I'm trying to wrap my mind around Stuart Armstrong's post on Doomsday argument, and to do so I've undertook the task of tabooing 'randomness' in the definitions of SIA and SSA.
My first attempt clearly doesn't work: "observers should reason giving the exact same degree of belief to any proposition of the form: 'I'm the first observer', 'I'm the second observer', etc." As it has been noted before many times, by me and by others, anthropic information changes the probability distribution, and any observer has at least a modicum of that. I suspect this conflict is what's thwarting my attempts at making sense of the topic.
the exact same degree of belief to any proposition of the form: 'I'm the first observer', 'I'm the second observer', etc.
Trying to assign the same degree of belief to infinitely many mutually exclusive options doesn't work. The probability of being an observer #1 is greater than the probability of being an observer #10^10, simply because some possible universes contain more than 1 but less than 10^10 observers.
I'm not sure how exactly the distribution should look; just saying in general that larger numbers have smaller probabilities. The exact distribut...
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