What does it look like to rotate and then renormalize?
There seem to be two answers. The first answer is that the highest probability event is the one farthest to the right. This event must be the entire . All we do to renormalize is scale until this event is probability 1.
If we rotate until some probabilities are negative, and then renormalize in this way, the negative probabilities stay negative, but rescale.
The second way to renormalize is to choose a separating line, and use its normal vector as probability. This keeps probability positive. Then we find the highest probability event as before, and call this probability 1.
Trying to picture this, an obvious question is: can the highest probability event change when we rotate?
Better to call it a rational estimate than an assumption.
It is perfectly rational to say to onesself “but if I refuse to look into anything which takes a lot of effort to get any evidence for, then I will probably miss out.” We can put math to that sentiment and use it to help decide how much time to spend investigating unlikely claims. Solutions along these lines are sometimes called “taking the outside view”.
For the sake of engaging with your points 1 thru 5, ProofOfLogic, Kindly, et al. are supposing the existence of a class of claims for which there exists roughly the same amount of evidence pro and con as exists for lucid dreaming. This includes how much we trust the person making the claim, how well the claim itself fits with our existing beliefs, how simple the claim is (ie, Occam’s Razor), how many other people make similar claims, and any other information we might get our hands on. So the assumption for the sake of argument is that these claims look just about equally plausible once everything we know or even suspect is taken into account.
It seems very reasonable to conclude that the best one can do in such a case is choose randomly, if one does in fact want to test out some claim within the class.
But suggestions as to what else might be counted as evidence are certainly welcome.