Gambling With Goff

Inferring a multiverse from fine-tuning still doesn't commit the inverse gambler's fallacy but it does show that the self-indication assumption is right.

Today I spoke with Philip Goff, philosopher extraordinaire, and one of the few people who seems to really get the difficulty of the many puzzles of consciousness. We spoke about just one topic—whether or not inferring a multiverse from fine-tuning of the universe’s constants commits the fallacy of understated evidence. I think it does not, and in fact, this is one of the complicated judgments I’m the most confident of—Goff disagrees.

One commits the fallacy of understated evidence if they don’t take into account the totality of some evidence but only consider a small part of it. For instance, if a person takes into account that someone had a knife at the scene of a crime, but ignores that the knife was a butter knife, that would be the fallacy of understated evidence. Goff claims that we observe that this universe is finely tuned—and that’s more likely if a greater share of universes are finely tuned. Therefore, we get evidence that a great percent of universes are finely-tuned, not just that this universe is finely-tuned.

The problem is that this claim falls apart when one thinks carefully about which universe this one is. Suppose there are two theories—T1 and T2. T1 predicts that there would be one finely-tuned universe while T2 predicts there would be 5 random universes and one of them would have to be finely-tuned. Now ask—does T1 make it likelier that this universe would be finely tuned?

The answer is no, even though if T1 is true, the prior odds that this universe is finely-tuned is 100% while it’s only 20% if T2 is true. That’s because we have uncertainty about which universe we’re in. On T1, we must be in the only universe. Let’s imagine that the universes are arranged from left to right—U1 is the furthest left universe and U5 is the furthest right universe (Philip, being a socialist, would hate U5).

There are then 6 possibilities of the theories and the universes we’re in that get the following share of the probability space:

T1 & U1 = .5

T2 & U1 = .1

T2 & U2 = .1

T2 & U3 = .1

T2 & U4 = .1

T2 & U5 = .1

Once we’re clear on the universes you might be in, it isn’t actually the case the T1 makes it likelier that you’d be in this universe. Because there’s a 40% chance that you’re in a universe that is incompatible with T1 (if you’re in U2, U3, U4, or U5), T2 explains fine-tuning just as well as T1.

So if we assume that two theories predict the same number of observers and we’re precise about your uncertainty about where you are across the theories, then your existence in the universe that you’re in doesn’t actually favor either over the other.

Here’s another way to see this, from an example I gave to Philip. Suppose that there’s a casino of some size—it could have just one room, it could have infinity. Every time the casino gets a royal flush, a random baby is created. You get created in the casino. Do you get evidence that the casino has more rooms? Answer: yes. Yet on Goff’s view this wouldn’t be the case, for the odds that this room would have a person are no higher, by Goff’s logic, on the hypothesis that there are more rooms.

But now let’s assume the number of observers is not the same. Assume instead that there are 10 universes and 2 theories. T1 says every universe is life-permitting, T2 says that only one universe at random is life-permitting. Well then it does make sense to infer that T1 is 10x likelier than T2, if they have an equal prior, if you find yourself in a life-permitting universe. This is for the reason Goff says—it predicts with greater probability that this universe, in particular, would be life-permitting.

In other words, if we’re precise about one’s uncertainty about which universe one is in and assume two theories predict the same number of observers, the inverse gambler’s fallacy falls flat. But if two theories don’t predict the same number of observers then the theory that predicts more observers is more likely, for exactly the reasons identified by IGF proponents.

Thus, only by accepting the self-indication assumption (which I’ve defended here, here, here, here, here, here, here, here, here), according to which your existence gives you evidence for the existence of more people, can we make sense of how to reason about multiverses and inverse gamblers.