VoteFair representation ranking

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VoteFair representation ranking is a Proportional-representation (PR) vote-counting method that uses ranked ballots and selects a candidate to win the second seat in a two-seat legislative district. The second-seat winner represents the voters who are not well-represented by the first-seat winner. Any single-winner election method that uses ranked ballots and pairwise counting can be used for the popularity calculations.

This method can be repeated, such as to select the winners of the second and fourth seats in a five-seat district.

Description[edit | edit source]

This method first identifies which voters are well-represented by the first-seat winner. Then a reduced influence is calculated for these ballots. Their influence is determined by the extent to which they exceed the 50% majority minimum that is needed to elect the first-seat winner. The remaining ballots have full influence. Using these adjusted influence levels, the most popular of the remaining candidates becomes the second-seat winner.

This method ignores which political party each candidate is in, yet the winners typically are from different political parties.

If a district has 5 seats, the third-seat winner and the fourth-seat winner are identified using the same steps that were used to fill the first two seats. In this case the fifth-seat winner would be determined by asking voters to indicate their favorite political party, calculating which party is most under-represented, looking at just the ballots that indicate that party as their favorite, and identifying the most popular candidate from that party.

Calculation steps[edit | edit source]

After the winner of the district's first seat is identified, the following steps calculate which candidate wins the second seat.

  1. Identify the ballots that rank the first-seat winner as their first — highest-ranked — choice. (If there are no such ballots, no ballots will be ignored in the next step.)
  2. Completely ignore the ballots identified in step 1, and use the remaining ballots to identify the most popular candidate from among the remaining candidates. (If no ballots were identified in step 1, then use all the ballots.) This candidate will not necessarily be the second-seat winner. Instead, this candidate is used in step 4 to identify which ballots are from voters who are well-represented by the first-seat winner.
  3. Again consider all the ballots.
  4. Identify the ballots in which the first-seat winner is preferred over the candidate identified in step 2. This step identifies the ballots from voters who are well-represented by the first-seat winner. Note that the only way for a voter to avoid having his or her ballot identified in this step is to express a preference that significantly reduces the chances that the preferred candidate will be ranked as most popular.
  5. Proportionally reduce the influence of the ballots identified in step 4. (This step reduces the influence of the voters who are well-represented by the first-most representative choice.) This calculation uses the following sub-steps:
    1. Count the number of ballots that were identified in step 4.
    2. Subtract half the number of total ballots.
    3. The result represents the ballot-number-based influence deserved for the ballots identified in step 4.
    4. Divide the ballot-number-based influence number by the number of ballots identified in step 4.
    5. The result is the fraction of a vote that is allowed for each ballot identified in step 4.
  6. Based on all the ballots, but with reduced influence for the ballots identified in step 4, identify the most popular candidate from among the remaining candidates. This candidate becomes the second-seat winner.

Example[edit | edit source]

The ballots below are interpreted as if the four cities were competing for two seats in a legislature.

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

The Condorcet-Kemeny method identifies Nashville as the most popular candidate, meaning it wins the first seat.

VoteFair representation ranking identifies Memphis as the winner of the second seat.

The following details show how the second-seat winner is identified.

  • 26% of the ballots rank the most popular candidate (Nashville) as their first choice.
  • Looking at only the remaining 74% of the ballots, the most popular candidate (according to the Condorcet-Kemeny method) is Memphis.
  • 58% of the ballots rank Nashville higher than Memphis.
  • 58% exceeds 50% (the minimum majority) by 8% (the excess beyond majority).
  • 8% divided by 58% equals 0.1379 which is used as the weight for each of the 58% of the ballots that rank Nashville higher than Memphis.
  • Full weight for the ballots that do not rank Nashville higher than Memphis, combined with a weight of 0.1379 (about 14%) for the remaining ballots (that do rank Nashville higher than Memphis), identifies (according to the Condorcet-Kemeny method) the most popular candidate to be Memphis.

Memphis is declared the winner of the second seat. This candidate represents the voters who are not well-represented by the first-seat winner (Nashville).

History[edit | edit source]

VoteFair representation ranking was created by Richard Fobes while writing the book titled Ending The Hidden Unfairness In U.S. Elections, and is described in that book as part of the full VoteFair Ranking system.

This method has been used anonymously by non-governmental organizations that conduct their elections using the website.

External links[edit | edit source]

Open-source VoteFair Ranking software which calculates VoteFair representation ranking results using the Condorcet-Kemeny method for popularity calculations