One thing that MMA has going for it as a competitive art is that it's well optimized for the specific type of fighting that takes place in an MMA ring. Some advocates will insist that the types of confrontations which take place in the ring are "real fighting," and anything which less effectively prepares one for the ring is not as effective in a "real fight," but it would be more accurate to say that MMA matches are a certain kind of fight, one which approximates only a certain subset of encounters one might have outside the ring.
For example, if one is hired as a bouncer at a club, it's certainly probable that one will eventually be involved in "real fights," where a person is seriously trying to hurt you without any rules to hold them back. But they'll overwhelmingly be untrained people with a lot of alcohol in them, who, at the very least for the sake of your job if not out of ethical concern, you should try to avoid injuring too badly. MMA training would be poorly optimized for these sort of encounters, as it's stripped of a lot of pain compliance techniques which would be handy in such a situation, and emphasizes many techniques which could result in your getting fired or possibly being sued or serving jail time.
If you're mugged, you'd be facing a violent encounter where your assailant almost certainly has a weapon, there may be multiple assailants involved, and facing you in a fight is not their top priority. Generically speaking, the standard advice for these situations is "give them your money," in which case no sort of martial arts training would leave you more prepared than any other, but some schools will teach not just techniques, but tactics for defending oneself in such a situation. An MMA school is unlikely to offer students such preparation, since that's time they could be spending learning to better kick the ass of one guy in the ring.
A law enforcement officer, again, is likely to face "real fights" with people who may be high on drugs, wielding weapons, in large groups, or some combination of the above, where the objective is generally to restrain and arrest, or if their own lives are threatened, to respond with lethal force using deadly weapons.
And so on and so forth. One on one brawls of the sort that MMA training optimizes for actually form a fairly small and avoidable portion of all violent encounters, but it's hard to arrange realistic comparative tests between martial artists of ability in any other kind of fight.
Related: The Martial Art of Rationality
One principle in the martial arts is that arts that are practiced with aliveness tend to be more effective.
"Aliveness" in this case refers to a set of training principles focused on simulating conditions in an actual fight as closely as possible in training. Rather than train techniques in a vacuum or against a compliant opponent, alive training focuses on training with movement, timing, and energy under conditions that approximate those where the techniques will actually be used.[1]
A good example of training that isn't alive would be methods that focused entirely on practicing kata and forms without making contact with other practitioners; a good example of training that is alive would be methods that focused on verifying the efficacy of techniques through full-contact engagement with other practitioners.
Aliveness tends to create an environment free from epistemic viciousness-- if your technique doesn't work, you'll know because you won't be able to use it against an opponent. Further, if your technique does work, you'll know that it works because you will have applied it against people trying to prevent you from doing so, and the added confidence will help you better apply that technique when you need it.
Evidence from martial arts competitions indicates that those who practice with aliveness are more effective than others. One of the chief reasons that Brazilian jiu-jitsu (BJJ) practitioners were so successful in early mixed martial arts tournaments was that BJJ-- a martial art that relies primarily on grappling and the use of submission holds and locks to defeat the opponent-- can be trained safely with almost complete aliveness, whereas many other martial arts cannot.[2]
Now, this is not to say that one should only attempt to practice martial arts under completely realistic conditions. For instance, no martial arts school that I am aware of randomly ambushes or attempts to mug its students on the streets outside of class in order to test how they would respond under truly realistic conditions.[3]
Even in the age of sword duels, people would train with blunt weapons and protective armor rather than sharp weapons and ordinary clothes. Would training with sharp weapons and ordinary clothes be more alive than training with blunt weapons and protective armor? Certainly, but the trainees wouldn't be! And yet training with blunt weapons is still useful-- the fact that training does not fully approximate realistic conditions does not intrinsically mean it is bad.
That being said, generally speaking martial arts training that is more alive-- that better approximates realistic fighting conditions-- is more effective within reasonable safety margins. There is a growing consensus among students of martial arts who are looking for effective self-defense techniques that the specific martial art one practices is not hugely relevant, and that what matters more is the extent to which the training does or doesn't use aliveness.
Aliveness and Rationality
So, that's all well and good-- but how can we apply these principles to rationality practice?
While martial arts training has very clear methods of measuring whether or not skills work (can I apply this technique against a resisting opponent?), rationality training is much murkier-- measuring rationality skills is a nontrivial problem.
Further, under normal circumstances the opponent that you are resisting when applying rationality techniques is your own brain, not an external enemy.[4] This makes applying appropriate levels of resistance in training difficult, because it's very easy to cheat yourself. The best method that I have found thus far is lucid dreaming, as forcing your dreaming brain to recognize its true state through the various hallucinations and constructed memories associated with dreaming is no easy task.
That being said, I make no claims to special or unique knowledge in this area. If anyone has suggestions for useful methods of "live" rationality practice, I'd love to hear them.
[1] For further explanation, see Matt Thornton's classic video "Why Aliveness?"
[2] If your plan is to choke someone until they fall unconscious, it is possible to safely train for this with nearly complete aliveness by wrestling against an opponent and simply releasing the chokehold before they actually fall unconscious. By contrast, it is much harder to safely train to punch someone into unconsciousness, and harder still to safely train to break people's necks.
[3] The game of Assassins does do this, but usually follows rules that are constrained enough to make it a suboptimal method of training.
[4] There are some contexts in which rationality techniques are applied in order to overcome an external enemy. Competitive games and some sports are a good method of finding practice in this respect. For instance, in order to be a competitive Magic: The Gathering player, you need to engage many epistemic and instrumental rationality skills. Competitive poker can offer similar development.