There is at least one case in which an apparent instance of the conjunction fallacy is not fallacious. It happens when we consider bounded rational agents rather than the more idealized unbounded rational agents typical of Bayesianism. Bounded rationality assumes that there may be some limits on the cognitive powers of the agent and looks at a concept of rationality within these constraints. In many ways it is more relevant to human decision making than unbounded rationality, though it is much less theoretically developed. In certain cases, it is (boundedly) rational to assign a higher probability to a stronger claim than one would assign to a weaker version, if the stronger claim helps to explain why the weaker one might be true (and some other conditions are met). Consider this test question (try it for yourself, with Group 1 first):
Group 1: What is your degree of belief in the following:
a) Cats can’t see better than humans in complete darkness
Now stop and think of your degree of belief, then go on
Group 2: What is your degree of belief in the following:
b) Cats can’t see better than humans in complete darkness and no animals can see in complete darkness.