[EM] Raynaud

[Chris Benham]

James G-A,
You wrote (Fri.Mar.18):

> 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.

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
eliminated candidate, which seems to render it less meaningful.
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?
/

> "Raynaud (GL):  Until one candidate remains, repeatedly eliminate the 
> candidate with the fewest votes in any of the pairwise comparisons 
> among the remaining candidates."
>
> Brief and succinct enough?  In a previous post I identified two other 
> possible versions of  Raynaud,  "Pairwise Opposition" (or WV) and  
> Margins.
> So why "Gross Loser"?  Because it is the only version that meets 
> Woodall's  Plurality criterion. 

> I think that I understand your definitions. Can you prove that 
> Raynaud(GL) meets this criterion?
>
/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
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.

> Raynaud(GL) meets (mutual)Majority, all the Condorcet properties, 
> Plurality, Clone Independence, of course mono-add-plump
> and mono-append, and NZIS (i.e. there are no zero-info. strategy 
> incentives).
>
> 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. 

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
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.

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
except make it more likely that the less preferred of the two candidates 
will win.

> Because it is far less vulnerable to Burying, I do actually prefer it 
> to the "defeat droppers"!
>
> 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... 

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
Raynaud(GL) meets and the Defeat-droppers fail, I'll save that for a 
later post.


Chris  Benham



/
/
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://lists.electorama.com/pipermail/election-methods-electorama.com/attachments/20050319/db15dcb8/attachment-0003.htm>