It has been claimed on this site that the fundamental question of rationality is "What do you believe, and why do you believe it?".
A good question it is, but I claim there is another of equal importance. I ask you, Less Wrong...
What are you doing?
And why are you doing it?
Sure.
Here's an argument:
Suppose there is a dichotomy of beliefs, X and Y, their probabilities are Px and Py, and the utilities of having each belief is Ux and Uy. Then, the average utility of having belief X is PxUx and the utility of having belief Y is Py\Uy. You "should" choose having the belief (or set of beliefs) that maximizes average utility, because having beliefs are actions and you should choose actions that maximize utility.
What is the flaw in this argument?
For me, the flaw that you should identify is that you should choose beliefs that are most likely to be true, rather than those which maximize average utility. But this is a normative argument, rather than a logical flaw in the argument.
Normally, you should keep many competing beliefs with associated levels of belief in them. The mindset of choosing the action with estimated best expected utility doesn't apply, as actions are mutually exclusive, while mutually contradictory beliefs can be maintained concurrently. Even when you consider which action to carry out, all promising candidates should be kept in mind until moment of execution.