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The irrelevant information principle for collective probabilistic reasoning. (English) Zbl 1297.68221

Summary: Within the framework of discrete probabilistic uncertain reasoning a large literature exists justifying the maximum entropy inference process, ME, as being optimal in the context of a single agent whose subjective probabilistic knowledge base is consistent. In particular Paris and Vencovská completely characterised the ME inference process by means of an attractive set of axioms which an inference process should satisfy. More recently the second author extended the Paris-Vencovská axiomatic approach to inference processes in the context of several agents whose subjective probabilistic knowledge bases, while individually consistent, may be collectively inconsistent. In particular he defined a natural multi-agent extension of the inference process ME called the social entropy process, SEP. However, while SEP has been shown to possess many attractive properties, those which are known are almost certainly insufficient to uniquely characterise it. It is therefore of particular interest to study those Paris-Vencovská principles valid for ME whose immediate generalisations to the multi-agent case are not satisfied by SEP. One of these principles is the Irrelevant Information Principle, a powerful and appealing principle which very few inference processes satisfy even in the single agent context. In this paper we will investigate whether SEP can satisfy an interesting modified generalisation of this principle.

MSC:

68T37 Reasoning under uncertainty in the context of artificial intelligence
03B48 Probability and inductive logic
94A17 Measures of information, entropy
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