My answer to the question asked in the paper’s title is: akratic action-acting contrary to what one believes or knows is the best course of action open to one, or “weakness of will”—is not rational at all, according to Aristotle (here restricting myself to his discussion of akrasia in the Nicomachean Ethics, VII. 1-3). In saying that it is ‘not rational at all,’ I have in mind that there is no “intellectual,” or “cognitive,” faculty at work which so much as helps to bring about the akratic act-there is, in other words, no way in which the akrates “figures out” how to perform the akratic act.
Mooney, Patrick, "Aristotle on Akratic Action: How Rational Is It?" (1998). The Society for Ancient Greek Philosophy Newsletter. 453.