User:KelvinVoskuijl/Coombs with Bottom Two Runoff
Coombs with Bottom Two Runoff is a electoral method in which in each round the pairwise loser of two candidates with the most last places is eliminated.
Example
Imagine that Tennessee is having an election on the location of its capital. The population of Tennessee is concentrated around its four major cities, which are spread throughout the state. For this example, suppose that the entire electorate lives in these four cities, and that everyone wants to live as near the capital as possible.
The candidates for the capital are:
- Memphis, the state's largest city, with 42% of the voters, but located far from the other cities
- Nashville, with 26% of the voters, near the center of Tennessee
- Knoxville, with 17% of the voters
- Chattanooga, with 15% of the voters
The preferences of the voters would be divided like this:
| 42% of voters (close to Memphis) |
26% of voters (close to Nashville) |
15% of voters (close to Chattanooga) |
17% of voters (close to Knoxville) |
|---|---|---|---|
|
|
|
|
| All possible pairs of choice names |
Number of votes with indicated preference | ||
|---|---|---|---|
| Prefer X over Y | Equal preference | Prefer Y over X | |
| X = Memphis Y = Nashville |
42% | 0 | 58% |
| X = Memphis Y = Chattanooga |
42% | 0 | 58% |
| X = Memphis Y = Knoxville |
42% | 0 | 58% |
| X = Nashville Y = Chattanooga |
68% | 0 | 32% |
| X = Nashville Y = Knoxville |
68% | 0 | 32% |
| X = Chattanooga Y = Knoxville |
83% | 0 | 17% |
The initial rankings are 42% Memphis, 26% Nashville, 17% Knoxville, and 15% Chattanooga.
In the first elimination round Memphis and Knoxville are compared to each other. Memphios is eliminated because it loses the pairwise comparison to Knoxville (42%-58%), so Memphis is eliminated Their first preferences are now transferred to Nashville, which now has a majority of votes, so is elected now.