Yes, this is a good point. Maybe we can strengthen the “weak-MLL” criterion in other ways while preserving existence. For example, we can consider the “p-dominance” condition Pr[v(B)>v(A)]≤1−p and look for an LL that is “weak p-maximal” for the highest possible p. The function on the LHS is lower-semincontinuous, hence there exists a maximal p for which a weak p-maximal LL exists.
Yeah, I believe this works, and that it feels too weak.
For example, if there is a unanimous winner, you only have to pick them half the time, and can do whatever you want the other half of the time.
Yes, this is a good point. Maybe we can strengthen the “weak-MLL” criterion in other ways while preserving existence. For example, we can consider the “p-dominance” condition Pr[v(B)>v(A)]≤1−p and look for an LL that is “weak p-maximal” for the highest possible p. The function on the LHS is lower-semincontinuous, hence there exists a maximal p for which a weak p-maximal LL exists.