Bucklin voting
Encyclopedia
Bucklin voting is a class of voting system
s 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.
(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.
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.
.
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
. 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two states, it was found to violate the state constitution and overturned; in the remainder of states using it, it was repealed.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.
, the mutual majority criterion
and the monotonicity criterion
.
Bucklin voting without equal rankings allowed fails the Condorcet criterion
, independence of clones criterion
, 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.
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 because they are not a second-place choice of competitors.
Chattanooga voters could cause their candidate to win by bullet voting. However, if they did, they might force Nashville voters to retaliate in kind, which would leave Nashville as the winner. Knoxville voters, who would know that a bullet strategy had no hope for them, would then be enough, though barely, to protect Nashville from bullet voting by Memphis.
Voting system
A voting system or electoral system is a method by which voters make a choice between options, often in an election or on a policy referendum....
s 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
Grand Junction, Colorado
The City of Grand Junction is the largest city in western Colorado. It is a city with a council–manager government form that is the county seat and the most populous city of Mesa County, Colorado, United States. Grand Junction is situated west-southwest of the Colorado State Capitol in Denver. As...
, and is also known as the Grand Junction system. As in Majority Judgment
Majority Judgment
Majority Judgment is a single-winner voting system proposed by Michel Balinski and Rida Laraki. Voters freely grade each candidate in one of several named ranks, for instance from "excellent" to "bad", and the candidate with the highest median grade is the winner. If more than one candidate has the...
, the Bucklin winner will be one of the candidates with the highest median ranking or rating.
Voting process
Voters are allowed rank preference ballotsPreferential voting
Preferential voting is a type of ballot structure used in several electoral systems in which voters rank candidates in order of relative preference. For example, the voter may select their first choice as '1', their second preference a '2', and so on...
(first, second, third, etc.).
First choice votes are first counted. If one candidate has a majority
Majority
A majority is a subset of a group consisting of more than half of its members. This can be compared to a plurality, which is a subset larger than any other subset; i.e. a plurality is not necessarily a majority as the largest subset may consist of less than half the group's population...
, 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
Majority
A majority is a subset of a group consisting of more than half of its members. This can be compared to a plurality, which is a subset larger than any other subset; i.e. a plurality is not necessarily a majority as the largest subset may consist of less than half the group's population...
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
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
Majority Judgment
Majority Judgment is a single-winner voting system proposed by Michel Balinski and Rida Laraki. Voters freely grade each candidate in one of several named ranks, for instance from "excellent" to "bad", and the candidate with the highest median grade is the winner. If more than one candidate has the...
. 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.
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 could allow an organized 51% to win all three seats in the first round, so this system does not give proportional representationProportional representation
Proportional representation is a concept in voting systems used to elect an assembly or council. PR means that the number of seats won by a party or group of candidates is proportionate to the number of votes received. For example, under a PR voting system if 30% of voters support a particular...
.
History and usage
The method was proposed by CondorcetMarquis de Condorcet
Marie Jean Antoine Nicolas de Caritat, marquis de Condorcet , known as Nicolas de Condorcet, was a French philosopher, mathematician, and early political scientist whose Condorcet method in voting tally selects the candidate who would beat each of the other candidates in a run-off election...
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
Progressive Era
The Progressive Era in the United States was a period of social activism and political reform that flourished from the 1890s to the 1920s. One main goal of the Progressive movement was purification of government, as Progressives tried to eliminate corruption by exposing and undercutting political...
. 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
Oklahoma primary electoral system
The Oklahoma primary electoral system is a voting system used to elect one winner from a pool of candidates using preferential voting. Voters rank candidates in order of preference, and their votes are initially allocated to their first-choice candidate. If, after this initial count, no candidate...
, 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 criterionMajority criterion
The majority criterion is a single-winner voting system criterion, used to compare such systems. The criterion states that "if one candidate is preferred by a majority of voters, then that candidate must win"....
, the mutual majority criterion
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...
and the monotonicity criterion
Monotonicity criterion
The monotonicity criterion is a voting system criterion used to analyze both single and multiple winner voting systems. A voting system is monotonic if it satisfies one of the definitions of the monotonicity criterion, given below.Douglas R...
.
Bucklin voting without equal rankings allowed fails the Condorcet criterion
Condorcet criterion
The Condorcet candidate or Condorcet winner of an election is the candidate who, when compared with every other candidate, is preferred by more voters. Informally, the Condorcet winner is the person who would win a two-candidate election against each of the other candidates...
, independence of clones criterion
Independence of clones criterion
In voting systems theory, the independence of clones criterion measures an election method's robustness to strategic nomination. Nicolaus Tideman first formulated the criterion, which states that the addition of a candidate identical to one already present in an election will not cause the winner...
, later-no-harm, participation
Participation criterion
The participation criterion is a voting system criterion. It is also known as the "no show paradox". It has been defined as follows:* In a deterministic framework, the participation criterion says that the addition of a ballot, where candidate A is strictly preferred to candidate B, to an existing...
, consistency, reversal symmetry
Reversal symmetry
Reversal symmetry is a voting system criterion which requires that if candidate A is the unique winner, and each voter's individual preferences are inverted, then A must not be elected. Methods that satisfy reversal symmetry include Borda count, the Kemeny-Young method, and the Schulze method...
, the Condorcet loser criterion
Condorcet method
A Condorcet method is any single-winner election method that meets the Condorcet criterion, which means the method always selects the Condorcet winner if such a candidate exists. The Condorcet winner is the candidate who would beat each of the other candidates in a run-off election.In modern...
and the independence of irrelevant alternatives criterion
Independence of irrelevant alternatives
Independence of irrelevant alternatives is an axiom of decision theory and various social sciences.The word is used in different meanings in different contexts....
.
If equal and skipped rankings are allowed, Bucklin passes or fails the same criteria as 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 because they are not a second-place choice of competitors.
Chattanooga voters could cause their candidate to win by bullet voting. However, if they did, they might force Nashville voters to retaliate in kind, which would leave Nashville as the winner. Knoxville voters, who would know that a bullet strategy had no hope for them, would then be enough, though barely, to protect Nashville from bullet voting by Memphis.
See also
- List of democracy and elections-related topics
- Voting systemVoting systemA voting system or electoral system is a method by which voters make a choice between options, often in an election or on a policy referendum....
- Plurality voting systemPlurality voting systemThe plurality voting system is a single-winner voting system often used to elect executive officers or to elect members of a legislative assembly which is based on single-member constituencies...
- Instant-runoff votingInstant-runoff votingInstant-runoff voting , also known as preferential voting, the alternative vote and ranked choice voting, is a voting system used to elect one winner. Voters rank candidates in order of preference, and their ballots are counted as one vote for their first choice candidate. If a candidate secures a...
- Approval votingApproval votingApproval voting is a single-winner voting system used for elections. Each voter may vote for as many of the candidates as the voter wishes. The winner is the candidate receiving the most votes. Each voter may vote for any combination of candidates and may give each candidate at most one vote.The...
- Borda countBorda countThe Borda count is a single-winner election method in which voters rank candidates in order of preference. The Borda count determines the winner of an election by giving each candidate a certain number of points corresponding to the position in which he or she is ranked by each voter. Once all...
- Oklahoma primary electoral systemOklahoma primary electoral systemThe Oklahoma primary electoral system is a voting system used to elect one winner from a pool of candidates using preferential voting. Voters rank candidates in order of preference, and their votes are initially allocated to their first-choice candidate. If, after this initial count, no candidate...
- Plurality voting system