theorem and then applying De Groot’s method for reaching a consensus (whenever possible) yields the same as by first reaching a consensus and the applying Bayes theorem to the unanimous p.m.
The key point of the proof is that the transition matrix is also updated in every iteration when sample information is considered by means of the predictive distribution.

MSC:

62C10 Bayesian problems; characterization of Bayes procedures

Citations:

Zbl 0282.92011
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Full Text: DOI

References:

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