Bucklin voting
From Wikipedia, the free encyclopedia
Bucklin voting is the name of a voting system that can be used for single-member and multi-member districts. It is also known as the Grand Junction system after Grand Junction, Colorado where it was first proposed.
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[edit] 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 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.
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.
[edit] Usage
This method was used in many political elections in the United States in the early 20th century. In most states it was eventually repealed and in a few states, it was found to violate the state constitution.
[edit] 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, participation, consistency, reversal symmetry, the Condorcet loser criterion and the independence of irrelevant alternatives criterion.
[edit] Example application
Imagine that the population of Tennessee, a state in the United States, is voting 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 one of these four cities, and that they would like the capital to be established as close to their city 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
- 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) |
|---|---|---|---|
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| 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.
[edit] 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.
[edit] See also
- List of democracy and elections-related topics
- Voting system
- Plurality voting system
- Instant-runoff voting
- Approval voting
- Borda count
- Majority choice approval (a Bucklin variant)
