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Bucklin voting

From Academic Kids

Bucklin is a voting system that can be used for single-member districts and also multi-member districts. It is also known as the Grand Junction system after Grand Junction, Colorado, where it was first proposed.

Contents

How does it work?

Voters are allowed rank preference ballots (first, second, third, etc.).

First choice votes are first counted. If one candidate has a majority, that candidate wins. Otherwise the second choices are added to the first choices. Again, if a candidate with a majority vote is found, the winner is the candidate with the most votes in that round. Lower rankings are added as needed.

A majority is defined as half the number of voters, similar to Absolute majority. Since after the first round there are more votes cast than voters, it is possible more than one candidate to have majority support. This makes Bucklin a variation of approval voting.

For multi-member districts, voters mark as many first choices as there are seats to be filled. Voters mark the same number of second and further choices. In some localities, the voter was required to mark a full set of first choices for his or her ballot to be valid.

Where is it used?

This method was used in many political elections in the United States in the early 20th Century. In most states it was repealed and in a few states it was found to violate the state constitution.

Satisfied and failed criteria

Bucklin satisfies the majority criterion, the mutual majority criterion, monotonicity, and the strong defensive strategy criterion.

It fails the Condorcet criterion, clone independence, participation, consistency, the Condorcet loser criterion and the independence of irrelevant alternatives criterion.

An example

Imagine an election for the capital of Tennessee, a state in the United States that is over 500 miles (800 km) east-to-west, and only 110 miles (180 km) north-to-south. In this vote, the candidates for the capital are Memphis, Nashville, Chattanooga, and Knoxville. The population breakdown by metro area is as follows:

Tennesee's four cities are spread throughout the state
  • Memphis: 826,330
  • Nashville: 510,784
  • Chattanooga: 285,536
  • Knoxville: 335,749

If the voters cast their ballot based strictly on geographic proximity, the voters' sincere preferences might be as follows:

42% of voters (close to Memphis)
  1. Memphis
  2. Nashville
  3. Chattanooga
  4. Knoxville

26% of voters (close to Nashville)

  1. Nashville
  2. Chattanooga
  3. Knoxville
  4. Memphis

15% of voters (close to Chattanooga)

  1. Chattanooga
  2. Knoxville
  3. Nashville
  4. Memphis
17% of voters (close to Knoxville)
  1. Knoxville
  2. Chattanooga
  3. Nashville
  4. Memphis
City Round 1 Round 2
Memphis 42 42
Nashville 26 68
Chattanooga 15 58
Knoxville 17 32

The first round has no majority winner. Therefore the second rank votes are added. This moves Nashville and Chatanooga above 50%, so a winner can be determined. Since Nashville is supported by a higher majority (68% versus 58%), Nashville is the winner.

Voter strategy

Voters supporting a strong candidate have a advantage to "Bullet Vote" (Only offer one ranking), in hopes that other voters will add enough votes to help their candidate win. This strategy is most secure if the supported candidate appears likely to gain many second rank votes.

In the above example, Memphis voters have the most first place votes and might not offer a second preference in hopes of winning, but it fails because they are not a second favorite from competitors.

See also

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