[EM] A new election method...

Roy royone at yahoo.com
Thu Aug 9 13:26:37 PDT 2001

Buddha Buck <bmbuck at 1...> wrote:
> list the candidates in order of descending first-place votes...
> Use this listing as a seed for a single-elimination tournament, 
> with a candidate advancing in the tournament if he, compared
> head-to-head with his opponent, is defeated.
> Eliminate the "winner" of the single-elimination tournament, and 
> relist/eliminate, etc until a single candidate remains.

Although it does use elimination, the relisting doesn't change any of 
the comparisons: B vs C will be 80:120 in every round. So there's 
really no need to have multiple comparisons to eliminate a candidate. 
Just start with one candidate, and compare him to each of the others. 
As long as he wins, you keep moving through the list. When he gets 
beat, you have to take your winner through all remaining contenders.

I'd call the method "Running the Gauntlet". I'm sure it's been 
invented many times.

I think the IRV people would recommend that the candidate with the 
fewest first-place votes is the one to start with (as he's the one 
who has to survive the most contests to win).

> 70 C
> 50 B     B
> 50 D    D    D
> 30 A

1st contest: A vs. D (105:95). Winner: A (D is eliminated).
2nd contest: A vs. B (30:170). Winner: B (A is eliminated).
3rd contest: B vs. C (80:120). Winner, and still champeen, C!

If there is a Smith cycle, the order of comparison matters (it's the 
only thing that distinguishes any Condorcet method from another). 
What I've suggested here is effectively tie-breaking by plurality (I 
think). Your tie-breaking method is obscure, but determined by the 
listing (or re-listing) order. I think it has a bias against the 
candidates with more first-place votes.

Since they use the first-place count to order the comparisons, I 
suspsect both methods could exhibit non-monotonicity by swapping 
positions between a Smith set member and a non-member at some point.

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