Talk:Coombs' method

Description of 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)

What means last place?

What does Coombs' method propose to do, if no-one is ranked last by an absolute majority?

How does the method find the looser of a respective round, if some voters rank only their first preferences?

"What does Coombs' method propose to do, if no-one is ranked last by an absolute majority?"

This is a flaw of coombs method (also present on instant runoff) JUST having the most amount of first places is not enought to be considered the best, but JUST having the most amount of last places votes is enought to be considered the winner.

Anyway, wikipedia talk pages arent forums and here is not the place to discuss here the system possible flaws. But to answer your question, it doenst need to have an absolute majority to be removed from the list of candidates, it just need to have an majority.177.92.128.26 (talk) 16:04, 8 August 2016 (UTC)

Absolute Majority of Simple Majority?

Should absolute mojority be replaced with Simple majority? I think it is better to call it like that? After all there is an article about it. Aknxy 19:42, 7 June 2006 (UTC)

Simple Majority is not 51

I think the line "In the first round, no candidate has an absolute majority of first place votes (51)." has to be corrected. It is understood as 51% of the votes. But actually Simple Majority is 50%+1 votes. Aknxy 19:45, 7 June 2006 (UTC)

Later-no-harm Criterion

To settle a debate in another discussion, does this method satisfy the Later-no-harm criterion? I would assert that it does. The Coombs' Method does not count subsequent choices (i.e. choices after the first) unless previous choices (i.e. choices of higher preference) are eliminated. Therefore, listing subsequent preferences will not hurt the probability of the primary candidate winning. 129.115.29.151 (talk) 00:53, 3 October 2008 (UTC)

Sorry, I think you must be confused. I'm sure Coombs' can fail LNH because it looks at the LOWEST preferences first. Tom Ruen (talk) 01:02, 3 October 2008 (UTC)

If you re-read Coombs' you will see that ONLY THE HIGHEST PREFERENCES that HAVE NOT BEEN ELIMINATED are counted (just like Instant Runoff Voting, which satisfies LNH). Adding secondary choices actually increases the chances your primary choice will not be eliminated (i.e. the most disliked candidate is eliminated first). If a voter's primary candidate is eliminated it can only be because the other voters greatly disliked that candidate. 129.115.29.151 (talk) 23:42, 7 October 2008 (UTC)

No. ONLY THE LOWEST PREFERENCES that HAVE NOT BEEN ELIMINATED are counted. Handsome 23:06, 8 October 2008 (UTC)

So you're telling me if I was the only participant and I marked my ballot like so:
1) Alice
2) Bob
3) Cindy
Cindy (my lowest preference) would win the election? Tastywheat (talk - contribs) 07:25, 19 October 2008 (UTC)

No. Please re-read the definition of Coombs' method. Handsome 09:57, 20 October 2008 (UTC)

I have read the definition, which is why I posed such an obviously wrong example to prove that for the purposes of COUNTING votes, the HIGHEST non-eliminated preferences are considered, and for the purposes of ELIMINATION, the LOWEST non-eliminated preferences are considered. If I am still wrong on this then please give an example of later-no-harm failure so we can end this discussion. 129.115.251.22 (talk) 01:22, 23 October 2008 (UTC)

Try this 3 candidate example {A,B,C}, 19 voters. Maybe I won't make a mistake!?

• BALLOT SET 1:
  1. ABC 5 votes
  2. ACB 3 votes
  3. BAC 1 vote
  4. BCA 5 votes
  5. CAB 2 votes
  6. CBA 3 votes

ROUND 1: A=8, B=6, C=5. No majority winner, count last:

LAST RANK COUNT: A=8, B=5, C=6 votes. (Eliminate A)

ROUND 2: B=11, C=8 (B wins)

• BALLOT SET 2: (Same election but A voters adjust their second choices ALL in support of B)
  1. ABC 8 votes
  2. ACB 0 votes
  3. BAC 1 vote
  4. BCA 5 votes
  5. CAB 2 votes
  6. CBA 3 votes

ROUND 1: (Same) A=8, B=6, C=5. No majority winner, count last:

LAST RANK COUNT: A=8, B=2, C=9 votes. (Eliminate C)

Round 2: A=10, B=9 (A wins)

So this example shows that LOWER-PREFERENCES among A-voters can move A between winning or losing. To me this contradicts later-no-harm. Tom Ruen (talk) 02:08, 23 October 2008 (UTC)

Okay, there is obviously a discrepancy with the later-no-harm definition. I'll discuss the definition then come back to this. Tastywheat (talk - contribs) 19:19, 23 October 2008 (UTC)