Val also used an upside-down W-diagram with the two worlds at the top and the four beliefs at the bottom, to emphasize the idea that the world is there first, and is fixed, and we have only a choice of what to believe within a fixed world, not a choice of which background world to live in.
I don't know what a "W-diagram" is (and a simple Google search didn't help), so I don't see how this works. Perhaps a picture could help explain.
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Ah, I think I see it. So on top it has the possible worlds, and on the bottom each world branches into the possible consequences in that world of having each of the possible beliefs.
Yep.