Followup to: Quantum Russian Roulette; The Domain of Your Utility Function

The only way to win is cheat
And lay it down before I'm beat
and to another give my seat
for that's the only painless feat.

Suicide is painless
It brings on many changes
and I can take or leave it if I please.

-- M.A.S.H.

Let us pretend, for the moment, that we are rational Expected Utility Maximisers. We make our decisions with the intention of achieving outcomes that we judge to have high utility. Outcomes that satisfy our preferences. Since developments in physics have led us to abandon the notion of a simple single future world our decision making process must now grapple with the notion that some of our decisions will result in more than one future outcome. Not simply the possibility of more than one future outcome but multiple worlds, each of which with different events occurring. In extreme examples we can consider the possibility of staking our very lives on the toss of a quantum die, figuring that we are going to live in one world anyway!

How do preferences apply when making decisions with Many Worlds? The description I’m giving here will be obvious to the extent of being trivial to some, confusing to others and, I expect, considered outright wrong by others. But it is the post that I want to be able to link to whenever the question “Do you believe in quantum immortality?” comes up. Because it is a wrong question!

Katja Grace has just presented an ingenious model, claiming that SIA combined with the great filter generates its own variant of the doomsday argument. Robin echoed this on Overcoming Bias. We met soon after Katja had come up with the model, and I signed up to it, saying that I could see no flaw in the argument.

Unfortunately, I erred. The argument does not work in the form presented.

First of all, there is the issue of time dependence. We are not just a human level civilization drifting through the void in blissful ignorance about our position in the universe. We know (approximately) the age of our galaxy, and the time elapsed since the big bang.

How is this relevant? It is relevant because all arguments about the great filter are time-dependent. Imagine we had just reached consciousness and human-level civilization, by some fluke, two thousand years after the creation of our galaxy, by an evolutionary process that took two thousand years. We see no aliens around us. In this situation, we have no reason to suspect any great filter; if we asked ourselves "are we likely to be the first civilization to reach this stage?" then the answer is probably yes. No evidence for a filter.

Imagine, instead, that we had reached consciousness a trillion years into the life of our galaxy, again via an evolutionary process that took two thousand years, and we see no aliens or traces of aliens. Then the evidence for a filter is overwhelming; something must have stopped all those previous likely civilizations from emerging into the galactic plane.

So neither of these civilizations can be included in our reference class (indeed, the second one can only exist if we ourselves are filtered!). So the correct reference class to use is not "the class of all potential civilizations in our galaxy that have reached our level of technological advancement and seen no aliens", but "the class of all potential civilizations in our galaxy that have reached our level of technological advancement at around the same time as us and seen no aliens". Indeed, SIA, once we update on the present, cannot tell us anything about the future.

But there's more.