mitchell,
I think Eliezer recognizes the the vagueness of “world” but sees it as a problem for single-worlders. This is what he seems to be saying here:
We have specific reasons to be highly suspicious of the notion of only one world. The notion of “one world” exists on a higher level of organization, like the location of Earth in space; on the quantum level there are no firm boundaries (though brains that differ by entire neurons firing are certainly decoherent). How would a fundamental physical law identify one high-level world?
Remember, that-which-exists at any moment does not just consist of a set of worlds, but a set of worlds each with a complex number attached. And that-which-exists in the next moment is—the same set of worlds, but now with different complex numbers attached.
You seem to be talking about the wavefunction, which is a complex function defined over the configuration space (a set of configurations each with a complex number attached). But in that case you seem to be confusing a world with a configuration. A configuration defines only position. (Assuming we’re talking about positional configuration space.)
It seems I can save myself some trouble explaining by quoting Eliezer:
If Conway’s Game of Life managed to support a multiverse, then a single universe in this multiverse would not correspond to a cell. It would correspond to some section of the whole pattern quite a bit larger than a single cell—a section which was for the most part causally separated from the rest of the pattern. And this section might move around over Conway’s gameboard (or whatever it’s called), just as a glider can move across Conway’s gameboard.