[EM] For Marku: dropping & "not there"

[LAYTON Craig]

Mike wrote (in part):

>Markus continues:
>
>It doesn't make much sense to say that "when you eliminate something
>then it's no longer there" as long as one doesn't say what it means
>when although the candidate X and the candidate Y are still there the
>pairwise comparison X:Y "is not longer there".
>
>I reply:
>
>Markus is right: It doesn't make much sense to say that the defeat
>is no longer there unless we know what it means for something to be
>no longer there. Markus, I suggest that avail yourself of the services
>of a translator, to facilitate your participation in this list.

I apologise for butting into your argument, but it seems that the
communication difficulty you are experiencing has nothing whatsoever to do
with Markus' language skills.  What a pairwise election method does can be
viewed in two ways; it produces a winning candidate or it produces a winning
opinion.  If an election method produces a winning candidate, the situation
is fairly straightforward; you can drop a pairwise comparison and that
pairwise comparison is no longer there.

However, if an election method produces a winning opinion, it is impossible
to remove a pairwise comparison without killing a candidate.  The idea being
that each majority opinion on each pairwise comparison is put alltogether to
get an overall opinion.  If that opinion contradicts itself, you have to
change it so it doesn't contradict itself - which involves inverting the
pairwise comparisons with the smallest majority.  Every pairwise comparison
is still there, because otherwise you don't get a complete opinion.  Markus
has come to the conclusion that this is what Condorcet means when he
discusses opinions and eliminating defeats.

I hope this might clarify your discussion a bit.