Example edit
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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Suppose that voters each used the NPP-FFE method to give preference to their closest city and approval to their next two closest options with their furthest option being disapproved.
| Voter from/ City Choice |
Memphis | Nashville | Chattanooga | Knoxville | Total |
|---|---|---|---|---|---|
| Memphis | 84 (42 × P) | -13 (26 × D) | -7.5 (15 × D) | -8.5 (17 × D) | 55 |
| Nashville | 42 (42 × A) | 52 (26 × P) | 15 (15 × A) | 17 (17 × A) | 126 |
| Chattanooga | 42 (42 × A) | 26 (26 × A) | 30 (15 × P) | 17 (17 × A) | 115 |
| Knoxville | -21 (42 × D) | 26 (26 × A) | 15 (15 × A) | 34 (17 × P) | 54 |
Nashville, the capital in real life, likewise wins in the example. If there were a runoff between Nashville and Chattanooga, then Nashville would win again by 68% to 32%.
For comparison, note that traditional first-past-the-post would elect Memphis, even though most citizens consider it the worst choice, because 42% is larger than any other single city. Instant-runoff voting would elect the 2nd-worst choice (Knoxville), because the central candidates would be eliminated early. A Two-round system would have a runoff between Memphis and Nashville where Nashville would win.