[EM] Sincere methods

[James Green-Armytage]

Hi Gervase,
	Some quick replies follow...

>If you want something a bit more strategic resistant, Reynaud(Margins) 
>might be a good step up.  I was thinking about this recently in relation 
>to the recent Approval 'Elimination' Condorcet thread and the Reynaud 
>thread.  Chris Benham mentioned it in passing in the recent Reynaud
>thread.
>
>If I got it right, the method can be summarised as "While there is no 
>Condorcet Winner, eliminate the candidate with the worst MinMax(Margins) 
>'score'".  

	Raynaud successively eliminates candidates with the strongest defeat
against them.

>I don't know whether this method is monotonic or not.

	I don't think it is.
>
>I get the feeling that Reynaud(Margins) is going to be the best you're 
>going to get with regards to a reasonable strategic resistant Margins 
>Pairwise method.

	I don't think that Raynaud is especially strategy resistant, whether with
margins or winning votes. I'll repeat what I told Chris:
	Assume that the three sincere defeats are A>B A>C and B>C. 
	In Raynaud, supporters of B need to make a fake C>A defeat which is the
strongest of the three. (If order of defeat strengths is CA > AB?BC... B
wins.)
	In defeat dropping methods, supporters of B need to make a fake C>A
defeat so that the A>B defeat is the weakest of the three. (If order of
defeat strengths is CA?BC > AB ... B wins.)
	So, which of these strategies is usually harder to pull off? Depends on
the situation, right? In my little 46-44-10 example, then the Raynaud
strategy would be harder, because the one and only possible "C" candidate
does so poorly in sincere pairwise comparisons, and so some of the B>A>C
voters would have to vote B=C>A to pull it off. However, I'd expect that
in most serious multicandidate scenarios there would be at least one
available "C" candidate such that B voters could make a fake C>A defeat
that was bigger than the other two... And I'm starting to imagine the
messy complications... Defeat dropping methods at least have the
constraint that the A>B defeat needs to be weaker than the B>C defeat to
begin with. No, I'm guessing that using Raynaud won't help too much on the
strategy front...
...
	Anyway, if strategy is an issue, I wouldn't suggest a margins method at
all. If strategy isn't an issue, then we're in la-la-land anyway, so it
doesn't matter too much what voting method we use.

my best,
James