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James G-A,<br>
You wrote (Fri.Mar.18):<br>
<blockquote type="cite">I agree that Raynaud is easy to explain. I
don't know about Gross Loser,
though... Winning votes is most intuitive to me. "This candidate was
opposed by 60% of voters in a pairwise contest! Eliminate him! Bam!" I
guess the GL equivalent would be "This candidate only got 30% of the
vote in a pairwise contest! Eliminate him! Bam!" I dunno... maybe.</blockquote>
The % sign here is a bit out of place and potentially misleading. I
think GL is much more intuitive than WV (or PO) because the opposition
could be from a subsequently<br>
eliminated candidate, which seems to render it less meaningful. <br>
In GL, you are looking at the pairwise matrix among remaining
candidates and then you eliminate the loser with the smallest tally.
What could be more natural than that?<br>
<i>
<blockquote type="cite">"Raynaud (GL): Until one candidate remains,
repeatedly eliminate the candidate with the fewest votes in any of the
pairwise comparisons among the remaining candidates."
<br>
<br>
Brief and succinct enough? In a previous post I identified two other
possible versions of Raynaud, "Pairwise Opposition" (or WV) and
Margins.
<br>
So why "Gross Loser"? Because it is the only version that meets
Woodall's Plurality criterion.
</blockquote>
<blockquote type="cite">I think that I understand your definitions. Can
you prove that
Raynaud(GL) meets this criterion?<br>
<br>
</blockquote>
</i>Yes! Plurality says that if any x has more first-place votes than y
has above-last-place votes, then y can't win. Of course x pairwise
beats y, and x's first-place votes contribute<br>
to x's score in all x's pairwise contests. x has more of these votes
than y has above-last-place votes; so while y is still around x can't
be eliminated. Therefore y can't win. <br>
<br>
<blockquote type="cite">Raynaud(GL) meets (mutual)Majority, all the
Condorcet properties, Plurality, Clone Independence, of course
mono-add-plump
<br>
and mono-append, and NZIS (i.e. there are no zero-info. strategy
incentives).
<br>
<br>
</blockquote>
<blockquote type="cite">Personally, I don't care a lot about random
fill incentive... but are you
sure that it doesn't exist in this method? It seems like it would
generate
some sort of queer incentive, but I don't know exactly what kind yet.
</blockquote>
I didn't mention random-fill incentives. I now think that with the
right combination of other properties, a random-fill incentive can on
balance be a good thing! I object far more<br>
to the "equal-rank near the top" incentive that exists for some voters
(including "zero-info." voters) in equal-ranking allowed Winning Votes
defeat-dropper.<br>
<br>
Am I sure that Raynaud(GL) meets NZIS? Yes. In the zero-info case, the
voter declining to participate in a paiwise comparison in which the
voter has a preference does nothing<br>
except make it more likely that the less preferred of the two
candidates will win.<br>
<br>
<blockquote type="cite">Because it is far less vulnerable to Burying, I
do actually prefer it to the "defeat droppers"!
<br>
<br>
</blockquote>
<blockquote type="cite">Hang on a moment... when did we establish that
Raynaud was far less
vulnerable to burying than defeat dropping methods?? I mean, if it is,
that's great, but I don't remember anyone demonstrating that...
</blockquote>
Looking at it more closely, I may have exaggerated. Probably instead
of "far less" I should have written "significantly". But I do have a
weak Burial-related criterion that<br>
Raynaud(GL) meets and the Defeat-droppers fail, I'll save that for a
later post.<br>
<br>
<br>
Chris Benham<br>
<br>
<br>
<br>
<i><br>
</i><br>
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