I am with you in disagreeing with Eirenicon's assertion that self drowning in a bucket is impossible with probability 1, though I believe with high probability that it is difficult beyond the ability of most people. I was mainly objecting to your assertion that this couldn't be studied.
Also, merely holding your breath is not dangerous. You would pass out before suffering any permanent damage, and breathe normally while unconscious. It would be dangerous in an environment, such as under water, in which you could breathe normally after passing out.
Followup to: The Strangest Thing An AI Could Tell You
Brain damage patients with anosognosia are incapable of considering, noticing, admitting, or realizing even after being argued with, that their left arm, left leg, or left side of the body, is paralyzed. Again I'll quote Yvain's summary:
A brief search didn't turn up a base-rate frequency in the population for left-arm paralysis with anosognosia, but let's say the base rate is 1 in 10,000,000 individuals (so around 670 individuals worldwide).
Supposing this to be the prior, what is your estimated probability that your left arm is currently paralyzed?
Added: This interests me because it seems to be a special case of the same general issue discussed in The Modesty Argument and Robin's reply Sleepy Fools - when pathological minds roughly similar to yours update based on fabricated evidence to conclude they are not pathological, under what circumstances can you update on different-seeming evidence to conclude that you are not pathological?