Talk:Coombs' method

I believe the following is an accurate description of Coombs' method:

If at any time one candidate has a majority of first place votes, then this is the winner. As long as this is not the case, the candidate with the most last place votes is eliminated.

Unfortunately the article describes a different method; it appears to be a modification meant to always elect a Condorcet winner if it exists. -- 212.127.214.105 20:22, 9 Sep 2003 (EDT)

The article as it previously was written was describing Hare (more commonly known as "Instant Runoff"). Coombs is not Instant Runoff. My description of Coombs' method is accurate to the best of my knowledge. I've misplaced my research notebook so I can't cite my exact sources, but here's a thread loosely describing the method (at the time, I thought it was called the "Spokane method")

It always eliminates the Condorcet loser, but doesn't necessarily elect the Condorcet winner, from what I understand. I would have to really go spulunking through my material to find the example, though. -- RobLa 08:01, 10 Sep 2003 (UTC)

In the same thread I saw this post. And then there's of course still the external link in the article. So it looks like you're mistaken. A Condorcet winner will never get a majority of last place votes regardless of how many other candidates would be considered at the time, so the method currently described is a Condorcet method.

Here is an example where Coombs will not choose the Condorcet winner:

3:A>B>C

1:A>C>B

2:B>A>C

1:B>C>A

3:C>A>B

3:C>B>A

Condorcet winner: C

Coombs winner: A

Instant Runoff winner: C

BTW, it wasn't me who misrepresented Coombs as Instant Runoff in the article, so you don't have to tell me they're different. -- 212.127.214.105 17:07, 10 Sep 2003 (UTC)

Fair enough. I could be wrong with my definition, so feel free to change it to what you think it is, and I'll modify only if I find a reasonably authoritative source that says otherwise. I've got photocopies of more formal literature where I originally learned this stuff, and as soon as I find it, I'll double check it.

Regarding Condorcet equivalence though, you write: A Condorcet winner will never get a majority of last place votes, so the method currently described is a Condorcet method.. In cases where there exists a true majority of last place votes, you are correct. However, in cases where there's an Instant Runoff-style "majority" through transfers, I believe that the Condorcet winner could potentially muster enough quasi-last place votes to be eliminated. --- RobLa 05:31, 12 Sep 2003 (UTC)