Example

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42% of voters
26% of voters
15% of voters
17% of voters
  1. Memphis
  2. Nashville
  3. Chattanooga
  4. Knoxville
  1. Nashville
  2. Chattanooga
  3. Knoxville
  4. Memphis
  1. Chattanooga
  2. Knoxville
  3. Nashville
  4. Memphis
  1. Knoxville
  2. Chattanooga
  3. Nashville
  4. Memphis
 
Tennessee and its four major cities: Memphis in the far west; Nashville in the center; Chattanooga in the east; and Knoxville in the far northeast

Suppose Tennessee is holding an election on the location of its capital. The population is split between four cities, and all the voters want the capital to be as close to them as possible. The options are:


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.