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JulianMorrison comments on Rationality is Systematized Winning - Less Wrong
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Rationalists are the ones who win when things are fair, or when things are unfair randomly over an extended period. Rationality is an advantage, but it is not the only advantage, not the supreme advantage, not an advantage at all in some conceivable situations, and cannot reasonably be expected to produce consistent winning when things are unfair non-randomly. However, it is a cultivable advantage, which is among the things that makes it interesting to talk about.
A rationalist might be unfortunate enough that (s)he does not do well, but ceteris paribus, (s)he will do better. Maybe that could be the slogan - "rationalists do better"? With the implied parenthetical "(than they would do if they were not rationalists, with the caveat that you can concoct unlikely situations in which rationality is an impediment to some values of "doing well")".
"You can't reliably do better than rationality in a non-pathological universe" is probably closer to the math.
It's impossible to add substance to "non-pathological universe." I suspect circularity: a non-pathological universe is one that rewards rationality; rationality is the disposition that lets you win in a nonpathological universe.
You need to attempt to define terms to avoid these traps.
Pathological universes are ones like: where there is no order and the right answer is randomly placed. Or where the facts are maliciously arranged to entrap in a recursive red herring where the simplest well-supported answer is always wrong, even after trying to out-think the malice. Or where the whole universe is one flawless red herring ("God put the fossils there to test your faith").
"No free lunch" demands they be mathematically conceivable. But to assert that the real universe behaves like this is to go mad.
Since we learn reason from the universe we're in, if we were in a universe you're referring to as "pathological", we (well, sentients, if any) would have learned a method of arriving at conclusions which matched that. Likewise, since the universe produced math, I don't think it has any meaning to talk of whether universes with different fundamental rules are "mathematically conceivable".
http://en.wikipedia.org/wiki/No_free_lunch_in_search_and_optimization
No search algorithm beats random picking in the totally general case. This implies the totally general case must include an equal balance of pathology and sanity. Intuitively, a problem could be structured so every good decision gives a bad result.
Edit: this post gives a perfect example of a pathological problem: there is only one decision to be made, a Bayesian loses, a random picker gets it right half the time and an anti-Bayesian wins.
However we seem to be living in a sane universe.
(likewise the fairness language of the parent post)