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Encyclopedia > 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. The Democracy Series Liberal democracy History of democracy Representative democracy Representation Voting Voting systems Elections Elections by country Elections by calender Politics Politics by country Political campaigns Political science Political philosophy Political parties Parties by country Parties by name Parties by ideology Voting systems are methods (algorithms) for groups of...


How does it work?

Voters are allowed rank preference ballots (first, second, third, etc.). The term preferential voting (or preference voting) has several different meanings: A ranked ballot or preferential voting system is a type of voting system in which each voter casts their vote by ranking candidates in order of preference. ...

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 for more than one candidate to have majority support. This makes Bucklin a variation of approval voting. Absolute majority is a supermajoritarian voting requirement which is stricter than a simple majority. ... Approval voting is a voting system used for elections, in which each voter can vote for as many or as few candidates as the voter chooses. ...

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 In most states it was repealed and in a few states it was found to violate the state constitution.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. The majority criterion is a voting system criterion, used to objectively compare voting systems. ... The mutual majority criterion is a criterion used to compare voting systems. ... A voting system is monotonic if it satisfies the monotonicity criterion, given below. ... The introduction of this article does not provide enough context for readers unfamiliar with the subject. ...

It fails the Condorcet criterion, clone independence, participation, consistency, the Condorcet loser criterion and the independence of irrelevant alternatives criterion. The Condorcet candidate or Condorcet winner of an election is the candidate who, when compared in turn with each of the other candidates, is preferred over the other candidate. ... Strategic nomination is the manipulation of an election through its candidate set (compare this to tactical voting, where the manipulation comes from the voters). ... Statement of Criterion Adding one or more ballots that vote X over Y should never change the winner from X to Y. Complying Methods Plurality voting, Approval voting, Cardinal Ratings, Borda count, and Woodalls DAC method all pass the Participation Criterion. ... A voting system is consistent if, when the electorate is divided arbitrarily into two parts and separate elections in each part result in the same alternative being selected, an election of the entire electorate also selects that alternative. ... Any election method conforming to the Condorcet criterion is known as a Condorcet method. ... Independence of irrelevant alternatives is an axiom often adopted by social scientists as a basic condition of rationality. ...

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: State nickname: Volunteer State Other U.S. States Capital Nashville Largest city Memphis (largest metropolitan area is Nashville) Governor Phil Bredesen (D) Official languages English Area 109,247 km² (36th)  - Land 106,846 km²  - Water 2,400 km² (2. ...

  • 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: Census. ...

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

  Results from FactBites:
Bucklin voting - Wikipedia, the free encyclopedia (476 words)
Bucklin is a voting system that can be used for single-member districts and also multi-member districts.
Bucklin satisfies the majority criterion, the mutual majority criterion, the Monotonicity criterion, the summability criterion, the Non-compulsory support criterion and the strong defensive strategy criterion.
In this vote, the candidates for the capital are Memphis, Nashville, Chattanooga, and Knoxville.
Encyclopedia: Voting system (9865 words)
A voting system is a process that allows a group of people to express their tolerances or preferences about a number of options, and then selects one or more of those options, typically in a way meant to satisfy many of the voters.
Voting is best known for its use in elections and is often seen as the defining feature of democracy, where the options are candidates for public office, and the preferences of the citizens determine who gets to hold those offices.
Votes are transferred between candidates in a manner similar to instant runoff voting, but in addition to transferring votes from candidates who are eliminated, votes are also transferred from candidates who already have a quota.
  More results at FactBites »



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