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Dead men tell tales: falling out of love with SIA
SIA is the Self Indication Assumption, an anthropic theory about how we should reason about the universe given that we exist. I used to love it; the argument that I've found most convincing about SIA was the one I presented in this post. Recently, I've been falling out of love with SIA, and moving more towards a UDT version of anthropics (objective probabilities and total impact of your decision being of a specific type, including in all copies of you and enemies with the same decision process). So it's time I revisit my old post, and find the hole.
The argument rested on the plausible sounding assumption that creating extra copies and killing them is no different from if they hadn't existed in the first place. More precisely, it rested on the assumption that if I was told "You are not one of the agents I am about to talk about. Extra copies were created to be destroyed," it was exactly the same as hearing "Extra copies were created to be destroyed. And you're not one of them."
But I realised that from the UDT/TDT perspective, there is a great difference between the two situations, if I have the time to update decisions in the course of the sentence. Consider the following three scenarios:
- Scenario 1 (SIA):
Two agents are created, then one is destroyed with 50% probability. Each living agent is entirely selfish, with utility linear in money, and the dead agent gets nothing. Every survivor will be presented with the same bet. Then you should take the SIA 2:1 odds that you are in the world with two agents. This is the scenario I was assuming.
- Scenario 2 (SSA):
Two agents are created, then one is destroyed with 50% probability. Each living agent is entirely selfish, with utility linear in money, and the dead agent is altruistic towards his survivor. This is similar to my initial intuition in this post. Note that every agents have the same utility: "as long as I live, I care about myself, but after I die, I'll care about the other guy", so you can't distinguish them based on their utility. As before, every survivor will be presented with the same bet.
Here, once you have been told the scenario, but before knowing whether anyone has been killed, you should pre-commit to taking 1:1 odds that you are in the world with two agents. And in UDT/TDT precommitting is the same as making the decision.
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Anthropic reasoning and correlated decision making
There seems to be some confusion on how to deal with correlated decision making - such as with absent-minded drivers and multiple copies of yourself; any situation in which many agents will allreach the same decision. Building on Nick Bostrom's division-of-responsibility principle mentioned in Outlawing Anthropics, I propose the following correlated decision principle:
CDP: If you are part of a group of N individuals whose decision is perfectly correlated, then you should reason as if you had a 1/N chance of being the dictator of the group (in which case your decision is applied to all) and a (N-1)/N chance of being a dictatee (in which case your decision is ignored).
What justification could there be to this principle? A simple thought experiment: imagine if you were one of N individuals who had to make a decision in secret. One of the decisions is opened at random, the others are discarded, and each person has his mind modified to believe that what was decided was in fact what they decided. This process is called a "dictator filter".
If you apply this dictator filter any situation S, then in "S + dictator filter", you should reason as in the CDP. If you apply it to perfectly correlated decision making, however, then the dictator filter changes nothing at all to anyone's decision - hence we should treat "perfectly correlated" as isomorphic to "perfectly correlated + dictator filter", which establishes the CDP.
Used alongside the SIA, this solves many puzzles on this blog, without needing advanced decision theory.
Avoiding doomsday: a "proof" of the self-indication assumption
The doomsday argument, in its simplest form, claims that since 2/3 of all humans will be in the final 2/3 of all humans, we should conclude it is more likely we are in the final two thirds of all humans who’ve ever lived, than in the first third. In our current state of quasi-exponential population growth, this would mean that we are likely very close to the final end of humanity. The argument gets somewhat more sophisticated than that, but that's it in a nutshell.
There are many immediate rebuttals that spring to mind - there is something about the doomsday argument that brings out the certainty in most people that it must be wrong. But nearly all those supposed rebuttals are erroneous (see Nick Bostrom's book Anthropic Bias: Observation Selection Effects in Science and Philosophy). Essentially the only consistent low-level rebuttal to the doomsday argument is to use the self indication assumption (SIA).
The non-intuitive form of SIA simply says that since you exist, it is more likely that your universe contains many observers, rather than few; the more intuitive formulation is that you should consider yourself as a random observer drawn from the space of possible observers (weighted according to the probability of that observer existing).
Even in that form, it may seem counter-intuitive; but I came up with a series of small steps leading from a generally accepted result straight to the SIA. This clinched the argument for me. The starting point is:
A - A hundred people are created in a hundred rooms. Room 1 has a red door (on the outside), the outsides of all other doors are blue. You wake up in a room, fully aware of these facts; what probability should you put on being inside a room with a blue door?
Here, the probability is certainly 99%. But now consider the situation:
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