The most stable method for resolving a vote would always have the same option win, regardless of the votes.
The least stable method for resolving a vote would randomly pick the winner regardless of the votes. Clearly neither of these are the slightest bit desirable, so I think we should ignore stability as a criteria. Instead of stability, I think it's a good idea to use the criteria documented at www.electionmethods.org. Thanks, -- Raul