New conference paper: Conglomerable natural extension
Conglomerable natural extension (preprint pdf)
by Enrique Miranda, Marco Zaffalon and Gert de Cooman
Abstract: We study the weakest conglomerable model that is implied by desirability or probability assessments: the conglomerable natural extension. We show that taking the natural extension of the assessments while imposing conglomerability—the procedure adopted in Walley’s theory—does not yield, in general, the conglomerable natural extension (but it does so in the case of the marginal extension). Iterating this process produces a sequence of models that approach the conglomerable natural extension, although it is not known, at this point, whether it is attained in the limit. We give sufficient conditions for this to happen in some special cases, and study the differences between working with coherent sets of desirable gambles and coherent lower previsions. Our results indicate that it might be necessary to re-think the foundations of Walley’s theory of coherent conditional lower previsions for infinite partitions of conditioning events.
Accepted for presentation at ISIPTA’11 and for publication in the ISIPTA’11 Proceedings.
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