Bucklin voting

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.

How does it work?

Voters are allowed rank preference ballots - first, second, third.

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.

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 In most states it was repealed and in a few states it was found to violate the state constitution.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 criteria

Bucklin satisfies the Plurality criterion, the Majority criterion for solid coalitions, Monotonicity, Later-no-help, and Minimal Defense (which implies satisfaction of the Strong Defensive Strategy criterion). It fails the Condorcet criterion, Clone Independence, Participation, and Later-no-harm.

An 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

City	Round 1	Round 2
Memphis	42	42
Nashville	26	68
Chatanooga	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.

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