"If X wins and Y loses, and Y beats Z pairwise and Z beats X pairwise, then removing candidate Z from all ballots, leaving those ballots otherwise unchanged, shall not cause Y to win and X to lose."
Not sure if it's weak enough to let in Shulze or RP, though. If X has a beatpath to Y that goes through Z, and X is depending on that beatpath, then removing Z could make X lose. This even weaker version addresses that issue:
"If X wins and Y loses, and Y beats Z pairwise and Z beats X pairwise, and X does not have a beatpath to Y through Z, then removing candidate Z from all ballots, leaving those ballots otherwise unchanged, shall not cause Y to win and X to lose."
A third possibility for weakening INI is to preserve the margins provision of the original, and add the beatpath provision:
"If X wins and Y loses, and margin(X,Z) <= margin(Y,Z), and X does not have a beatpath to Y through Z, then removing candidate Z from all ballots, leaving those ballots otherwise unchanged, shall not cause Y to win and X to lose."
I actually like this last version best, at least on initial examination. My original margins-based concept of "nonsupporting" is preserved, and improved by the requirement that Z does not provide a beatpath from X to Y, since that beatpath could also be interpreted as supporting the "X beats Y" proposition. Markus, does your method pass this version?
-- Richard
---- Election-methods mailing list - see http://electorama.com/em for list info
