IMO the requirements are a combination of stability and compactness—these trade off against each other, and the important thing is the rate at which you get evidence for which debater is dishonest while exploring the tree.
iiuc, the stability definition used here is pretty strong—says that the error in the parent is smaller than the largest error across the children. So any argument structure where errors can accumulate (like a conjunctive argument, or a proof which requires all the steps to be correct) is out.
The requirements are stability, compactness, and A-provability (meaning that the first player Alice knows how to correctly answer claims). It’s important that A-probability is a requirement, as otherwise you can do silly things like lifting up to multilinear extensions of your problem over finite fields, and then there will always been lots of independent evidence which can be turned into stability.
IMO the requirements are a combination of stability and compactness—these trade off against each other, and the important thing is the rate at which you get evidence for which debater is dishonest while exploring the tree.
iiuc, the stability definition used here is pretty strong—says that the error in the parent is smaller than the largest error across the children. So any argument structure where errors can accumulate (like a conjunctive argument, or a proof which requires all the steps to be correct) is out.
The requirements are stability, compactness, and A-provability (meaning that the first player Alice knows how to correctly answer claims). It’s important that A-probability is a requirement, as otherwise you can do silly things like lifting up to multilinear extensions of your problem over finite fields, and then there will always been lots of independent evidence which can be turned into stability.