Can an irrational agent reason himself to rationality?

When an agent that accepts transitivity of preferences as a principle of rationality finds himself expressing intransitive preferences, he has to change some of his expressed preferences so that transitivity will be restored. When such an agent also believes in the existence of some independent betterness relation among the alternatives over which he forms his preferences, it is reasonable to demand that the way he changes his intransitive expressed preferences will be sensitive to his beliefs regarding this betterness relation. It is shown that under two natural conditions for such sensitivity, in case there are infinitely many alternatives, the agent must end up being indifferent between all alternatives except two. Some implications of this result for ethics are discussed.