If you experienced psychic powers as being real in a way consistent and sustained enough that, for example, over thirty years people became well able to study and control them, and your local neighborhood Psi Corps was as familiar a figure as your local neighborhood police, I doubt that thirty years from now you would be huddled up in a ball with your fingers in your ears saying "this isn't real, this isn't real".

Perhaps in this case you should taboo "reality" and "hallucination" and talk about whether an experience is consistent and sustained. An experience of psychic powers may be inconsistent - for example, when you say "Look at me move this weight with my mind", your friend says "You're just sitting there with an intent look on your face and nothing's happening" - or more subtle, in that you hallucinate your friends approving but not other obvious consequences, like you winning the Randi Prize, scientists taking you off to study, or a gradual shift in society's view of the physical versus the spiritual. A sufficiently consistent hallucination would be strong evidence that it's not a hallucination at all, unless you believe your brain could predict the way society would develop post-psychic powers and could feed you all the appropriate stimuli forever - in which case you have minimal reason to believe your normal pre-psychic life isn't a hallucination too.

Or it may not be sustained. For example, you may have a relatively vivid hallucination of being in a world with psychic powers, but it only lasts a few minutes before you end up back in the real world and people tell you you've been in a coma the whole time.

If you find yourself in a world with psychic powers, or Omega, or whatever, then the longer it stays consistent and sustained, the greater the probability with which you can predict that acting as if the powers or Omega are real is the way to go, either because they are real or because your hallucination is so vivid and complex that you know acting as if they're real will have the same results as if they are real.

You could also try giving a small amount of probability to the "real" hypothesis and a large amount to the "hallucination" hypothesis. Then, as it becomes gradually clearer and clearer that nothing you do can break you out of the hallucination and satisfy your aims in reality, all the actions in the "hallucination" hypothesis have equal utility and it's the utilities in the "real" branch that should guide your actions.

...this kind of makes me want to write rationalist Thomas Covenant fanfiction, which would probably be a bad idea.

(nods) These sorts of situations really do arise.

A couple of years ago, shortly after some significant brain damage, I had some very emotionally compelling experiences of the sort typically described as "supernatural." And so I asked myself the question: what's more likely? That the things I experienced happening actually did happen? Or that I was hallucinating due to brain damage?

I eventually bit the bullet and accepted that "hallucinating" was overwhelmingly more likely... but it was not an easy thing to do.

Should we have, on first observing the results of the double split experiment, concluded that we are insane instead of inventing quantum mechanics?

I agree with you that the "I am insane/dreaming" hypothesis is much, much stronger than is given credit in most supernatural/Omega-type scenarios.

On the other hand, if I was to read through a lengthy scientific paper detailing a respectable process which showed significant indicators of telepathic ability and posited a believable, testable mechanism, and at every point during this process I was, for example, physically capable of turning the lights on and off, people seemed to speak in understandable English, I got hungry after several hours of not eating, I experienced going to sleep and waking up, etc., etc. then I doubt that "I am insane" would continue strictly dominating the hypothesis "people are psychic."

There are so many tests for sanity that verification of it should be fairly easy, unless you are insane in such a specific way that you only hallucinate a single scientific paper which you have discussed extensively with others in your imagination; or your imagination is vastly powerful, enough to create an entire functioning world which may be sufficient to say that some abstract "solipsism" really isn't decision-theoretically important.

I believe the point of Omega is to make it easier to set up hypothetical situations without getting fixated to much on irrelevant details.

Something worth pondering: conditional on you being in fact strongly psychotic - on your perceptions having gone so rotten that your brain populates the world with Omegas and waistcoat-clad white rabbits - is there any course of action worth pursuing any longer? Deciding to see a psychiatrist may not have a high correlation with actually seeing a psychiatrist, you might end up blubbering incomprehensibly at your friendly neighbourhood crack dealer instead.

Effectively, this would drastically reduce or even nullify the weight you should give to the insanity hypothesis. If insanity made you able to undergo the actions you consciously chose only, say, 10% of the time, whereas the "Omega exists" scenario does not similarly hamper you, then you should divide by 10 the weight you gave to the option of assuming insanity.

And now I realise the obvious answer - that there are many orders of magnitude of difference between the likelihood of personal brain damage and that of Omega appearing, while I don't see the reasoning above eliminating more than two or three. Still, I'm leaving this comment since it seems there's something worthwhile in it.

A problem with the insanity hypothesis is that "non-sane perception" is a non-apple. You can dismiss any perception, even the perception that everyone around you saw the same incredible things you did, by saying the whole thing is a hallucination. No, it's worse than merely being a non-apple, it's an invisible dragon. It can automatically expand to cover any observation at all.

I think you're right to conclude you're insane in the case of Omega. It sufficiently parallels traditional delusions and doesn't even make sense even if what you see and here are true (why if this super-intelligence exists is it offering me weird bets to test game theory paradoxes?). In any case the though experiments just assume Omega is honest, in real life you would require a proof before you started handing him money.

The psy thing seems altogether different from me. People don't hallucinate scientific studies, it just doesn't fit with any known pattern of delusion. Moreover, the hypothesis, while contrary to our current understanding of the world, isn't nearly as a priori implausible as an honest and omniscient AI appearing at your front door.

So far as I know, seeing evidence that supports an unlikely general hypothesis doesn't match any standard sort of insanity.