You can't talk about what happened during the game _in specifics_; you can of course confirm that the game was played according to the rules and that the outcome was not misreported.
Here's the thing though: Depending on what was said in the conversation BOTH parties may have a vested interest in keeping the specifics secret. Only via an independent third party observer can there even be a remote chance [Edit: of knowing] that any rules were followed.
> That's at least four people who you think are just outright lying.
I'm saying that there is a chance of that being the case, but that without any kind of third party confirmation we cannot know either way. Also see homeopathy.
> Eliezer would presumably have tried to cheat against them, too.
Not necessarily. Losing occasionally is a good strategy when running a con.
You've gone from there being only a "remote chance" that the rules were followed, and "I don't trust anyone involved" - to there being "a chance" that they were broken.
Under common interpretations of those phrases, that's a massive swing in your confidence levels.
Sorry for being unclear. My personal position is agnostic. I do not know if they're being earnest. At the same time i can imagine ways of this going down that would make it worthwhile for all parties involved to lie. This means my expected result is indeed "they lied", but i have no strong conviction in this.
I also misspoke in my earlier comment, i meant "remote chance of knowing that any rules were followed". I didn't mean to imply any confidence on the size of the chance, since we actually don't know enough to make such a judgement call.
If you'd go to that level of collusion, you could just fake logs. At the point where both sides are in on it, there's basically nothing that they could say that would be convincing.
You can always assume all participants lied about how the game went. Just add an implicit "assuming they didn't, ..." and the discussion is still valid.
At that point any discussion is moot though, since the only point of discussion is "what exact argument as used to convince", yet if both parties lied, then there is no such argument in the first place.
Since neither party is going to disclose the exact arguments, this discussion is still equivalent to "what arguments could be used to convince..." and you can have it regardless of whether or not the parties lied about the experiment's result.