[EM] Weak INI -- three possibilities

[Richard Moore]

The following is a somewhat weaker version of INI:

"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