Bucklin voting is a class of voting methods that can be used for single-member and multi-member

districts A district is a type of administrative division that, in some countries, is managed by the local government. Across the world, areas known as "districts" vary greatly in size, spanning regions or counties, several municipalities, subdivisions o ...

. As in highest median rules like the majority judgment, the Bucklin winner will be one of the candidates with the highest median ranking or rating. It is named after its original promoter, the

Georgist Georgism, also called in modern times Geoism, and known historically as the single tax movement, is an economic ideology holding that, although people should own the value they produce themselves, the economic rent derived from land—including ...

politician

James W. Bucklin James is a common English language surname and given name: *James (name), the typically masculine first name James * James (surname), various people with the last name James James or James City may also refer to: People * King James (disambiguat ...

of Grand Junction, Colorado, and is also known as the Grand Junction system.

Voting process

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 A majority, also called a simple majority or absolute majority to distinguish it from #Related terms, related terms, is more than half of the total.Dictionary definitions of ''majority'' aMerriam-Webster majority A majority, also called a simple majority or absolute majority to distinguish it from #Related terms, related terms, is more than half of the total.Dictionary definitions of ''majority'' aMerriam-Webster Borda voting The Borda count is a family of positional voting rules which gives each candidate, for each ballot, a number of points corresponding to the number of candidates ranked lower. In the original variant, the lowest-ranked candidate gets 0 points, th ...

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 vote. When used with a cardinal voting scale instead of ordinal ranking, Bucklin's balloting method is the same as that of highest median rules like the Majority Judgment. However, Bucklin's selection algorithm starts with the highest rated votes and adds lower ones until a median winner is reached, whereas Majority Judgment starts with the median votes and removes them until all but one candidate is eliminated. Due to this difference, Bucklin passes some

voting criteria There are a number of different criteria which can be used for voting systems in an election: *Condorcet criterion *Condorcet loser criterion *Consistency criterion * Homogeneity criterion *Independence of clones criterion *Independence of irreleva ...

that Majority Judgment fails, and vice versa.

Bucklin applied to multiwinner elections

Bucklin was used for multiwinner elections. 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 ( block voting) could allow an organized 51%, or the largest minority in a contest with three or more slates, to win all three seats in the first round, so this method does not give proportional representation.

History and usage

The method was proposed by

Condorcet Marie Jean Antoine Nicolas de Caritat, Marquis of Condorcet (; 17 September 1743 – 29 March 1794), known as Nicolas de Condorcet, was a French philosopher and mathematician. His ideas, including support for a liberal economy, free and equal pu ...

in 1793. 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. Bucklin voting was first used in 1909 in Grand Junction, Colorado, and then used in more than sixty other cities including Denver and San Francisco. 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, 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.

Satisfied and failed criteria

Bucklin voting satisfies the majority criterion, the

mutual majority criterion The mutual majority criterion is a criterion used to compare voting systems. It is also known as the majority criterion for solid coalitions and the generalized majority criterion. The criterion states that if there is a subset S of the candidate ...

and the monotonicity criterion. Bucklin voting without equal rankings allowed fails the Condorcet criterion, independence of clones criterion,Tideman, 2006, ibid 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 highest median rules like the Majority Judgment.

Example application

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

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.

References

;Specific ;General
Municipal Voting System Reform: Overcoming the Legal Obstacles (History of use of Bucklin voting in Duluth, Minnesota in 1912)

Non-proportional multi-winner electoral systems Single-winner electoral systems Preferential electoral systems Non-monotonic electoral systems

Notes

{{notelist