From the Wikipedia article on Problems with SIA:
“One of the most prominent objections to SIA concerns Bostrom’s ‘presumptuous philosopher’ scenario. In this example, the non-anthropic evidence has led scientists to place equal credence on two rival cosmological theories T1 and T2. ‘According to T1 the world is very, very big but finite and there are a total of a trillion trillion observers in the cosmos. According to T2, the world is very, very, very big but finite and there are a trillion trillion trillion observers.’ Just as the scientists are preparing to run a cheap experiment that will definitively rule out one of the two theories, they are interrupted by a philosopher who believes SIA. He argues that the experiment is a waste of effort as T2 is a trillion times as likely to be true as T1. Bostrom finds this conclusion absurd and believes that it should thoroughly discredit SIA.”
I agree with Bostrom that this is ludicrous. However, I don’t think such presumptuousness should follow from SIA.
SIA can tell us that worlds with more observers are more likely, conditional on our existence. Those worlds may be large and scientifically rich, or they may be small worlds bloated with causally disconnected regions. Without observable consequences, the distinction collapses.
To close this loophole, a theory would need to specify the number of unobservable observers. But this is impossible in principle. Science deals in empirical evidence, not unfalsifiable claims. The veracity of scientific hypotheses should not hinge on the supposed existence of gremlins.
Making empirical predictions directly from SIA is misguided. SIA is epistemologically interesting; it tells us how self-locating evidence works, but it cannot bear the weight of scientific rigour.