Monotonicity stops vote-negating
Methods that are not monotonic appear to negate votes: as the popularity rises, the candidate changes from a winner into a loser. The Alternative Vote is not monotonic. The local behaviour of a preferential voting method can be modelled with an algorithm that: (a) applies weighting numbers to the counts of the ballot papers, and that then (b) adds those products to subtotals. The Alternative Vote can exhibit an apparent weighting of -0.5. The actual algorithm only has positive weights.
Methods that are not monotonic can demand that voters (papers) vote insincerely or else lose power.