They key is probably to test someone without letting them know you are testing them. If I ran a martial arts dojo and wanted to make sure my students were really super badass ninjas, I would give them a convincing looking "test" that included things you would expect to see: strength, speed, form, technique, success in actual matches, etc.
This would have very little weighting in the actual grade, however. The real test would be some sort of surprise fight or fights where the student has no idea that the fight is actually one of the tests. Perhaps he (or she) is followed by the assailant until an opportunity to pick a fight arises.
The main advantage of the surprise test is that it is much hard to game. Imperfect metrics are much more likely to say something meaningful about the student in this surprise situation than if the student knows the test is coming.
When it comes to the rationality dojo, there are numerous normally easy-to-game heuristics that could be used, for example:
edit: notice that lists are not working. edit 2: never mind, editing seemed to fix them.
I doubt that it would be practical to analyze all of the information and get a single number as a measure of the student's rationality. At the top of all of these tests would have to be someone whose judgment on matters of rationality can be trusted. This may be the most difficult part
Also note that this form of testing would probably be expensive.
See artemis fowl and the butler training.
I strongly suspect that there is a possible art of rationality (attaining the map that reflects the territory, choosing so as to direct reality into regions high in your preference ordering) which goes beyond the skills that are standard, and beyond what any single practitioner singly knows. I have a sense that more is possible.
The degree to which a group of people can do anything useful about this, will depend overwhelmingly on what methods we can devise to verify our many amazing good ideas.
I suggest stratifying verification methods into 3 levels of usefulness:
If your martial arts master occasionally fights realistic duels (ideally, real duels) against the masters of other schools, and wins or at least doesn't lose too often, then you know that the master's reputation is grounded in reality; you know that your master is not a complete poseur. The same would go if your school regularly competed against other schools. You'd be keepin' it real.
Some martial arts fail to compete realistically enough, and their students go down in seconds against real streetfighters. Other martial arts schools fail to compete at all—except based on charisma and good stories—and their masters decide they have chi powers. In this latter class we can also place the splintered schools of psychoanalysis.
So even just the basic step of trying to ground reputations in some realistic trial other than charisma and good stories, has tremendous positive effects on a whole field of endeavor.
But that doesn't yet get you a science. A science requires that you be able to test 100 applications of method A against 100 applications of method B and run statistics on the results. Experiments have to be replicable and replicated. This requires standard measurements that can be run on students who've been taught using randomly-assigned alternative methods, not just realistic duels fought between masters using all of their accumulated techniques and strength.
The field of happiness studies was created, more or less, by realizing that asking people "On a scale of 1 to 10, how good do you feel right now?" was a measure that statistically validated well against other ideas for measuring happiness. And this, despite all skepticism, looks like it's actually a pretty useful measure of some things, if you ask 100 people and average the results.
But suppose you wanted to put happier people in positions of power—pay happy people to train other people to be happier, or employ the happiest at a hedge fund? Then you're going to need some test that's harder to game than just asking someone "How happy are you?"
This question of verification methods good enough to build organizations, is a huge problem at all levels of modern human society. If you're going to use the SAT to control admissions to elite colleges, then can the SAT be defeated by studying just for the SAT in a way that ends up not correlating to other scholastic potential? If you give colleges the power to grant degrees, then do they have an incentive not to fail people? (I consider it drop-dead obvious that the task of verifying acquired skills and hence the power to grant degrees should be separated from the institutions that do the teaching, but let's not go into that.) If a hedge fund posts 20% returns, are they really that much better than the indices, or are they selling puts that will blow up in a down market?
If you have a verification method that can be gamed, the whole field adapts to game it, and loses its purpose. Colleges turn into tests of whether you can endure the classes. High schools do nothing but teach to statewide tests. Hedge funds sell puts to boost their returns.
On the other hand—we still manage to teach engineers, even though our organizational verification methods aren't perfect. So what perfect or imperfect methods could you use for verifying rationality skills, that would be at least a little resistant to gaming?
(Added: Measurements with high noise can still be used experimentally, if you randomly assign enough subjects to have an expectation of washing out the variance. But for the organizational purpose of verifying particular individuals, you need low-noise measurements.)
So I now put to you the question—how do you verify rationality skills? At any of the three levels? Brainstorm, I beg you; even a difficult and expensive measurement can become a gold standard to verify other metrics. Feel free to email me at sentience@pobox.com to suggest any measurements that are better off not being publicly known (though this is of course a major disadvantage of that method). Stupid ideas can suggest good ideas, so if you can't come up with a good idea, come up with a stupid one.
Reputational, experimental, organizational:
Finding good solutions at each level determines what a whole field of study can be useful for—how much it can hope to accomplish. This is one of the Big Important Foundational Questions, so—
Think!
(PS: And ponder on your own before you look at the other comments; we need breadth of coverage here.)