James, You wrote (Tue.Mar.8):
I recognize that Raynaud fails monotonicity, but personally I don't consider that to be a big deal. Raynaud is arguably the most intuitively obvious pairwise tally method. I'm not willing to argue that Raynaud is superior to defeat-dropping pairwise methods, but I do feel that it should continue to be part of the conversation.
I agree with your positive remarks about Raynaud here. I regard Raynaud(Gross Loser) as one of the easy-to-explain contenders.
"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.
One of his examples: 09 abc 06 b 10 c
C>A 10-9 (m 1) A>B 9-6 (m 3) B>C 15-10 (m 5)
The candidate that is defeated by the greatest margin is C and also the candidate with the greatest pairwise opposition (i.e. the loser of the pairwise comparison in which the
winner got the most votes) is C, so the Margins and Pairwise Opposition versions both eliminate C and then A wins.
But C has more first-place votes than A has above-last-place votes, so the Plurality criterion bars A from winning. Raynaud(GL) eliminates B and then C wins.
This example from Steve Eppley's site demonstrates that all versions of Raynaud fail his "Minimal Defense" criterion.
46 zyz
10 y
10 yzx
34 zyx
Y>X 54-46 (m8) X>Z 46-44 (m2) Z>Y 80-20 (m60)
Here is Woodall's demonstration that Raynaud (all versions) fails Mono-raise:
7 abc 7 bca 6 cab
c has the most decisive defeat here, by b, and so c is eliminated and a is elected. But if you replace two of the bca ballots by abc, then b has the most decisive defeat, by a, and so b is eliminated and c is elected.
Raynaud(GL) has a very similar set of properties to another good method, Woodall's "CNTT,AV" (or Smith,IRV).
"CNTT,AV: elect the CW if there is one.Otherwise, do an IRV count on the original ballots and elect the remaining Smith set member when all-but-one of them have been eliminated."
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). Because it is far less vulnerable to Burying, I do actually prefer it to the "defeat droppers"!
Chris Benham
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