I think for debate you can fix the circular argument problem by requiring debaters to ‘pay’ (sacrifice some score) to recurse on a statement of their choice. If a debater repeatedly pays to recurse on things that don’t resolve before the depth limit, then they’ll lose.
Hmm, I was imagining that the honest player would have to recurse on the statements in order to exhibit the circular argument, so it seems to me like this would penalize the honest player rather than the circular player. Can you explain what the honest player would do against the circular player such that this “payment” disadvantages the circular player?
EDIT: Maybe you meant the case where the circular argument is too long to exhibit within the debate, but I think I still don’t see how this helps.
Ah, yeah. I think the key thing is that by default a claim is not trusted unless the debaters agree on it. If the dishonest debater disputes some honest claim, where honest has an argument for their answer that actually bottoms out, dishonest will lose—the honest debater will pay to recurse until they get to a winning node. If the the dishonest debater makes some claim and plan to make a circular argument for it, the honest debater will give an alternative answer but not pay to recurse. If the dishonest debater doesn’t pay to recurse, the judge will just see these two alternative answers and won’t trust the dishonest answer. If the dishonest debater does pay to recurse but never actually gets to a winning node, they will lose. Does that make sense?
If the dishonest debater disputes some honest claim, where honest has an argument for their answer that actually bottoms out, dishonest will lose—the honest debater will pay to recurse until they get to a winning node.
This part makes sense.
If the the dishonest debater makes some claim and plan to make a circular argument for it, the honest debater will give an alternative answer but not pay to recurse. If the dishonest debater doesn’t pay to recurse, the judge will just see these two alternative answers and won’t trust the dishonest answer.
So in this case it’s a stalemate, presumably? If the two players disagree but neither pays to recurse, how should the judge make a decision?
Both debaters make claims. Any claims that are only supported by circular arguments will be ignored. If an honest claim that’s supported by a good argument is disputed, the honest debater will pay to recurse, and will give their good argument
This was a very interesting comment (along with its grandparent comment), thanks—it seems like a promising direction.
However, I’m still confused about whether this would work. It’s very different from judging procedure outlined here; why is that? Do you have a similarly detailed write-up of the system you’re describing here?
I’m actually less concerned about loops and more concerned about arguments which are infinite trees, but the considerations are similar. It seems possible that the proposal you’re discussing very significantly addresses concerns I’ve had about debate.
I was trying to describe something that’s the same as the judging procedure in that doc! I might have made a mistake, but I’m pretty sure the key piece about recursion payments is the same. Apologies that things are unclear. I’m happy to try to clarify, if there were particular aspects that seem different to you.
Yeah, I think the infinite tree case should work just the same—ie an answer that’s only supported by an infinite tree will behave like an answer that’s not supported (it will lose to an answer with a finite tree and draw with an answer with no support)
It seems possible that the proposal you’re discussing very significantly addresses concerns I’ve had about debate.
I think for debate you can fix the circular argument problem by requiring debaters to ‘pay’ (sacrifice some score) to recurse on a statement of their choice. If a debater repeatedly pays to recurse on things that don’t resolve before the depth limit, then they’ll lose.
Hmm, I was imagining that the honest player would have to recurse on the statements in order to exhibit the circular argument, so it seems to me like this would penalize the honest player rather than the circular player. Can you explain what the honest player would do against the circular player such that this “payment” disadvantages the circular player?
EDIT: Maybe you meant the case where the circular argument is too long to exhibit within the debate, but I think I still don’t see how this helps.
Ah, yeah. I think the key thing is that by default a claim is not trusted unless the debaters agree on it.
If the dishonest debater disputes some honest claim, where honest has an argument for their answer that actually bottoms out, dishonest will lose—the honest debater will pay to recurse until they get to a winning node.
If the the dishonest debater makes some claim and plan to make a circular argument for it, the honest debater will give an alternative answer but not pay to recurse. If the dishonest debater doesn’t pay to recurse, the judge will just see these two alternative answers and won’t trust the dishonest answer. If the dishonest debater does pay to recurse but never actually gets to a winning node, they will lose.
Does that make sense?
This part makes sense.
So in this case it’s a stalemate, presumably? If the two players disagree but neither pays to recurse, how should the judge make a decision?
Both debaters make claims. Any claims that are only supported by circular arguments will be ignored. If an honest claim that’s supported by a good argument is disputed, the honest debater will pay to recurse, and will give their good argument
This was a very interesting comment (along with its grandparent comment), thanks—it seems like a promising direction.
However, I’m still confused about whether this would work. It’s very different from judging procedure outlined here; why is that? Do you have a similarly detailed write-up of the system you’re describing here?
I’m actually less concerned about loops and more concerned about arguments which are infinite trees, but the considerations are similar. It seems possible that the proposal you’re discussing very significantly addresses concerns I’ve had about debate.
I was trying to describe something that’s the same as the judging procedure in that doc! I might have made a mistake, but I’m pretty sure the key piece about recursion payments is the same. Apologies that things are unclear. I’m happy to try to clarify, if there were particular aspects that seem different to you.
Yeah, I think the infinite tree case should work just the same—ie an answer that’s only supported by an infinite tree will behave like an answer that’s not supported (it will lose to an answer with a finite tree and draw with an answer with no support)
That’s exciting!