This has the side effect that A* doesn’t need to be involved
I thought the thing A* was doing was giving a measure of “answer differently” that was more reliable than something like ‘string comparison’. If B’s answer is “dog” and B*’s answer was “canine”, then hopefully those get counted as “the same” in situations where the difference is irrelevant and “different” in situations where the difference is relevant. If everything can be yes/no, then I agree this doesn’t lose you much, but I think this reduces the amount of trickery you can detect.
That is, imagine one of those games where I’m thinking of a word, and you have to guess it, and you can ask questions that narrow down the space of possible words. One thing I could do is change my word whenever I think you’re getting close, but I have to do so to a different word that has all the properties I’ve revealed so far. (Or, like, each time I could answer in the way that leaves me with the largest set of possible words left, maximizing the time-to-completion.) If we do the thing where B says the word, and B* gets to look at B’s notes up to point X and say B’s word, then the only good strategy for B is to have the word in their notes (and be constrained by it), but this is resistant to reducing it to a yes/no question. (Even if the question is something like “is there a word in B’s notes?” B* might be able to tell that B will say “yes” even tho there isn’t a word in B’s notes; maybe because B says “hey I’m doing the strategy where I don’t have a word to be slippery, but pretend that I do have a word if asked” in the notes.)
A wins outright if B and B* answer differently.
As stated, I think this has a bigger vulnerability; B and B* just always answer the question with “yes.” One nice thing about yes/no questions is that maybe you can randomly flip them (so one gets “does B think the animal is a dog?” and the other gets “does B think the animal is not a dog?”) so there’s no preferred orientation, which would eat the “always say yes” strategy unless the question-flipping is detectable. (Since A is the one asking the question, A might limit themselves to easily reversible questions, but this constrains their ability to clamp down on trickery.)
As stated, I think this has a bigger vulnerability; B and B* just always answer the question with “yes.”
Remember that this is also used to advance the argument. If A thinks B has such a strategy, A can ask the question in such a way that B’s “yes” helps A’s argument. But sure, there is something weird here.
I thought the thing A* was doing was giving a measure of “answer differently” that was more reliable than something like ‘string comparison’. If B’s answer is “dog” and B*’s answer was “canine”, then hopefully those get counted as “the same” in situations where the difference is irrelevant and “different” in situations where the difference is relevant. If everything can be yes/no, then I agree this doesn’t lose you much, but I think this reduces the amount of trickery you can detect.
That is, imagine one of those games where I’m thinking of a word, and you have to guess it, and you can ask questions that narrow down the space of possible words. One thing I could do is change my word whenever I think you’re getting close, but I have to do so to a different word that has all the properties I’ve revealed so far. (Or, like, each time I could answer in the way that leaves me with the largest set of possible words left, maximizing the time-to-completion.) If we do the thing where B says the word, and B* gets to look at B’s notes up to point X and say B’s word, then the only good strategy for B is to have the word in their notes (and be constrained by it), but this is resistant to reducing it to a yes/no question. (Even if the question is something like “is there a word in B’s notes?” B* might be able to tell that B will say “yes” even tho there isn’t a word in B’s notes; maybe because B says “hey I’m doing the strategy where I don’t have a word to be slippery, but pretend that I do have a word if asked” in the notes.)
As stated, I think this has a bigger vulnerability; B and B* just always answer the question with “yes.” One nice thing about yes/no questions is that maybe you can randomly flip them (so one gets “does B think the animal is a dog?” and the other gets “does B think the animal is not a dog?”) so there’s no preferred orientation, which would eat the “always say yes” strategy unless the question-flipping is detectable. (Since A is the one asking the question, A might limit themselves to easily reversible questions, but this constrains their ability to clamp down on trickery.)
Remember that this is also used to advance the argument. If A thinks B has such a strategy, A can ask the question in such a way that B’s “yes” helps A’s argument. But sure, there is something weird here.