[S]ometimes an agent is more rational for acting against her better judgment than she would be if she acted in accordance with her best judgment... there are cases where following her best judgment would make the agent significantly irrational, while acting akratically would make her only trivially so. (p.36)
This is so in cases where one's "best judgment" is itself completely irrational -- a point I previously made in my post on 'Subjective Oughts'. Though this fact is often neglected, I don't think there's any sane view of rationality on which S believes that φ-ing is rational implies that S rationally ought to φ. Even on the most 'internalist' views, e.g. coherentism, it's possible to have false beliefs about what would be most coherent. That is, I might think that believing P is rational (and would increase the coherence of my belief-set), when in fact this is false and my belief set would be more coherent on the whole were it to contain not-P instead. Coherentism then straightforwardly entails that I ought to believe not-P, despite the fact that I believe that I rationally ought to believe P. The higher-order judgment is just wrong. And the same may be true in case of practical rationality, i.e. I may hold false views about what I rationally ought to do or desire. Following my judgment, in such a case, would not in fact be rational.
Once stated explicitly like this, the point seems very obviously correct. I guess one possible point of resistance could arise in readers who fail to distinguish what Arpaly calls an "account" of rationality from an "instruction manual". (Cf. the traditional distinction between the 'criteria of rightness' and a 'decision procedure'.) Obviously an instruction manual can't contain advice of the form, "Go against your all-things-considered better judgment", or "Do X, for a reason other than that this rule advises it", or "Don't think of an elephant". None of this is advice you can follow. Nonetheless, they may be true statements of what it would in fact be most rational for you to do in the circumstances. As I keep stressing, trying hard is no guarantee of rationality. Sometimes (though hopefully not often) one's efforts may even be counterproductive* -- this is perhaps most familiar in case of neurotic "over-analyzing", but another example would be overriding one's reliable (reasons-responsive) gut instincts with bad reasoning or rationalizations.
One virtue of Arpaly's discussion is that she highlights how (implicitly) familiar this point is in everyday life. We're all familiar with the idea of "a man who has some 'crazy notions' sometimes but whose common sense prevails 'in real life.'" (p.49) Most people aren't philosophers, or even particularly competent reasoners, so their explicit judgments may end up being downright dopey. If they fully internalized and acted on these dopey explicit beliefs, we might consider these folks fanatics. But because Uncle Bob doesn't really 'live out' or act on his dopey "best judgment" -- being instead restrained by his implicit "common sense", practical wisdom, and basic human decency (though he doesn't consciously realize it) -- we may judge that he is rational enough on the whole. His irrationality is restricted to his explicit beliefs, and he's otherwise ("in real life") not so bad. Akrasia -- failing to act on his explicit 'better judgment' -- thus makes him comparatively more rational than the fanatic he otherwise would have been. (Though of course he'd be even more rational if he didn't have such dopey explicit beliefs in the first place.)
* Stronger still: sometimes any attempt at explicit deliberation might prove to be essentially less-than-optimally rational. This point is more familiar in the context of ethics, where we may be required to respond directly to a person in need rather than mediating our response by any kind of deliberate moral theorizing. The person who considers the permissibility of saving his drowning wife before jumping in clearly has "one thought too many", as Bernard Williams puts it. We want people to be sensitive to moral considerations, but that doesn't require -- and sometimes precludes -- consciously deliberating about such things.