In Ellsberg paradox, decision makers that are partially informed about the actual probability distribution violate the expected utility paradigm. This paper develops a theory of decision making with a partially specified probability. The paper takes an axiomatic approach using Anscombe-Aumann's...

A likelihood order is defined over linear subspaces of a finite dimensional Hilbert space. It is shown that such an order that satisfies some plausible axioms can be represented by a quantum probability in two cases: pure state and uniform measure