What role does "counting histories" play in Deutsch's critique of the "simulation argument"?

Question

In his book The Beginning of Infinity, David Deutsch argues that there is a problematic assumption behind the simulation argument that "virtually all instances of us are in ... simulations and not in the original world" since

counting the number of instances of oneself is no guide to the probability one ought to use ... We should be counting histories not instances.

What is meant by the distinction between histories and instances and how does that distinction create problems for the simulation hypothesis?

Answer 1

(This is a rather old question, but I'm just picking up the book and having a look. The quote is on p. 454 of my copy of the book.)

His analogy is with puff pastry.

This is my interpretation of what Deutsch wrote:

Suppose we are only given that we are somewhere (on a layer) in the puff pastry. What is the probability that we are somewhere in a layer (instance) above a small circle around some (x, y) in the horizontal plane?

He argues that in physics (QM), this probability is provided by counting histories (paths, via layers, from anywhere to any and all layers above (x, y)) by measure, and not by the (relative) number of layers above (x, y)), which (the latter) would typically give you the wrong physical answer.

He further argues 1) that the simulation argument should likewise ignore the number of layers (since we know from QM that that's wrong), and 2) that it doesn't have a known way of counting simulations/histories. Therefore, the simulation argument hinges on an open problem.