Bucklin voting

Bucklin voting is the name of a voting system 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 also known as the Grand Junction system.

Voting process

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 in that round. 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. This makes Bucklin a variation of approval voting. (No example in public elections of such a multiple majority is known.)

Since preferences are counted one rank at a time, organized voters who agree on one candidate before the election would be at an advantage to voters who support several similar candidates. If there are two candidates who appeal to the Yellow party, and five who split the vote of the Purple party, it may take four preference rounds before each of the Purple party voters support each other enough to elect a Purple party candidate, whereas the Yellow party would have caste all of its votes for the two Yellow party candidates after just the second round. This makes Bucklin voting in between plurality voting and approval voting.

Bucklin applied to multiwinner elections

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 caste three simultaneous votes for three seats could allow an organized 51% to win all three seats in the first round.

Usage

This method was used in many political elections in the United States in the early 20th century, as were many other experimental election methods during the progressive era. In all states it was eventually repealed or, in two states, it was found to violate the state constitution. In Minnesota, it was ruled unconstitutional, in a decision that disallowed votes for multiple candidates, in opposition to some voters' single expressed preference,^[1] and in Oklahoma, the method required voters to rank more than one candidate, when there were more than two, or the vote would not be counted, and the preferential primary was, for that reason, found unconstitutional.^[2]

Satisfied and failed criteria

Bucklin voting satisfies the majority criterion, the mutual majority criterion and the monotonicity criterion.

It 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.

Example application

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:

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 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

• List of democracy and elections-related topics
• Voting system
  • Plurality voting system
  • Instant-runoff voting
  • Approval voting
  • Borda count

Notes

References

• Municipal Voting System Reform: Overcoming the Legal Obstacles (History of use of Bucklin voting in Duluth, Minnesota in 1912)
• Grand Junction people: James Bucklin