Before revision:  As known in the literature, Maximum Likelihood (ML) updating provides one method of such refinement. The present paper provides an axiomatization of ML for preferences admit Maxmin Expected Utility (MEU) representation. ML and Full Bayesian (FB ) are two updating rules with polar opposite methods of refining ambiguous beliefs . The present paper proposes and axiomatizes a new updating rule, Relative Maximum Likelihood (RML), for when a DM's conditional preference is not as extreme as either case.
After revision:  As known in the literature, Maximum Likelihood (ML) updating indicates one example of such a refinement, whereas Full Bayesian (FB) updating does not allow for any refinement. In fact, ML and FB are the two extremes of refining beliefs with likelihood in updating. To capture behaviors between these two extremes, the present paper proposes and axiomatizes a new updating rule, Relative Maximum Likelihood (RML), for when a DM's conditional preference is not as extreme as either case.