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Further evidence against independence preservation in expert judgement synthesis. (English) Zbl 0619.62011

The authors present arguments against the following recommendation to a decision maker: form your own probability distribution by combining the opinions of a number of experts in such a way as to preserve any form of expert agreement regarding the indepence of the events of interest.
It is shown that for probability spaces containing at least five points a large class of seemingly reasonable combination methods excludes all independence preserving formulas except those which pick a single expert. In the case where at most four alternatives are present, the same conditions admit a richer variety of non-dictatorial methods which are also characterized.
Reviewer: M.Huškova

MSC:

62C99 Statistical decision theory
39B99 Functional equations and inequalities
62A01 Foundations and philosophical topics in statistics
62C05 General considerations in statistical decision theory
91B06 Decision theory
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