LW - Doomsday Argument and the False Dilemma of Anthropic Reasoning by Ape in the coat

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Welcome to The Nonlinear Library, where we use Text-to-Speech software to convert the best writing from the Rationalist and EA communities into audio. This is: Doomsday Argument and the False Dilemma of Anthropic Reasoning, published by Ape in the coat on July 5, 2024 on LessWrong.
Doomsday Inference
Can we use probability theory to estimate how many people there will be throughout the whole human history? Sure. We can build a probability model, that takes into account birth rates, possible existential hazards, ways to mitigate them and multiple other factors. Such models tend not to be very precise, so we would have pretty large confidence intervals but, we would still have some estimate.
Hmm... this sounds like a lot of work for not much of a result. Can't we just use the incredible psychic powers of anthropics to circumvent all that, and get a very confident estimate just from the fact that we exist? Consider this:
Suppose that there are two indistinguishable possibilities: a short human history, in which there are only 100 billion people and a long human history, in whichthere are 100 trillion people. You happen to be born among the 6th 10-billion group of people. What should be your credence that the history is short?
As short and long history are a priori indistinguishable and mutually exclusive:
P(Short)=P(Long)=1/2
Assuming that you are a random person among all the people destined to be born:
P(6|Short)=1/10
P(6|Long)=1/10000
According to the Law of Total Probability:
P(6)=P(6|Short)P(Short)+P(6|Long)P(Long)=0.05005
Therefore by Bayes' Theorem:
P(Short|6)=P(6|Short)P(Short)/P(6)>0.999
We should be extremely confident that humanity will have a short history, just by the fact that we exist right now.
This strong update in favor of short history solely due to the knowledge of your birth rank is known as the Doomsday Inference. I remember encountering it for the first time. I immediately felt that it can't be right. Back in the day I didn't have the right lexicon to explain why cognition engines can't produce knowledge this way. I wasn't familiar with the concept of noticing my own confusion. But I've already accustomed myself with several sophisms, and even practiced constructing some myself.
So I noticed the familiar feeling of "trickery" that signaled that one of the assumptions is wrong.
I think it took me a couple of minutes to find it. I recommend for everyone to try to do it themselves right now. It's not a difficult problem to begin with, and should be especially easy if you've read and understood my sequence on Sleeping Beauty problem.
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Did you do it?
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Well, regardless, there will be more time for it. First, let's discuss the fact that both major anthropic theories SSA and SIA accept the doomsday inference, because they are crazy and wrong and we live in an extremely embarrassing timeline.
Biting the Doomsday Bullet
Consider this simple and totally non-anthropic probability theory problem:
Suppose there are two undistinguishable bags with numbered pieces of paper. The first bag has 10 pieces of paper and the second has 10000. You were given a random piece of paper from one of the bags and it happens to have number 6. What should be your credence that you've just picked a piece of paper from the first bag?
The solution is totally analogous to the Doomsday Inference above:
P(First)=P(Second)=1/2
P(6|First)=1/10
P(6|Second)=1/10000
P(6)=P(6|First)P(First)+P(6|Second)P(Second)=0.05005
P(First|6)=P(6|First)P(First)/P(6)=0.05/0.05005>0.999
But here there is no controversy. Nothing appears to be out of order. This is the experiment you can conduct and see for yourself that indeed, the absolute majority of cases where you get the piece of paper with number 6 happen when the paper was picked from the first bag.
And so if we accept this logic here, we should also accept the Doomsday Inference, shouldn't we? Unless you want to defy Bayes' theorem itself! Maybe the ability to predict the ...