Nanson's method

Nanson's method is a electoral method devised by mathematician Edward J. Nanson in 1882. In this method in every round all candidates that are on or beneath the average Borda score are eliminated each round, and the ballots are recounted as if those candidates never were on the ballot,

Example

Tennessee's four cities are spread throughout the state

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)
Memphis Nashville Chattanooga Knoxville	Nashville Chattanooga Knoxville Memphis	Chattanooga Knoxville Nashville Memphis	Knoxville Chattanooga Nashville Memphis

This gives the following points table:

Voters Candidate	Memphis	Nashville	Knoxville	Chattanooga		Score
Memphis	42×3=126	0	0	0		126
Nashville	42×2 = 84	26×3 = 78	17×1 = 17	15×1 = 15		194
Knoxville	0	26×1 = 26	17×3 = 51	15×2 = 30		107
Chattanooga	42×1 = 42	26×2 = 52	17×2 = 34	15×3 = 45		173

As there were a total of 600 Borda points, and 600/4 = 150, we eliminate Memphis and Knoxville. This leaves us with Nashville and Chattanooga, which have 68 and 32 points respectively. This means Nashville wins.