8: Quantum Suicide Confirmation Performed

This is a bit of a two pipe problem, to put it mildly. Statistical inference is not my speciality, so I may need to consult my good friend Cornelius on this matter. I can say that I have, to my satisfaction, performed the confirmation. My choice of death was not the customary revolver, but a much simpler device involving  a number of transformers and everyday domestic mains electricity  applied to the temples. In fact, there was no reason to introduce any paraphernalia such as unstable isotopes, far less military issue firearms. I simply had to assure myself that there was a way  in which the wave-function of the electrons in the system could 'collapse' which would not result in my death, or injury Not as straightforward as it sounds. I devised a trip system on a parallel circuit which would prevent a non-lethal voltage, but of course the trip system was itself subject to quantum effects. In the end the apparatus was something of a fudge. It was possible that the system could deliver a devastating but non-lethal shock, but the odds of it doing so it a way that would leave me conscious were extremely low. In the end I was reasonably happy that the odds were as follows:
1: Death. Overwhelmingly likely.
2: No effect. Extremely unlikely.
3: Horrible injury. Much less likely than 2.
The probabilistic relationship between 2 and 3 was my only concern, and I was satisfied that in this respect the arrangement was 'safe' in that 3 was somewhere in the order of 1 to 10 million times less likely than 2.  Note that 2 would also arise in the unlikely event of a waveform collapse which would result in a non-lethal shock, thus  causing the failsafe to engage, whereas 3 would be the result of a non-lethal shock and a failure of the failsafe device.

Now, here is the rub. Say I am convinced that the confirmation was indeed successful. What should you the rational impartial observer believe? I would suggest that you should not believe me. In fact, I should say that your credence value should fall as mine increases, as follows.

Let us first say that the value r  represents my reliabilty, from your point of view. This may be relatively high or low, but will be between 1 and 0. If you are simply reading this online, you may be very sceptical indeed, whereas if you have inspected my laboratory and met me in person, I should very much hope this value would be much higher. It is simply a numerical measure of the extent to which you trust me to carry out the experiment correctly and truthfully report the results. Whatever this value is, you have a prior credence value \(r_{1}\).
On the basis of my reported results, you should be able to rationally calculate a posterior credence value \(r_{2}\) using simple Bayesian reasoning; \(r_{2}\) is simply  \(P (r|E)\) where E is the evidence, the successful completion of the confirmation. This is given by \[P(r|E)=\frac{P(r)P(E|r)}{P(E)}\]
Note that this case is quite different from normal scientific confirmation. Here, the strength of the evidence is directly related to its a priori improbabilty. As more iterations of the experiment are run, the more P(E|r) approaches 1 and P(E) approaches 0. Ultimately, anything is more likely than the fact that I have successfully conducted the experiment successfully: I must be lying or mistaken.
Furthermore, I must begin to doubt my own reliability, for like most scientists, I am always aware of the possibility that I have made a mistake. I lost count. The probability of the null hypothesis, that the sequence of non-death results is a result of chance, is now well over \(10^{^{100}}\).  At this point in time, it occurs to me that it is far more likely that I am wrong in some way, that I simply cannot have carried out the experiment as I believe I have done.  It also occurs to me that any sentient being in my position would draw the same conclusion, and that there could be that which is true, but any rational analysis must conclude is false. Of course, I could be wrong.