On Negative Conglomerability

We focus on the notion of negative conglomerability. This is far less known than its counterpart, conglomerability. Both relate to the combination of conditional and unconditional information, with the latter taking in particular a foundational role in the special case of infinite partitions of the possibility space. The two notions look superficially very similar and are even equivalent in the case of precise probabilistic models. In the present paper, we do a thorough technical study of their relations with other main concepts in the literature, such as marginal extension and dilation, both in the precise and imprecise case. Moreover, we discuss why they are somewhat surprisingly different from the prescriptive point of view, in that conglomerability has a rationality stance that its negative counterpart has not.