Not particularly. I use 4 but with P(W|S) = P(W) which renders it valid. (We're not talking about two side-by-side universes, but about prior probabilities on physical law plus a presumption of survival.)
You mean you use method 2. Except you don't, or you would come to the same conclusion that I do. Are you claiming that P(W|S)= P(W)? Ok, I suspect you may be applying Nick Bostrom's version of observer selection: hold the probability of each possible version of the universe fixed independent of the number of observers, then divide that probability equally amongst the observers. Well, that approach is BS whenever the number of observers differs between possible universes, since if you imagine aliens in the universe but causally separate, the probabilities would depend on their existence.
Also, does it really make sense to you, intuitively, that you should get a different result given two actually existing universes compared to two possible universes?
This could only reflect uncertainty that anthropic reasoning was valid. If you were certain anthropic reasoning were valid (I'm sure not!) then you would make no such update. In practice, after surviving a few hundred rounds of quantum suicide, would further survivals really seem to call for alternative explanations?
As I pointed out earlier, if there was even a tiny chance of the machine being broken in such a way as to appear to be working, that probability would dominate sooner or later.
One last thing: if you really believe that annihilational events are irrelevant, please do not produce any GAIs until you come to your senses.
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?