Bucklin voting

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Bucklin voting is a class of voting systems that can be used for single-member and multi-member districts. It is named after its original promoter, James W. Bucklin of Grand Junction, Colorado, and is also known as the Grand Junction system. As in Majority Judgment, the Bucklin winner will be one of the candidates with the highest median ranking or rating.

Voting process[edit]

Bucklin rules varied, but here is a typical example:

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 accumulated. Lower rankings are added as needed.

A majority is determined based on the number of valid ballots. Since, after the first round, there may be more votes cast than voters, it is possible for more than one candidate to have majority support.

Variants and relationships to other systems[edit]

The term Bucklin Voting refers to the process of counting all votes on all ballots that are above some threshold, and then adjusting that threshold down until a majority is reached. In some variants which have been used, equal ranking was allowed at some or all ranks. Some variants had a predetermined number of ranks available (usually 2 or 3), while others had unlimited ranks. There were also variants were akin to Borda voting in that lower-ranked votes counted for less.

The Bucklin procedure is one way to ensure that the winning candidate will be among those with the highest median rating. Another system with this property is Majority Judgment. Although Majority Judgment does not use the Bucklin procedure, it can be considered as a Bucklin system with a rated ballot, that is, one which allows equal or skipped rankings.[according to whom?]

Bucklin applied to multiwinner elections[edit]

Bucklin was used for multiwinner elections.[citation needed] For multi-member districts, voters marked as many first choices as there are seats to be filled. Voters marked 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. However, allowing voters to cast three simultaneous votes for three seats could allow an organized 51% to win all three seats in the first round, so this system does not give proportional representation.

History and usage[edit]

The method was proposed by Condorcet in 1793.[1] It was re-invented under its current name and used in many political elections in the United States in the early 20th century, as were other experimental election methods during the progressive era. In two states, it was found to violate the state constitution and overturned; in the remainder of states using it, it was repealed. In Minnesota, it was ruled unconstitutional, in a decision that disallowed votes for multiple candidates, in opposition to some voters' single expressed preference,[2] and in a variant used in Oklahoma, the particular application required voters in multi-candidate elections to rank more than one candidate, or the vote would not be counted; and the preferential primary was therefore found unconstitutional. The canvassing method itself was not rejected in Oklahoma.[3]

Satisfied and failed criteria[edit]

Bucklin voting satisfies the majority criterion, the mutual majority criterion and the monotonicity criterion.[4]

Bucklin voting without equal rankings allowed fails the Condorcet criterion, independence of clones criterion,[5] later-no-harm, participation, consistency, reversal symmetry, the Condorcet loser criterion and the independence of irrelevant alternatives criterion.

If equal and skipped rankings are allowed, Bucklin passes or fails the same criteria as Majority Judgment.

Example application[edit]



The candidates for the capital are:

  • 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
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 Chattanooga 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[edit]

Voters supporting a strong candidate have an incentive to bullet vote (offer only one first-rank vote), 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 the strategy fails, unless other voters also bullet vote, because they are not a second-place choice of competitors.

If all Memphis voters bullet vote, Chattanooga voters could cause their city to win by all bullet voting. However, if all Nashville voters also do the same, Memphis would win on the fourth and final round. In that case, Knoxville voters could do nothing to change the outcome.

In this particular example (but not always), bullet voting benefits one group of voters only if another group or groups do it as well. The example shows that, depending upon who does it, bullet voting may distort the outcome and could be counterproductive for some voters who do it (here, those from Chattanooga and Nashville).

To prevent bullet voting, voters could be required to rank all candidates on the ballot. This would provide the voter with a disincentive to bullet vote, as the vote would not be counted unless all candidates are ranked.

See also[edit]


  1. ^ Principles and problems of government, Haines and Hanes, 1921
  2. ^ Brown v. Smallwood, 130 Minn. 492, 153 N. W. 953
  3. ^ Dove v. Oglesby, 114 Okla. 144, 244 p. 798
  4. ^ Collective decisions and voting: the potential for public choice, Nicolaus Tideman, 2006, p. 204
  5. ^ Tideman, 2006, ibid