Unfortunately, physical self-sampling without self-indication has odd consequences of its own. Consider the following thought experiment:
Physicists have conclusively figured out what the theory of everything is. We know roughly how the cosmos will behave until a trillion years into the future. However, it's still unclear what will happen at this point: either (T1) the universe will end, or (T2) the universe will continue for another trillion trillion years, but be unable to support intelligent life. A hard mathematical calculation can show which of these is true, but before doing the calculation, each theory has a 1/2 prior probability (in the same sense that before doing the calculation, you have a 1/10 subjective probability that the trillionth decimal digit of pi is a seven).Physicists want to schedule supercomputer time to determine the answer. Enter Presumptuous: "By physical self-sampling, the probability of T2 given our observations is only about one in a trillion. This calculation is a waste of money!"
She calculates as follows. P0(T1) = P0(T2) = 1/2. According to T2, the universe contains a trillion more space-time locations than according to T1. But according to both theories, the universe contains only one location consistent with our evidence. According to the definition given in the previous comment, this makes T2 much less likely that T1.
Intuitively, the argument is, "According to T2, there are a trillion more places we could have found ourselves at (at most of which we would not have been conscious observers, but taking that into account would be supernatural wonder tissue). So having found ourselves at this particular place is much more surprising according to T2."
But this argument doesn't sound very convincing to me. From where do we get this supposed lottery over space-time locations? At least, the argument sounds much less intuitively convincing than the following: "Our uncertainty is mathematical, and our observations would be exactly the same according to each theory -- we can't conclude anything about the mathematical result from the fact that one would destroy the universe, while the other would only leave it barren."
In the next comment, I'll develop that intuition into a more formal argument supporting self-indication.
Recently the Large Hadron Collider was damaged by a mechanical failure. This requires the collider to be warmed up, repaired, and then cooled down again, so we're looking at a two-month delay.
Inevitably, many commenters said, "Anthropic principle! If the LHC had worked, it would have produced a black hole or strangelet or vacuum failure, and we wouldn't be here!"
This remark may be somewhat premature, since I don't think we're yet at the point in time when the LHC would have started producing collisions if not for this malfunction. However, a few weeks(?) from now, the "Anthropic!" hypothesis will start to make sense, assuming it can make sense at all. (Does this mean we can foresee executing a future probability update, but can't go ahead and update now?)
As you know, I don't spend much time worrying about the Large Hadron Collider when I've got much larger existential-risk-fish to fry. However, there's an exercise in probability theory (which I first picked up from E.T. Jaynes) along the lines of, "How many times does a coin have to come up heads before you believe the coin is fixed?" This tells you how low your prior probability is for the hypothesis. If a coin comes up heads only twice, that's definitely not a good reason to believe it's fixed, unless you already suspected from the beginning. But if it comes up heads 100 times, it's taking you too long to notice.
So - taking into account the previous cancellation of the Superconducting Supercollider (SSC) - how many times does the LHC have to fail before you'll start considering an anthropic explanation? 10? 20? 50?
After observing empirically that the LHC had failed 100 times in a row, would you endorse a policy of keeping the LHC powered up, but trying to fire it again only in the event of, say, nuclear terrorism or a global economic crash?