Coherent Models for Discrete Possibilistic Systems

We consider discrete possibilistic systems for which the available information is given by one-step transition possibilities and initial possibilities. These systems can be represented by a collection of variables satisfying a possibilistic counterpart of the Markov condition. This means that, given the values assumed by a selection of variables, the possibility that a subsequent variable assumes some value is only dependent on the value taken by the most recent variable of the selection. The one-step transition possibilities are recovered by computing the conditional possibility of any two consecutive variables. Under the behavioural interpretation as marginal betting rates against events these ‘conditional’ possibilities and the initial possibilities should satisfy the rationality criteria of ‘avoiding sure loss’ and ‘coherence’. We show that this is indeed the case when the conditional possibilities are defined using Dempster’s conditioning rule.