Why focus on the fullest set of swaps? An obvious alternative to “evaluate the hypothesis using the fullest set of swaps” is “evaluate the hypothesis by choosing the set of swaps allowed by H which make it look worse”.
I just now have realized that this is AFACIT equivalent to constructing your CaSc hypothesis adversarially—that is, given a hypothesis H, allowing an adversary to choose some other hypothesis H’, and then you run the CaSc experiment on join(H, H’).
One thing that is not equivalent to joins, which you might also want to do, is to choose the single worst swap that the hypothesis allows. That is, if a set of node values X={x1,x2,…} are all equivalent, you can choose to map all of them to e.g. x1. And that can be more aggressive than any partition of X which is then chosen-from randomly, and does not correspond to joins.
One thing that is not equivalent to joins, which you might also want to do, is to choose the single worst swap that the hypothesis allows. That is, if a set of node values X={x1,x2,…} are all equivalent, you can choose to map all of them to e.g. x1. And that can be more aggressive than any partition of X which is then chosen-from randomly, and does not correspond to joins.