User:Rspeer/Borda Count
From Wikipedia, the free encyclopedia
The Borda count is a voting system used for single-winner elections in which each voter rank-orders the candidates.
The Borda count was devised by Jean-Charles de Borda in June of 1770. It was first published in 1781 as Mémoire sur les élections au scrutin in the Histoire de l'Académie Royale des Sciences, Paris. It was used by the French Academy of Sciences beginning in 1784 to elect members until quashed by Napolean Bonaparte in 1800.
This form of voting is popular in determining awards for sports in the United States. It is used in determining the Most Valuable Player in Major League Baseball, by the Associated Press and United Press International to rank players in NCAA sports, and other contests. The Eurovision Song Contest also uses a positional voting method similar to the Borda count, with a different distribution of points.
The Borda count is used for parliamentary elections in country of Slovenia, the south Pacific islands of Nauru and Kiribati in modified versions, and was one of the voting methods employed in the Roman Senate beginning around the year 105. The Borda count and variations have been used in Ireland for non-electoral purposes, such as to achieve a consensus between participants including members of Sinn Fein, the Ulster Unionists, and the political wing of the UDA.
Additionally, the Borda count is used at the University of Michigan College of Literature, Science and the Arts to elect the Student Government and to elect the Michigan Student Assembly, and at the University of Missouri Graduate-Professional Council to elect its officers.
The Borda count is classified as a positional voting system because each rank on the ballot is worth a certain number of points. Other positional methods include first-past-the-post (plurality) voting, and minor methods such as "vote for any two" or "vote for any three".
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[edit] Procedures
Each voter rank-orders all the candidates on their ballot. If there are n candidates in the election, then the first-place candidate on a ballot receives n-1 points, the second-place candidate receives n-2, and in general the candidate in ith place receives n-i points. The candidate ranked last on the ballot therefore receives zero points.
The points are added up across all the ballots, and the candidate with the most points is the winner.
[edit] An example of an election
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 | First | Second | Third | Fourth | Points |
|---|---|---|---|---|---|
| Memphis | 42 | 0 | 0 | 58 | 126 |
| Nashville | 26 | 42 | 32 | 0 | 194 |
| Chattanooga | 15 | 43 | 42 | 0 | 173 |
| Knoxville | 17 | 15 | 26 | 42 | 107 |
Nashville is the winner in this election, as it has the most points. Nashville also happens to be the Condorcet winner in this case. While the Borda count does not always select the Condorcet winner as the Borda Count winner, it always ranks the Condorcet winner above the Condorcet loser. No other positional method can guarantee such a relationship.
[edit] Potential for tactical voting
The Borda count is vulnerable to burying and compromising; that is, instead of voting their honest preferences, voters can rank a strong candidate they somewhat like first, or rank a strong candidate they somewhat dislike last, to increase their chances of getting a result they prefer.
Voters in a Borda count election can usually see the potential for voting strategically: if there are only two candidates with a reasonable chance of winning, they will want to rank the candidate of those two they prefer first, and the other candidate last, to maximize the difference in points they contribute to the total.
[edit] Effect on factions and candidates
The Borda count is vulnerable to teaming: when more candidates run with similar ideologies, the probability of one of those candidates winning increases.
Therefore, under the Borda count, it is to a faction's advantage to run as many candidates in that faction as they possibly can, creating the opposite of the spoiler effect.
[edit] Comparison to other methods
Because so much opinion is involved in what makes a good voting system, voting systems are usually compared using mathematically-defined criteria. See voting system criterion for a list of such criteria. The Borda count satisfies the monotonicity criterion, the consistency criterion, the summability criterion, and the participation criterion. It does not satisfy the Condorcet criterion, the weak defensive strategy criterion, or various related criteria.
The Borda count differs from most other methods in a significant way: if a majority of voters rank one candidate in first place, that candidate is not guaranteed to win. This is sometimes called the majority criterion. This could be considered a disadvantage for Borda in political elections. However, Borda is mainly used in competitions, where not satisfying the majority criterion can add tension and intrigue to the result.
Donald G. Saari created a mathematical framework for evaluating positional methods in which he showed that Borda has fewer opportunities for strategic voting than other positional methods, such as plurality voting or "vote for two".
[edit] Variants
The Borda count method can be extended to include tie-breaking methods. Also, ballots that do not rank all the candidates can be allowed in one of two ways.
One way to allow leaving candidates unranked is to leave the scores of each ranking unchanged and give unranked candidates 0 points. For example, if there are 10 candidates, and a voter votes for candidate A first and candidate B second, leaving everyone else unranked, candidate A receives 9 points, candidate B receives 8 points, and all other candidates receive 0.
This, however, facilitates strategic voting in the form of bullet voting: voting only for one candidate and leaving every other candidate unranked. This variant makes a bullet vote more effective than a fully-ranked vote.
Another way, called the modified Borda count, is to assign the points up to k-1, where k is the number of candidates ranked on a ballot. For example, in the modified Borda count, a ballot that ranks candidate A first and candidate B second, leaving everyone else unranked, would give 2 points to A and 1 point to B.
[edit] Instant Borda Runoff
The Borda count can be combined with Instant Runoff Voting to create a hybrid election method that satisfies some desirable properties. This method is also called Nanson's method. The method works like this:
Candidates are voted for on ranked ballots as in the Borda count. Then, the points are tallied in a series of rounds. In each round, the candidate with the fewest points is eliminated, and the points are re-tallied as if that candidate were not on the ballot.
Instant Borda Runoff satisfies the Condorcet criterion: since Borda always ranks the Condorcet winner over the Condorcet loser, the Condorcet winner will never be eliminated. As compared with the Borda count, however, Instant Borda Runoff does not satisfy the summability criterion.
[edit] See also
- List of democracy and elections-related topics
- Voting system - many other ways of voting
- Voting system criterion
- First Past the Post electoral system
- Instant-runoff voting
- Approval voting
- Plurality voting
- Condorcet method
[edit] Further reading
- Chaotic Elections!, by Donald G. Saari (ISBN 0821828479), is a book that describes various voting systems using a mathematical model, and supports the use of the Borda count.
[edit] External links
- The de Borda Institute, Northern Ireland For a comparison of all the best known decision-making processes and electoral systems, see Beyond the Tyranny of the Majority. For a description of what might be a good way of doing things, see Defining Democracy. The matrix vote is described in The Politics of Consensus.
- The Symmetry and Complexity of Elections Article by mathematician Donald G. Saari shows that the Borda Count has relatively few paradoxes compared to other voting methods.
- Article by Alexander Tabarrok and Lee Spector Would using the Borda Count in the U.S. 1860 presidential election have averted the american Civil War?
- Article by Benjamin Reilly Social Choice in the South Seas: Electoral Innovation and the Borda Count in the Pacific Island Countries.
- A Fourth Grade Experience Article by Donald G. Saari observing the choice intuition of young children.
- Consequences of Reversing Preferences An article by Donald G. Saari and Steven Barney.
- Rank Ordering Engineering Designs: Pairwise Comparison Charts and Borda Counts Article by Clive L. Dym, William H. Wood and Michael J. Scott.
- Arrow's Impossibility Theorem This is an article by Alexander Tabarrok on analysis of the Borda Count under Arrow's Theorem.
- Article by Daniel Eckert, Christian Klamler, and Johann Mitlöhner On the superiority of the Borda rule in a distance-based perspective on Condorcet efficiency.
- On Asymptotic Strategy-Proofness of Classical Social Choice Rules An article by Arkadii Slinko.
- Non-Manipulable Domains for the Borda Count Article by Martin Barbie, Clemens Puppe, and Attila Tasnadi.
- Scoring Rules on Dichotomous Preferences Article mathematically comparing the Borda count to Approval voting under specific conditions by Marc Vorsatz.
- Cloning manipulation of the Borda rule An article by Jérôme Serais.
- Efficiency in Polling A non-technical article on the Borda count by Courtney Baird.
- Flash animation by Kathy Hays An example of how the Borda count is used to determine the Most Valuable Player in Major League Baseball.
