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There are a crapload of problems with this argument on my view.

Two of the biggest problems are:

(1) The assumption that two people have indeed accessed all of the same, publicly available evidence. There would be no feasible way to assess this, at least outside of imagining evidence about something completely novel to the people in question, so that they couldn't possibly have had evidence elsewhere, and where we're talking about a small, controlled body of evidence. (Or on the flipside, the assumption that they'd reach different conclusions just in case we stipulate-by-thought-experiment that they have accessed all of the same, publicly available evidence.)

(2) The idea that any two people have the same understanding of something (at least if they're rational).

Reply to Terrapin Station thank you! The second point is something I was considering too as a big problem. I am not sure what you mean by point 1 though?

Re point (1), he's positing that everyone not only is capable of accessing, but has indeed accessed all of the same publicly available evidence. That's a ridiculous thing to posit though. The publicly available evidence for something as broad as compatibilism/incompatibilism isn't something that we could possibly enumerate. That would be the case even if we were to just limit it to statements that people have explicitly made about compatibilism and incompatibilism. But the evidence isn't limited to that. It includes all sorts of other statements and all sorts of other (observations of) other behavior, too. The evidence one gains for something like that spans a lifetime, it spans countless experiences, many of which might not be immediately recognizable as evidence for (or against) something.

On the other hand, we could, for the sake of a thought experiment, simply stipulate that person A and person B have accessed all of the same publicly available evidence, and then wonder why rationally-ideal person A has reached a different conclusion than rationally-ideal person B, but that can't be anything more than a stipulation, in which case, maybe we're stipulating something that would never obtain. There's certainly no evidence that David Lewis reached a different conclusion than Van Inwagen on compatibilism where we're stipulating that they accessed the same evidence (because they didn't in fact access the same evidence, and we have no basis for saying that Lewis would go one way or other under our imagining that they really did access just the same information).

Reply to Terrapin Station ah ok yeah, i get what you are saying.

Reply to Terrapin Station do you think i could mention intuition in my essay?