# [EM] Other criterias

Elisabeth Varin/Stephane Rouillon stephane.rouillon at sympatico.ca
Wed Dec 4 22:08:40 PST 2002

```Mike --

I have continued studying criterias behavior.

A strong CW using your definition needs 51% of the votes against
any opponent.

First, with margins a strong CW exists too, but it needs at least
67 % support of the full electorate in each pairwise victory against
every opponent. The same is valid for (rm).
This is where Adam has the fun of searching a counter-example,
it is his turn...
If you replace the strong CW by this strong CW(margin), margin
would satisfy a SFC(margin) criteria. The same with (rm).

Maybe you would like to name it differently than strong CW(margin-rm)...

The stronger CW could be a valid name?

SFC can be viewed as criteria dependent. It is obvious to me now
that the SFC(wv) (the real and maybe only SFC you could say) is better
protecting from insincere truncation than SFC(margin-rm).

Second, it is possible to build a graphical representation to compare
these criterias.
Make a 2-D orthogonal basis, with one axis as winners and the other
loosers.
Take only the half quadrant where winners>loosers.
Each pair of coordinates of a point of the region represents a pairwise
victory or tie.
Draw the isolines for wv, margins and rm.
(wv) lines are horizontal or vertical, margins are at a 45 deg. angle
and (rm) all pass
by (0,0) like rays...
It seems to me that margins is the criteria that can be viewed as a
compromise between
the two others. Cute but not that useful.

Steph.

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