PPA 6: Indexical Models Don't Have Diversity Biases

[This is the sixth piece in my series on the Parametric Process Assumption (PPA), a new model of anthropics. You should start here if you are just seeing this for the first time.

The previous piece is "Improper Priors and the Infinite SIA."

TLDR:

• Neither the SSA nor SIA have any bias towards observer attributes which aren't directly correlated with the number of observers in the universe
• For the Basic Model, which we discuss more at the end of the series, this will apply to any properties of various species (physiology, local universe observations, etc.) which don't a priori tell us something about how long our species will survive.

The next piece is "Temporal Consistency and Texas Sharpshooting."]

Another misconception I had at one point was that the SIA produced a great bias for diversity than the SSA.

By diversity, I mean basically any measure of observers having different experiences from my own. That could mean the existence of a person having a different childhood from mine, or it could mean four-armed green-skinned aliens from the Andromeda Galaxy. Literally anything that isn’t directly correlated with the number of observers in the universe counts.

Both the SIA and SSA update on this type of information identically. To see why, let's start with a simple example where, with 50% probability, only humans exist, and with 50% probability we have a more diverse universe where in addition to the humans we also have an equal number of aliens. Unconditionally, the SIA does say the alien universe is more likely, but once we learn we are human, we revert to the universe prior and the bias disappears:

So, in practice, the conditional SIA is agnostic about observers different from us in ways we can observe, which includes all of our experiences up to this point.

What about the SSA? It is true that if you run the same scenario through the SSA, you will predictably find that conditioning on your humanity makes the aliens less likely to exist:

These examples were what originally convinced me that the SSA had a bias for less diversity, but they're actually focusing on the wrong things entirely. The second universe in this example isn't just more diverse, it's also contains twice as many observers, and we already know that the SIA prefers bigger universes. We could just as easily image a situation where the smaller universe was more diverse, and then it would be the SSA which updates to a bigger universe.

Consider for instance a universe prior where with 50% probability there are 4N humans, and with 50% probability there are N humans and N aliens. Putting both side-by-side (with the SSA on top and the SIA on bottom) it's immediately clear that the SSA puts twice as much relative weight onto the "Human + Alien" universe.

That's because anthropic biases only concern themselves with universe size. If you use a model where size and diversity aren't correlated, then anthropic biases won't play into it.

More broadly, the reason the first "Humans or Humans + Aliens" model is wrong is because it assumes that humans must exist no matter what, and the only real question is what else exists besides. If we don't privilege humans in this way, but rather consider them just one type of life that might have existed among many, then we'll find it a lot easier to construct examples where diversity doesn't matter.

For instance, suppose for the sake of argument we knew that the universe would independently produce exactly two different species, and this meant there were exactly 3 equally likely outcomes:

• Both were human
• One was human and one was alien
• Both were alien

In this case, regardless of whether we used the SSA or the SIA, both the unconditional and conditional distributions would be identical:

This sort of effect is the same we'll see in the Basic Model later in this series. There, the diversity variable will apply at a species-level, referencing any of an observer's various properties (physiology, distance to closest star, etc.) which don't a priori tell them something about how long their species will survive. Thanks to the results above, we will be able to safely ignore those variables in our analysis.

The next piece is "Temporal Consistency in Anthropics"

1. Specifically, anything that isn’t correlated with the longevity of your species and/or the universe size within your prior. In reality, any number of things could be unexpectedly correlated with longevity, but if you don’t have any a priori reason to model them as correlated, the SSA and SIA won’t have anything special to say about it.
2. This example can also be used to argue that the SSA is too sensitive to reference classes, since whether or not you include the aliens in your reference class changes the SSA's prediction. See this piece by Joe Carlsmith.That's a very valid critique of the SSA, but it's not the point where making here. We're assuming our reference class contains every possible observer.