In passing, I said:
From a statistical standpoint, lottery winners don't exist - you would never encounter one in your lifetime, if it weren't for the selective reporting.
And lo, CronoDAS said:
Well... one of my grandmothers' neighbors, whose son I played with as a child, did indeed win the lottery. (AFAIK, it was a relatively modest jackpot, but he did win!)
To which I replied:
Well, yes, some of the modest jackpots are statistically almost possible, in the sense that on a large enough web forum, someone else's grandmother's neighbor will have won it. Just not your own grandmother's neighbor.
Sorry about your statistical anomalatude, CronoDAS - it had to happen to someone, just not me.
There's a certain resemblance here - though not an actual analogy - to the strange position your friend ends up in, after you test the Quantum Theory of Immortality.
For those unfamiliar with QTI, it's a simple simultaneous test of many-worlds plus a particular interpretation of anthropic observer-selection effects: You put a gun to your head and wire up the trigger to a quantum coinflipper. After flipping a million coins, if the gun still hasn't gone off, you can be pretty sure of the simultaneous truth of MWI+QTI.
But what is your watching friend supposed to think? Though his predicament is perfectly predictable to you - that is, you expected before starting the experiment to see his confusion - from his perspective it is just a pure 100% unexplained miracle. What you have reason to believe and what he has reason to believe would now seem separated by an uncrossable gap, which no amount of explanation can bridge. This is the main plausible exception I know to Aumann's Agreement Theorem.
Pity those poor folk who actually win the lottery! If the hypothesis "this world is a holodeck" is normatively assigned a calibrated confidence well above 10-8, the lottery winner now has incommunicable good reason to believe they are in a holodeck. (I.e. to believe that the universe is such that most conscious observers observe ridiculously improbable positive events.)
It's a sad situation to be in - but don't worry: it will always happen to someone else, not you.
I get the feeling that I missed a lot of prediscussion to this topic. I am new here and new to these types of discussions, so if I am way off target please nudge me in the right direction. :)
If the statistics of winning a lottery are almost none, they are not none. As such, the chances of a lottery winner existing as time goes on increases with each lottery ticket purchased. (The assumption here is that "winner" simply means "holding the right ticket".)
Furthermore, it seems like the concept of the QTI is only useful if you already know what the probability of it being true /and/ find it helpful to consider yourself in the other variations as an extension of your personal identity. Otherwise, you are just killing yourself to prove a point to someone else.
But I really do not understand this:
"If the hypothesis 'this world is a holodeck' is normatively assigned a calibrated confidence well above 10-8, the lottery winner now has incommunicable good reason to believe they are in a holodeck."
Why are the probabilities of the world being a holodeck tied to the probability of guessing a number correctly? It seems like this is the same reasoning that leads people to believing in Jesus just because his face showed up on their potato chip. It just sounds like a teleological argument with a different target. Or was that the point and I missed it?
PS) Is it better to post once with three topics, or three times with one topic each?
I interpreted the last statement as follows:
IF you assign a probability higher than 10^(-8) to the hypothesis that you are in a holodeck
AND you win the lottery (which had a probabiltiy of 10^(-8) or thereabouts)
THEN you have good reason to believe you're in a holodeck, because you've had such improbable good fortune.
Correct me if I'm wrong on this.