# [EM] Relative Margin agrees with Mike & Blake

Elisabeth Varin/Stephane Rouillon stephane.rouillon at sympatico.ca
Sun Dec 8 13:12:57 PST 2002

MIKE OSSIPOFF wrote :

> >But if few of those who voted consider a particular pairwise
> >comparison important enough to vote on, that says something.
>
> Blake replied:
>
> That's why I don't consider a vote of 3 to 1 to be as decisive as 100 to
> 50 (I know you don't either).
>
> I reply:
>
> Correct. I don't, if those are the X>Y and Y>X figures in X's defeat
> of Y.

Relative margin itself would tell you that a 3 to 1 vote is less decisive
than a 100 to 50. It would not stop the method to lock the 3 to 1 victory first,

but because the methos contains other aspects than the only relative
margin criteria, it will never elect A(3) nor B(1) !

If either Blake or Mike had considered relative margins seriously,
they would have seen that if two pairwise are A(3) > B(1) and C(100) > D(50),
it is impossible to A nor B to win with ranked pair (rm).
It comes from the mathematical property of coherence when a ranked vote
contributes to several pairwise comparison. With many votes, some incoherence
like cycle can appear, but some further incoherence are impossible.
Relative margin takes advantage of this property so to minimize the relativeness

of compared pairs.
The previous remark is really mathematically "out of context".
I suppose it comes more from ignorance...
If you want to generalize that principle, it says that no pairwise participant
can win
ranked pair (rm) if the number of votes he received in a pairwise comparison
is less than half of the total of voters of any other pairwise comparison.
And as a consequence, if any candidate as a two third majority (relative to the
total number of voters not relative to the voters expressing a preference in
this comparison) against every other candidates, this candidate cannot lose
because of unsincere truncation.

Steph.

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