Jeffrey’s conditioning rule in neighbourhood models

Neighbourhoods of classical probability measures, presented in the form of interval probabilities, are studied in the paper. The main goal is a characterization of two important classes, convex and bi-elastic neighbourhoods. Those two classes are equivalently characterized through closure conditions with respect to Jeffrey’s rule of conditioning. Moreover, some other interpretations of the closure property are given, including a description of behaviour of conditional expectation under the lower and upper expectation operators. This description is useful for a better understanding of some models in the theory of choice under risk. Further, closure under Jeffrey’s rule can serve as an extension rule for partially determined interval probabilities.