The social entropy process: axiomatising the aggregation of probabilistic beliefs. (English) Zbl 1206.03025

Hosni, Hykel (ed.) et al., Probability, uncertainty and rationality. Pisa: Edizioni della Normale (ISBN 978-88-7642-347-5/hbk). Centro di Ricerca Matematica Ennio De Giorgi (CRM) Series (Nuova Serie) 10, 87-104 (2010).
From the introduction: The present work stems from a desire to combine ideas arising from two historically different schemes of probabilistic reasoning, each having its own axiomatic traditions, into a single broader axiomatic framework, capable of providing general new insights into the nature of probabilistic inference in a multiagent context. In the present sketch of our work we first describe briefly the background context, and we then present a set of natural principles to be satisfied by any general method of aggregating the partially defined probabilistic beliefs of several agents into a single probabilistic belief function. We will call such a general method of aggregation a social inference process. Finally we define a particular social inference process, the Social Entropy Process (abbreviated to SEP), which satisfies the principles formulated earlier. SEP has a natural justification in terms of information theory, and is closely related to the maximum entropy inference process: indeed it can be regarded as a natural extension of that inference process to the multiagent context.
By way of comparison, for any appropriate set of partial probabilistic beliefs of an isolated individual the well-known maximum entropy inference process, ME, chooses a probabilistic belief function consistent with those beliefs. We conjecture that SEP is the only “natural” social inference process which extends ME to the multiagent case, always under the assumption that no additional information is available concerning the expertise or other properties of the individual agents.
Proofs of the results in the present paper, while reasonably straight forward, have mostly not been included, but will be included in a more detailed version of this work which will appear elsewhere.
For the entire collection see [Zbl 1186.03005].


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