Coherence of rules for defining conditional possibility

Possibility measures and conditional possibility measures are given a behavioural interpretation as marginal betting rates against events. Under this interpretation, possibility measures should satisfy two consistency criteria, known as ‘avoiding sure loss’ and ‘coherence’. We survey the rules that have been proposed for defining conditional possibilities and investigate which of them satisfy our consistency criteria in two situations of practical interest. Only two of these rules satisfy the criteria in both cases studied, and the conditional possibilities produced by these rules are highly uninformative. We introduce a new rule that is more informative and is also coherent in both cases.