Your analogy is clouded by emotion, since it appeals to the notion that we shouldn't be able to pick some arbitrary number and then be able to compare the quali

Your analogy is clouded by emotion, since it appeals to the notion that we shouldn't be able to pick some arbitrary number and then be able to compare the quality of universes. Comparison of universes is multifaceted, so it seems nonsensical, but it actually becomes very possible when you reduce the universes to a single number, and thus make it a question about a probability space. Let's use your protocol. We arbitrarily choose a number R. Then we find out our universe's number A. So now our question is, what is the probability that B is further away from A than R (and in the same direction)? This might seem intractable because we don't know anything about the way A and B were chosen. But in fact, we don't need to. We're not actually trying to calculate the probability; we just want to know whether it's greater than zero. As initially posed, the problem is, "Out of all the possible distributions for A and B, and all the possible As and Bs for each distribution, is there a nonzero probability that B is further away from A than R (and in the same direction)?" Intuition might tell you no, since the interval [A,B] is always finite over a seemingly infinite range. But that doesn't account for the fact that "most" distributions are just as finite. And it's also easy to envision that there are an infinite number of distributions that will permit a B that meets that condition (especially given that there are just as many Bs on "that side" of R as there are on "this side"). Still, you may argue that we don't have an easy way to sum the probabilities over all the distributions. So we solve the problem by re-framing it in simpler terms. Instead of fixing R while varying A and B, we transform the problem by fixing A and B and varying R (which is completely under our control). And it turns out, if our distribution of R is positive everywhere, then regardless of A and B, there's a nonzero probability of R falling between them. We still need to sum over all possible distributions of A and B, but we've already shown that every term of the sum is positive. In the end, we might not know the exact value of that probability, but that's irrelevant to the problem.