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: SSA rejects anthropic shadow, too, published by jessicata on July 27, 2023 on LessWrong.

(or: "Please Do Anthropics with Actual Math")

The anthropic shadow argument states something like:

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!

or:

You can't use "we survived the cold war without nuclear war" as evidence of anything. Because of the anthropic principle, we could have blown up the human race in the 1960's in 99% of all possible worlds and you'd still be born in one where we didn't.

This argument has already been criticized (here, here). In criticizing it myself, I first leaned on reasoning about large universes (e.g. ones where there are 100 worlds with low nuclear risk and 100 with high nuclear risk in the same universe) in a way that implies similar conclusions to SIA, thinking that SSA in a small, single-world universe would endorse anthropic shadow. I realized I was reasoning about SSA incorrectly, and actually both SSA and SIA agree in rejecting anthropic shadow, even in a single-world universe.

Recapping the Doomsday Argument

To explain SSA and SIA, I'll first recap the Doomsday Argument. Suppose, a priori, that it's equally likely that there will be 1 billion humans total, or 1 trillion; for simplicity, we'll only consider these two alternatives. We could number humans in order (numbering the humans 1, 2, ...), and assume for simplicity that each human knows their index (which is the same as knowing how many humans there have been in the past). Suppose you observe that you are one of the first 1 billion humans. How should you reason about the probability that there will be 1 billion or 1 trillion humans total?

SSA reasons as follows. To predict your observations, you should first sample a random non-empty universe (in proportion to its prior probability), then sample a random observer in that universe. Your observations will be that observer's observations, and, ontologically, you "are" that observer living in that universe.

Conditional on being in a billion-human universe, your probability of having an index between 1 and 1 billion is 1 in 1 billion, and your probability of having any other index is 0. Conditional on being in a trillion-human universe, your probability of having an index between 1 and 1 trillion is 1 in 1 trillion, and your probability of having any other index is 0.

You observe some particular index that does not exceed 1 billion; say, 45,639,104. You are 1000 more times likely to observe this index conditional on living in a billion-human universe than a trillion-human universe. Hence, you conclude that you are in a billion-human universe with 1000:1 odds.

This is called the "doomsday argument" because it implies that it's unlikely that you have a very early index (relative to the total number of humans), so humans are likely to go extinct before many more humans have been born than have already been born.

SIA implies a different conclusion. To predict your observations under SIA, you should first sample a random universe proportional to its population, then sample a random observer in that universe. The probabilities of observing each index are the same conditional on the universe, but the prior probabilities of being in a given universe have changed.

We start with 1000:1 odds in favor of the 1-trillion universe, due to its higher population. Upon observing our sub-1-billion index, we get a 1000:1 update in favor of a 1-billion universe, as with SIA. These exactly cancel out, leaving the probability of each universe at 50%.

As Bostrom points out, both SSA and SIA have major counterintuitive implications. Better anthropic theories are desired. And yet, having some explicit anthropic theory at all helps to reason in a principled way that is consist...