What is Dempster-Shafer's model?

Several mathematical models have been proposed for the modelling of someone's degrees of belief. The oldest is the Bayesian model that uses probability functions. The upper and lower probabilities (ULP) model, Dempster's model, the evidentiary value model (EVM) and the probability of modal propositions somehow generalize the Bayesian approach. The transferable belief model (TBM) is based on other premises and uses belief functions. None of these models is THE best: each has its own domain of application. We spell out through examples what are the underlying hypotheses that lead to the selection of an adequate model for a given problem. We give indications on how to choose the appropriate model. The major discriminating criterion is: if there exists a probability measure with known values, use the Bayesian model, if there exists a probability measure but with some unknown values, use the ULP models, if the existence of a probability measure is not known, use the TBM. Dempster's model is essentially a special case of ULP model. The EVM and the probability of modal propositions (provability, necessity...) corresponds to a special use of the Bayesian model.