Let's suppose that if you believe that when you believe you have a chance X to succeed, you actually have a chance 0.75 X to succeed (because you can't stop your beliefs from influencing your behavior). The winning strategy seems to believe in 100% success, and thus succeed in 75% of cases. On the other hand, trying too much to find a value of X which brings exact predictions, would bring one to believing in 0% success... and being right about it. So in this (not so artificial!) situation, a rationalist should prefer success to being right.
But in real life, unexpected things happen. Imagine that you somehow reprogram yourself to genuinely believe that you have 100% of success... and then someone comes and offers you a bet: you win $100 if you succeed, and lose $10000 if you fail. In you genuinely believe in 100% success, this seems like an offer of free money, so you take the bet. Which you probably shouldn't.
For an AI, a possible solution could be this: Run your own simulation. Make this simulation believe that the chance of success is 100%, while you know that it really is 75%. Give the simulation access to all inputs and outputs, and just let it work. Take control back when the task is completed, or when something very unexpected happens. -- The only problem is to balance the right level of "unexpected"; to know the difference between random events that belong to the task, and the random events outside of the initially expected scenario.
I suppose evolution gave us similar skills, though not so precisely defined as in the case of AI. An AI simulating itself would need twice as much memory and time; instead of this, humans use compartmentalization as an efficient heuristic. Instead of having one personality that believes in 100% success, and another that believes in 75%, human just convices themselves that the chance of success is 100%, but prevents this belief from propagating too far, so they can take the benefits of the imaginary belief, while avoiding some of its costs. This heuristic is a net advantage, though sometimes it fails, and other people may be able to exploit it: to use your own illusions to bring you to a logical decision that you should take the bet, while avoiding a suspicion of something unusual. -- In this situation there is no original AI which could take over control, so this strategy of false beliefs is accompanied by a rule "if there is something very unusual, avoid it, even if it logically seems like the right thing to do". It means to not trust your own logic, which in a given situation is very reasonable.
I do this every day, correctly predicting I'll never succeed at stuff and not getting placebo benefits. Don't dare try compartmentalization or self delusion for the reasons Eliezer has outlined. Some other complicating factors. Big problem for me.
We in the rationalist community have believed feasible a dual allegiance to instrumental and epistemic rationality because true beliefs help with winning, but semi-autonomous near and far modes raise questions about the compatibility of the two sovereigns' jurisdictions: false far beliefs may serve to advance near interests.
First, the basics of construal-level theory. See Trope and Liberman, "Construal-Level Theory of Psychological Distance" (2010) 117 Psychological Review 440. When you look at an object in the distance and look at the same object nearby, you focus on different features. Distal information is high-level, global, central, and unchanging, whereas local information is low-level, detailed, incidental, and changing. Construal-level theorists term distal information far and local information near, and they extend these categories broadly to embrace psychological distance. Dimensions other than physical distance can be conceived as psychological distance by analogy, and these other dimensions invoke mindsets similar to those physical distance invokes.
I discuss construal-level theory in the blogs Disputed Issues and Juridical Coherence, but Robin Hanson at Overcoming Bias has been one of the theory's most prolific advocates. He gives the theory an unusual twist when he maintains that the "far" mode is largely consumed with the management of social appearances.
With this twist, Hanson effectively drives a wedge between instrumental and epistemic rationality because far beliefs may help with winning despite or even because of their falsity. Hanson doesn't shrink from the implications of instrumental rationality coupled with his version of construal-level theory. Based on research reports that the religious lead happier and more moral lives, Robin Hanson now advocates becoming religious:
Perhaps, like me, you find religious beliefs about Gods, spirits, etc. to be insufficiently supported by evidence, coherence, or simplicity to be a likely approximation to the truth. Even so, ask yourself: why care so much about truth? Yes, you probably think you care about believing truth – but isn’t it more plausible that you mainly care about thinking you like truth? Doesn’t that have a more plausible evolutionary origin than actually caring about far truth? ("What Use Far Truth?")
Instrumental rationalists could practice strict epistemic rationality if they define winning as gaining true belief, but though no doubt a dedicated intellectual, even Hanson doesn't value truth that much, at least not "far" truth. Yet, how many rationalists have cut their teeth on the irrationality of religion? How many have replied to religious propaganda about the benefits of religion with disdain for invoking mere prudential benefit where truth is at stake? As an ideal, epistemic rationality, it seems to me, fares better than instrumental rationality.