  This paper studies a new and more general axiomatization than one presented
previously for preference on likelihood gambles. Likelihood gambles describe
actions in a situation where a decision maker knows multiple probabilistic
models and a random sample generated from one of those models but does not know
prior probability of models. This new axiom system is inspired by Jensen's
axiomatization of probabilistic gambles. Our approach provides a new
perspective to the role of data in decision making under ambiguity. It avoids
one of the most controversial issue of Bayesian methodology namely the
assumption of prior probability.
