2 Anthropic Questions

Now, try the weakened causality argument that I have just emphasized in this chapter: had the bubonic plague killed more people, the observers (us) would not be here to observe. So it may not neccessarily be the property of diseases to spare us humans.

Fortunately, we know plenty about diseases from other species - where we don't need to be concerned with anthropic bias.

Your first question is different depending on some things. If you play the lottery for the usual reason (because people are irrational and cannot do math) then it is safe to say that you will not only be better off not doing any updating if you magically end up in the winners' pool, but you probabilistically have no idea what Bayes' theorem is. This is me looking at you, hypothetical irrational person.

However, if you buy a lottery ticket in order to test whether you're in a simulation, then you have to consider that one of four things is true:

1. You are not in a simulation.
2. You are in a simulation, and the simulators do not want you to know. In which case, do not bet on being able to find out. But it brings up more questions, like why are we able to talk about simulations at all?
3. You are in a simulation, and the simulators do want you to know. In which case, why use something esoteric like lotteries? It's an antiprediction that it would be something other than a lottery, like an angel appearing in your bedroom and telling you himself, or something.
4. You are in a simulation, and the simulators want sufficiently clever people to be able to figure out they're in a simulation.
5. Something I haven't thought of. I always include these on my lists but I never think about them because it's a tautology that I have not done so.

I think #4 is the only interesting possibility, so it might make sense to buy one lottery ticket, but that's not really very clever as tests go. I wouldn't recommend more than that, though; they're addicting. You could also attempt to perform private miracles to see if they work, though that's even less clever. I admit to having done this.

If the hypothesis "this world is a holodeck" is normatively assigned a calibrated confidence well above 10⁻⁸, the lottery winner now has incommunicable good reason to believe they are in a holodeck. (I.e. to believe that the universe is such that most conscious observers observe ridiculously improbable positive events.)

It isn't clear to me that I'm that much more likely to win the lottery if the world is a holodeck. Of all possible holodecks, why one in which I win the lottery? The world doesn't look like I'd expect it to if "most conscious observers observe ridiculously improbable positive events"; unless they just happened to start the simulation shortly before I won the lottery, and give people memories of a past that doesn't look like the future. And that in turn seems vastly unlikely even conditioning on "the world is a holodeck".

At least, when you win a lottery, assign the biggest probability to the possibility that it is a hoax or a mistake of some kind, since that is usually the case. Real winners are rare among those who get the impression they are.

Even, when you are watching the youtube poker game where FR just won over the AAAA, consider yourself one of those, who watch a fake, not a real event, probable one in several tens of millions. When you see a famous character in this movie, you can be pretty damn sure it's a hoax.

A hoax, a mistake, or an illusion are even more probable than a holodex.

For the second question:

Imagine there are many planets with a civilization on each planet. On half of all planets, for various ecological reasons, plagues are more deadly and have a 2/3 chance of wiping out the civilization in its first 10000 years. On the other planets, plagues only have a 1/3 chance of wiping out the civilization. The people don't know if they're on a safe planet or an unsafe planet.

After 10000 years, 2/3 of the civilizations on unsafe planets have been wiped out and 1/3 of those on safe planets have been wiped out. Of the remaining civilizations, 2/3 are on safe planets, so the fact that your civilization survived for 10000 years is evidence that your planet is safe from plagues. You can just apply Bayes' rule:

P(safe planet | survive) = P(safe planet) P(survive | safe planet) / P(survive) = 0.5 * 2/3 / 0.5 = 2/3

EDIT: on the other hand, if logical uncertainty is involved, it's a lot less clear. Supposed either all planets are safe or none of them are safe, based on the truth-value of a logical proposition (say, the trillionth digit of pi being odd) that is estimated to be 50% likely a priori. Should the fact that your civilization survived be used as evidence of the logical coin flip? SSA suggests no, SIA suggests yes because more civilizations survive when the coin flip makes all planets safe. On the other hand, if we changed the thought experiment so that no civilization survives if the logical proposition is false, then the fact that we survived is proof that the logical proposition is true.

Taleb has the second question mostly right. It is reasonable to be skeptical of a view which presents difficulties reasoning from the past to the future, but we have a lot of evidence that we're bad at reasoning from the past to the future, and the models that suggest anthropic issues are robust.

However, Bayes says that if we assign greater than 10^-8 prior probability to "strange" explanations

Well, don't do that then. Does 10^-8, besides being the chances of a ticket winning a typical big lottery, carry in addition the implied meaning "unimaginably small", "so small that one must consider all manner of weird other possibilities that in fact we have no way of assessing the probability of, but 10^-8 is so extraordinarily small that surely they must be considered alongside the simple explanation that my ticket won"? "How could we ever be 10^-8 sure of anything?"

Because I would dispute that. Consider someone who has a lottery ticket in their hand, for a draw about to be announced, with 1 chance in 100,000,000 of having the winning numbers. If their numbers are drawn, they must overcome 80dB of prior improbability to be persuaded of that. (It does not matter whether they know that is what they are doing: they are nonetheless doing that.) An impossible task? No, almost all jackpots in the Euromillions lottery (probability 1/76275360) are claimed. Ordinary people, successfully comparing two strings of seven numbers and getting the right answer. It is news when a Euromillions jackpot goes unclaimed for as little as one week.

One of the alternative hypotheses that one must consider, of course, is the mundane "I am mistaken: this is not a winning ticket, despite the fact that I have stared at the two sets of numbers and the date over and over and they still appear to be identical." I don't know how many false positives the claims line gets. But the jackpot is awarded at least every few weeks, and every time it is claimed by people who were not mistaken.

There is no such thing as a small number.

Why didn't the bubonic plague kill more people?

Why does it surprise him that it didn't? What is his evidence that the plague would have been expected to kill more people than it did?

Regarding the first question: We are making an argument here about what kind of advice we would want to give to people, and we are also considering a hypothesis under which most people aren't "conscious". Using a functionalist philosophy of mind, perhaps we can say that we cannot expect to change the behavior of non-conscious people by giving them advice. So then maybe there is no reason to want to advise anyone against updating in favor of a simulation hypothesis.

On the other hand, there is the hypothesis that everyone is "conscious", but we are in a simulation in which one particular person has good things happen to them. In that case, every time someone wins the lottery, we want to update in favor of a simulation hypothesis under which that person is special.

In the second case, the easy answer is, "How often do diseases wipe out other species?" That is, when possible, calibrate possibilities against similar events that don't involve anthropic questions. Our disease model tends to hold quite effectively for animals whose extinction would be harmless or even beneficial from the anthropic perspective.