Here's a criterion that I think is a stronger variant of mono-raise: If some candidate A is ranked ahead of another candidate B in the social ordering, then raising A on one or more ballots should not lead B to be ranked ahead of A. A method could pass monotonicity but fail pairwise monotonicity if it e.g. provides the social ordering B>C>A>D before A is raised, and it changes to D>A>B>C after. Are any methods known for passing mono-raise but not pairwise mono-raise? I can't think of any at the moment. -km