User:KelvinVoskuijl/Descending Baldwin Coalitions

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Descending Borda Coalitions is a electoral system similar to Descending Descending Solid Coalitions except it uses Borda counting and points totals. It was first described by Kelvin Voskuijl in 2024

Description

Every possible set of candidates is given a score equal to the Borda points of voters who are solidly committed to the candidates in that set. A voter is solidly committed to a set of candidates if he ranks every candidate in this set strictly above every candidate not in the set. At each counting step, all candidates who are not supported by the coalition are eliminated until one candidate remains, In a variant, the coalition points are recalculated ater every elimination.

Tennessee's four cities are spread throughout the state
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)
  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
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

Since no candidate has more than half of the points, we rank the coalitions

  • 600 {M,N,C,K}
  • 348 {N,C,K}
  • 252 {M,N,C}
  • 210 {M,N}
  • 160 {C,K}
  • 130 {N,C}
  • 126 {M}
  • 78 {N}
  • 51 {K}
  • 45 {C}


Since the coalition with the most points that does not involve Memphis, we re-rank the points:

Voters
Candidate
 Memphis Nashville Knoxville Chattanooga Score
Nashville 42×2 = 84 26×2 = 52 0 0 136
Knoxville 0 0 17×2 = 34 15×1 = 15 49
Chattanooga 42×1 = 42 26×1 = 26 17×1 = 17 15×2 = 30 115

Since there still is no majority for one choice, we now look to the coalition that has the next most points and would eliminate candates, which is 210 {M,N}. This leaves Nashville as only candaidate, so Nashville wins.

With reranked coalitions

If we use reranked coaltions,

then we get to the folllowing coalitions points

  • 300 {N,C,K}
  • 126 {M,N,C}
  • 84 {M,N}
  • 96 {C,K}
  • 78 {N,C}
  • 0 {M}
  • 52 {N}
  • 34 {K}
  • 30 {C}

Nashville would win.

With Dowdall scoring

With Dowdall scoring we would have the following table

Voters
Candidate
 Memphis Nashville Knoxville Chattanooga Score
Memphis 42×1=42 26×1/4 = 6.5 17×1/4 = 4.25 15×1/4 = 3.75 56.5
Nashville 42×1/2 = 21 26×1 = 26 17×1/3 = 5.6667... 15×1/3 = 5 57.667...
Knoxville 42×1/4 = 10.5 26×1/3 = 8.333... 17×1 = 17 15×1/2 = 7.5 43.667...
Chattanooga 42×1/3 = 14 26×1/2 = 13 17×1/2 = 8.5 15×1 = 15 50.5
  • 208 1/3 {M,N,C,K}
  • 106 1/3 {N,C,K}
  • 77 {M,N,C}
  • 63 {M,N}
  • 48 {C,K}
  • 39 {N,C}
  • 42 {M}
  • 26 {N}
  • 17 {K}
  • 15 {C}

'this article is still being created '

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