Suppose that Tennessee is holding an election on the location of its capital. The population is concentrated around four major cities. All voters want the capital to be as close to them as possible. The options are:
- Memphis, the largest city, but far from the others (42% of voters)
- Nashville, near the center of the state (26% of voters)
- Chattanooga, somewhat east (15% of voters)
- Knoxville, far to the northeast (17% of voters)
The preferences of each region's voters are:
| 42% of voters Far-West |
26% of voters Center |
15% of voters Center-East |
17% of voters Far-East |
|---|---|---|---|
|
|
|
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Dowdall
editIn Dowdall each ranking is equivalent to 1/n points.
Memphis is ranked first by 42% of the voters (42 points), and fourth by 58% (14,5 points) of voters, so gets 56.5 points
Nashville is ranked first by 26% of the voters (26 points), second by 42% of the voters, (21 points), and third by 32% (10 2/3) total 57 2/3 points.
Chattanooga is ranked first by 15% (15 points), second by 43%, (21,5 points), and third by 42% (14 points) totaling 50,5 points.
Knoxville is ranked first by 17% (17 points), second by 15% (7,5 points), third by 26% (8 2/3th), and fourth by 42 (10,5 points), totaling 43 2/3
Nashville has the most points and wins the election
Dowdall Nanson elimination
editIn case a majority of the points is needed, you can eliminate the candidate with the fewest points, which is Knoxville
now the rankings are different, Memphis is ranked third by 58 (19 1/3 points) so now has 61 1/3 points.
Nashville is ranked second by 74% (37 points) so now has 63 Chattanooga now is ranked first by 32% so now has 59 points
Still no majority, so Chattannoga is eliminated. Memphis is now ranked second by 58 (29), now totaling 71 points. Nashville is now ranking first with 58, now having 79 points
Nashville is the winner