I’m sure you’ve thought about this, but I’m curious why the following approach fails. Suppose we require the debaters to each initially write up a detailed argument in judge-understandable language and read each other’s argument. Then, during the debate, each debater is allowed to quote short passages from their opponent’s writeup. Honest will be able to either find a contradiction or an unsupported statement in Dishonest’s initial writeup. If Honest quotes a passage and says its unsupported, then dishonest has to respond with the supporting sentences.
Yep, this does work, but limits us to questions where the argument in judge-understandable language is short enough that the debaters can write the whole thing down. So if the debaters run in P-time at deployment time, this gives us MA, not PSPACE as originally hoped.
I just mean that this method takes order(length of argument in judge-understandable language) time. So if the argument is large then you’re going to need to let the debate run for a long time. This is as opposed to the previous hope that even if the argument tree is exp-sized, the debate can run in p-time
To be clear, I think this is a good suggestion and is close to how I imagine we’d actually run debate in practice. It just doesn’t get us beyond MA if the debaters only write P-size arguments.
Wonderful writeup!
I’m sure you’ve thought about this, but I’m curious why the following approach fails. Suppose we require the debaters to each initially write up a detailed argument in judge-understandable language and read each other’s argument. Then, during the debate, each debater is allowed to quote short passages from their opponent’s writeup. Honest will be able to either find a contradiction or an unsupported statement in Dishonest’s initial writeup. If Honest quotes a passage and says its unsupported, then dishonest has to respond with the supporting sentences.
Thanks!
Yep, this does work, but limits us to questions where the argument in judge-understandable language is short enough that the debaters can write the whole thing down. So if the debaters run in P-time at deployment time, this gives us MA, not PSPACE as originally hoped.
OK, I guess I’m a bit unclear on the problem setup and how it involves a training phase and deployment phase.
I just mean that this method takes order(length of argument in judge-understandable language) time. So if the argument is large then you’re going to need to let the debate run for a long time. This is as opposed to the previous hope that even if the argument tree is exp-sized, the debate can run in p-time
To be clear, I think this is a good suggestion and is close to how I imagine we’d actually run debate in practice. It just doesn’t get us beyond MA if the debaters only write P-size arguments.