The Rule of Monotonicity in Preferential Voting

(where the papers are like the ones of the Single Transferable Vote and the Alternative Vote)

Monotonicity: the rule requiring that support rises shall not harm

In [[voting system]]s, the a voting system can be said to be ”’monotonic”’ if it satisfies the following rule:

If candidate X loses, and the ballots are changed only by shifting preferences for X further away from the 1st (includes: dropping off the end of the paper), and without changing the relative position of all other preferences, then candidate X must still lose. The weight of papers does not change when shifting of X preferences occurs; but an exception is for shifting a preference naming X out of an “(X)” paper that names only candidate X. In that case the weight can reduce (and more votes can be removed than the “(X)” paper started with). The definition copes with papers with negative weights (counts).

There may be no authoritative definition. The definition above has some ideas distinctly stated: set of winners, candidate, ballot paper. and preferences on a ballot paper.