[EM] Weak INI -- three possibilities

Richard Moore moore3t1 at cox.net
Mon Apr 12 20:11:03 PDT 2004

```One more observation: The second criterion in my previous message
(quoted below) could be referred to as Weak Independence from
Contradictory Information. Loosely stated, ICI means "A method's
results should not depend on information that contradicts those results".

The strong form of ICI would be: "If X wins and Y loses, and Y has a
beatpath to X through 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."

The last criterion below is the best statement I can find that fits
the designation, "Weak INI".

-- Richard

--- Richard Moore wrote:
> 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
>
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```