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Information and probability: collectors and Shannon compositivity. (English) Zbl 0258.94015
Assume that some class of events is observed by a set of observers. Each of them evaluates the amount of information contained in one event according to his own scale or feelings. The problem, studied by J. Kampé de Fériet [C. R. Acad. Sci., Paris, Sér. A 269, 1081–1085 (1969; Zbl 0195.49003)] deals with the possibility of collecting the amount of information given by each observer, taking into account the reliability, or confidence in the observers. It has been assumed that this collection is represented by an operator (collector).
In the present paper the authors investigate the consistency between the existence of a collector and compositivity according to Shannon’s composition law when it is assumed that the confidence in each observer is also a function of the observed event. The main corollary is that this consistency implies a confidence which in general cannot depend on the event. This motivates information measures which do not imply probability (that is, which either are not compositive or do not obey Shannon’s composition law).
Reviewer: S. Kotz

MSC:
94A17 Measures of information, entropy
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