I’m a bit confused why you would make the debate length known to the debaters. This seems to allow them to make indefensible statements at the very end of a debate, secure in the knowledge that they can’t be critiqued. One step before the end, they can make statements which can’t be convincingly critiqued in one step. And so on.
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The most salient reason for me ATM is the concern that debaters needn’t structure their arguments as DAGs which ground out in human-verifiable premises, but rather, can make large circular arguments (too large for the debate structure to catch) or unbounded argument chains (or simply very very high depth argument trees, which contain a flaw at a point far too deep for debate to find).
If I assert “X because Y & Z” and the depth limit is 0, you aren’t intended to say “Yup, checks out,” unless Y and Z and the implication are self-evident to you. Low-depth debates are supposed to ground out with the judge’s priors / low-confidence in things that aren’t easy to establish directly (because if I’m only updating on “Y looks plausible in a very low-depth debate” then I’m going to say “I don’t know but I suspect X” is a better answer than “definitely X”). That seems like a consequence of the norms in my original answer.
In this context, a circular argument just isn’t very appealing. At the bottom you are going to be very uncertain, and all that uncertainty is going to propagate all the way up.
Instead, it seems like you’d want the debate to end randomly, according to a memoryless distribution. This way, the expected future debate length is the same at all times, meaning that any statement made at any point is facing the same expected demand of defensibility.
If you do it this way the debate really doesn’t seem to work, as you point out.
For my part I mostly care about the ambitious thesis.
If the two players choose simultaneously, then it’s hard to see how to discourage them from selecting the same answer. This seems likely at late stages due to convergence, and also likely at early stages due to the fact that both players actually use the same NN. This again seriously reduces the training signal.
If player 2 chooses an answer after player 1 (getting access to player 1′s answer in order to select a different one), then assuming competent play, player 1′s answer will almost always be the better one. This prior taints the judge’s decision in a way which seems to seriously reduce the training signal and threaten the desired equilibrium.
I disagree with both of these as objections to the basic strategy, but don’t think they are very important.
If I assert “X because Y & Z” and the depth limit is 0, you aren’t intended to say “Yup, checks out,” unless Y and Z and the implication are self-evident to you. Low-depth debates are supposed to ground out with the judge’s priors / low-confidence in things that aren’t easy to establish directly (because if I’m only updating on “Y looks plausible in a very low-depth debate” then I’m going to say “I don’t know but I suspect X” is a better answer than “definitely X”). That seems like a consequence of the norms in my original answer.
In this context, a circular argument just isn’t very appealing. At the bottom you are going to be very uncertain, and all that uncertainty is going to propagate all the way up.
If you do it this way the debate really doesn’t seem to work, as you point out.
For my part I mostly care about the ambitious thesis.
I disagree with both of these as objections to the basic strategy, but don’t think they are very important.