Coombs' method: Difference between revisions

Revision as of 22:52, 7 September 2003

Revision as of 07:44, 8 September 2003

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The '''Coombs' method''' is a [[voting system]] used for single-winner [[election]]s, in which each voter rank-orders the candidates. If there is a simple majority in people's first choice, the candidate who holds that majority wins. But if there is no simple majority, morea complicatedseries proceduresof takeeliminations placeoccurs. The Coombs' method was invented by [[Clyde Coombs]], hence the name.

==Procedures==

Each voter rank-orders all of the candidates on their ballot.

The method forworks tabulatingas is relatively simplefollows. First, if there is a simple majority in people's first choice, that candidate wins. If there isn't a simple majority, the candidate with thea leastmajority of last place votes is eliminated. Then, forIf the peopleno whosesuch candidate was elimatedexists, theirthe rankcandidate orderingwith getsthe shiftedmost upfirst byplace one.votes So,is fortemporarily example,eliminated iffrom myconsideration orderingfor wasperminent 1elimination. A, 2.Once C,a 3.perminently Beliminated andcandidate Ais was eliminatedfound, mythat newcandidate rankingis wouldfactored beout 1.of Cthe ballot, 2. B. Thenand the process is repeated. This is done until a single candidate is chosen by simple majorityremains.

==An example==

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<tr>

<td>

'''Group A: 42% of voters (close to Memphis)'''<br>

1. Memphis<br>

2. Nashville<br>

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</td>

<td valign="top">

'''Group B: 26% of voters (close to Nashville)'''<br>

1. Nashville<br>

2. Chattanooga<br>

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</td>

<td>

'''Group C: 15% of voters (close to Chattanooga)'''<br>

1. Chattanooga<br>

2. Knoxville<br>

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</td>

<td>

'''Group D: 17% of voters (close to Knoxville)'''<br>

1. Knoxville<br>

2. Chattanooga<br>

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</table>

Assuming all of the voters vote sincerely (strategic voting is discussed below), the results would be (goingas follows, by percentage). Note, these are the numbers of '''last place''' votes:

<table border="1">

<caption>Instant-runoffCoombs Method Election Results (last place votes)</caption>

<tr>

<th>City</th>

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<tr>

<th bgcolor="#ffc0c0">Memphis</th>

<td bgcolor="#ffc0c0">4258</td>

<td bgcolor="#ffc0c0e0e0ff">42<strike>58</strike> 0 </td>

<td bgcolor="#ffc0c0e0e0ff">42n/a</td>

</td>

</tr>

<tr>

<th bgcolor="#ffc0c0">Nashville</th>

<td bgcolor="#ffc0c0">260</td>

<td bgcolor="#ffc0c0">26<strike>0</strike> 32</td>

<td bgcolor="#e0e0ffffc0c0"><strike>2632 &lt;-winner with least last place votes</striketd>

0</td>

</tr>

<tr>

<th bgcolor="#ffc0c0">Chattanooga</th>

<td bgcolor="#ffc0c0">150</td>

<td bgcolor="#e0e0ffffc0c0"><strike>15</strike> 0 </td>

<td bgcolor="#e0e0ffffc0c0"> <strike>0</strike> 68 </td>

</td>

</tr>

<tr>

<th bgcolor="#ffc0c0">Knoxville</th>

<td bgcolor="#ffc0c0">1742</td>

<td bgcolor="#ffc0c0"><strike>1742</strike> 3268 </td>

<td bgcolor="#ffc0c0e0e0ff"><strike>3268</strike> 580 </td>

</tr>

</table>

Starting off, there is no candidate with a simple majority of first place votes. A series of eliminations now occurs:

Starting off, there is no simple majority. In the first round, Chattanooga, having the smallest vote, is eliminated. All of the votes for Chattanooga have Knoxville have a second choice, so they are transferred to Knoxville. There is still no simple majority. Now, Nashville has the smallest vote, so it is eliminated. The votes for Nashville have Chattanooga as a second choice, but as Chatanooga has been eliminated, they instead transfer to their third choice, Knoxville. No majority now either. Knoxville now has 58% of the vote, which is a simple majority, making it the winner.

* In the first round, Memphis, having a majority of last place votes (26+15+17=58), is eliminated.

* In the second round, Memphis is out of the running, and so must be factored out. The lowest ranked candidate on Group B's ballots is Knoxville, and the lowest ranked candidate on Group C and D's ballots is Nashville, so the votes are transferred accordingly. Knoxville now has a majority of last place votes, and is eliminated.

* In the third round, Knoxville is out of the running, and is factored out of the ballots. Now, the lowest ranked candidate on both Group A and Group B's ballots is Chatanooga, so these ballots now count against Chatanooga. Since Chatanooga has a majority against it, it is eliminated, leaving Nashville the winner.

==Potential for Tactical voting==

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==External Link==

*[http://condorcet.org/emr/methods.shtml#Coombs CondorsetCondorcet.org EMR: Coombs' method]