Updating confidence in beliefs

This paper develops a belief update rule under ambiguity, motivated by the maxim: in face of new information, retain those conditional beliefs which you are more confident, and relinquish only have less confidence. We provide preference-based axiomatisation, drawing on account confidence developed Hill (2013). The proposed constitutes general framework several existing rules for multiple priors (Full Bayesian, Maximum Likelihood) special cases, but avoids problems that these with updating complete ignorance. Moreover, it can handle surprising null events, such as crises or reasoning games, recovering traditional approaches, probability systems, cases.