Well, you have to consider the entire data set.ExpHP wrote:Oh, hey, how about this: Let O = "the event where you go on to publish a report about the outcome of your experiment."
If there are many worlds, or more specifically infinite worlds, performing the experiment once amounts to performing it an infinite number of times (once for each offshoot timeline). Half of those experiments will result in a published outcome, half will not. So, the probability of O in any given case is still 50%, just as it would have been if yours was the only universe. In the case that "you" in one of those universes is publishing a paper, that paper is considering only one arbitrarily selected data point out of the data set (due to a flaw in your perceptive abilities -- you can only observe one timeline per published paper), so it is not actually representative of the results.
The flaw is in the premises that P(O|M)=1 and P(O|C)=.5^n, which is a version of the fallacy of four terms. In the first premise, P(O) is interpreted to mean (Def. 1), "the probability that, in an infinite number of parallel experiments, in at least one outcome a researcher will survive to publish." In the second, P(O) is interpreted to mean (Def. 2), "the probability that, for n experiments in sequence, the single researcher will survive to publish." So, in fact, P(O) has two distinct definitions, one for each case; and the distinction is crucial. If we use either of these definitions for both hypotheses M and C, then P(O|M)=P(O|C) for all observers, whether in or out of the death chamber.