Conglomerable Coherent Lower Previsions

Abstract

Walley’s theory of coherent lower previsions builds upon the former theory by Williams with the explicit aim to make it deal with conglomerability. We show that such a construction has been only partly successful because Walley’s founding axiom of joint coherence does not entirely capture the implications of conglomerability. As a way to fully achieve Walley’s original aim, we propose then the new theory of conglomerable coherent lower previsions. We show that Walley’s theory coincides with ours when all conditioning events have positive lower probability, or when conditioning partitions are nested.