Multiverses: Is more better?

I'm sure you've all heard of the multiverse hypothesis, the idea that many different universes exist besides our own.  Perhaps you've also heard this argument in favor of the multiverse hypothesis:

If there exist multiple universes, humans are that much more likely to exist.  Therefore, we are much more likely to find ourselves in a multiverse than a lone universe.

This argument is similar to the fine-tuning argument.  But let's call it the "More is Better" argument.  I disagree with it.

Many Multiverses and Many Worlds

But first, we cannot call it "the multiverse hypothesis".  If I simply stated that there are multiple universes, this would provide no explanations and make no predictions, because I have said nothing about the nature of these multiple universes.  Literally anything is possible.  To formulate a useful hypothesis, we need to be more specific about the nature of the universes.  There are in fact many different multiverse hypotheses, each with different specifics.

There are a bunch of questions we can ask about any multiverse hypothesis.  Where does the idea come from?  Are the universes such that there is a unique way to count them?  If so, how many are there?  What things are possible in these universes?  Are we equally likely to find ourselves in any of the universes with humans?

For example, consider the Many Worlds hypothesis, which could be considered a multiverse hypotheses, but is unusual in some ways.  Many Worlds doesn't come from cosmology, but from certain interpretations of quantum mechanics.  Contrary to the title, there is in fact only one universe in Many Worlds.  However, this one universe is in a superposition of many quantum possibilities, and each of those possibilities might be considered an independent "universe" of sorts.

The unusual thing about Many Worlds is that it explicitly states that not every universe is equally likely.  Just because two universes contain me in it does not mean I am equally likely to find myself in either of those universes.  For example, take the following thought experiment.

Flip a coin.  If it's heads, make a quantum measurement which has 1000 possible outcomes.  If it's tails, don't do anything.  Now there are 1000 universes where you got heads, and 1 universe where you got tails.  Does this mean you were 1000 times more likely to get heads than tails?

There's very little point in counting the number of "universes" in Many Worlds, because each universe is not equally likely.  It would be like counting the pips on each side of a dice.  Just because one side has six pips and another side has only one does not mean that we are six times as likely to roll a 6 as we are to roll a 1.

Multiverses and Priors

Let's say we are comparing two hypotheses:

Hypothesis 1: There are ten universes.
Hypothesis 2: There are a hundred universes.

Let's suppose that each of these universes contains humans like ourselves.  There exist ten universes in which hypothesis 1 is true.  There exist a hundred universes in which hypothesis 2 is true.  Does this mean that hypothesis 2 is ten times more likely?  Not necessarily, I think.

It depends on your choice of prior probabilities.  Usually, because prior probabilities are based on complete ignorance, you want to give equal likelihood to each possibility.  But how do you count the possibilities?  Do you say, "There are 110 possible universes, and I am equally likely to land in any of them"?  Or do you say, "There are 2 possible multiverses (one with 10 universes, one with 100), and I am equally likely to land in either of them"?

In statistical analysis, it's common practice to try a few different prior probabilities, and see what results you get.  If you get completely different results from reasonably chosen priors, then that means the results are inconclusive.

What if there is only a 1% chance that any given universe contains humans like ourselves?  Does this change things?  Under hypothesis 1, there is a 90% chance that there are no humans at all.  Under hypothesis 2, there is a 37% chance that there are no humans at all.  Clearly, if the hypothesis predicts no humans, then it must be false.

But I can think of three ways to analyze it, with very different results:

1. Assign all universes equal prior probabilities.  Then calculate the conditional probability for each universe, given the condition that humans exist.  Hypothesis 2 is 10 times more likely than hypothesis 1.
2. Assign all multiverses equal prior probabilities.  Then calculate the conditional probability for each multiverse, given the condition that humans exist.  Hypothesis 2 is about 3.7 times as likely as hypothesis 1.
3. Assign all multiverses equal prior probabilities.  Then calculate the conditional probability for each universe, given the condition that humans exist.  Hypothesis 1 and 2 are equally likely.

The fact that we get three different results with three reasonable methods of analysis suggests that we need more evidence to reach a conclusion.

A better kind of evidence

If you want to argue about Many Worlds, I want to hear about interpretations of quantum mechanics, not about the sheer number of worlds proposed by it.  There are an absurd number of worlds in Many Worlds.  Supposedly, the number increases exponentially with entropy.  But this does mean that it is absurdly more likely than the alternative quantum interpretations?

There's a class of multiverse hypotheses that proposes independent universes with different initial conditions beyond our observable horizons.  This is plausible, but not because I think more is better.  It's because we suspect the universe is infinite in size, though we may only see part of it due to the finite speed of light and finite age.

Another kind of multiverse is the one where new universes are created as "bubbles" in the space-time of older universes.  I don't care how many bubbles it supposes.  If I wanted more evidence for this kind of multiverse, I would look to the theory of cosmological inflation, from which the idea arises.

I don't have anything against the idea of a multiverse.  I just prefer that they are supported by scientific theory, not philosophical arguments.  If that means being inconclusive, then so be it.