Divisive Conditioning: Further Results on Dilation

Timothy Herron, Teddy Seidenfeld, and Larry Wasserman


Conditioning can make imprecise probabilities uniformly more imprecise. We call this effect ``dilation.'' In a previous paper, Seidenfeld and Wasserman (1993) established some basic results about dilation. In this paper, we further investigate dilation in several models. In particular, we consider conditions under which dilation persists under marginalization and we quantify the degree of dilation. We also show that dilation manifests itself asymptotically in certain robust Bayesian models and we characterize the rate at which dilation occurs. Key words and phrases: Conditioning, dilation, -contamination, imprecise probabilities, total variation distance.