# User:KelvinVoskuijl/Descending Borda Coalitions

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. It is unknown if it is a Condorcet method.

## 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.

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
VotersCandidate Memphis Nashville Knoxville Chattanooga 42×3=126 0 0 0 126 42×2 = 84 26×3 = 78 17×1 = 17 15×1 = 15 194 0 26×1 = 26 17×3 = 51 15×2 = 30 107 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}

The coalition witht the most points does not involve Memphis, so we eliminate that, candidate, then the next coalition does not involve Knoxville, so we eliminate that, the next coaltion does not involve Chattanooga, so we eliminate Chattanooga, which only leaves Nashville,

### 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

VotersCandidate Memphis Nashville Knoxville Chattanooga 42×1=42 26×1/4 = 6.5 17×1/4 = 4.25 15×1/4 = 3.75 56.5 42×1/2 = 21 26×1 = 26 17×1/3 = 5.6667... 15×1/3 = 5 57.667... 42×1/4 = 10.5 26×1/3 = 8.333... 17×1 = 17 15×1/2 = 7.5 43.667... 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}