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The '''Borda count''' is a [[voting system]] devised by Jean-Charles de Borda (who was apparently preceded by Nicholas of Cusa [http://www-gap.dcs.st-and.ac.uk/~history/HistTopics/Voting.html]), used for single or multiple-seat [[election]]s. It is used for parliamentary elections in Nauru and Slovenia. This form of voting is also extremely popular in determining awards for sports in the United States. It is used in determining the Most Valuable Player in Major League Baseball, the national championship of college football, the Eurovision Song Contest, as well as many others.
The [[Borda count]] is a [[voting system]] used for single-winner [[election]]s [[preferential voting|in which each voter rank-orders the candidates]].
== Procedures ==
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. This method was devised by Borda to fairly elect members to the [[French Academy of Sciences]] and was used by the Academy beginning in 1784 until quashed by [[Napoleon]] in 1800.
A number ''n'' is selected; this number can be smaller than or equal to the number of candidates. Each voter lists their top ''n'' choices, in order of preference.
Borda elections use [[Preferential_voting|rank preference ballots]].
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".
A first-place rank is worth ''n'' points, a second-place rank is worth ''n''-1
==Procedures==
points, down to an ''n''th rank being worth 1 point. A candidate's score is the sum of the number of points they received. The highest-scoring candidate is elected.
In the trivial case of ''n''=1, this is mathematically identical to plurality voting.
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 ''i''th place receives ''n-i'' points. The candidate ranked last on the ballot therefore receives zero points.
In the trivial (limiting case) of n=∞, allowing truncated preferences, this is mathematically identical to [[approval voting]]. This is approximately true for large ''n'' the votes offered to ranked candidates will be approximately equal and nonranked candidates will all get zero votes. Example, if ''n''=10, and I rank only only three choices, they each get 10,9,8 votes respectively, normalized to 1.0, 0.9, 0.8 votes, close to 1.0 vote for an equivalent vote offered in Approval.
The points are added up across all the ballots, and the candidate with the most points is the winner.
If all candidates are to be ranked, the number of points given per candidate can be reduced by one (so that a first-place rank is worth ''n''-1 points and the last-place ranks is worth no points at all). This variation has the (possibly convenient) property that the number of possible points per candidate will be between 0 and (''c''-1)*''v'' inclusive, where ''c'' is the number of candidates and ''v'' the number of voters.
== An example of an election==
== An Example ==
{{Tenn_voting_example}}
|-
!Memphis
|42||0||0||58||126226
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!Nashville
|26||42||32||0||194294
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!Chattanooga
|15||43||42||0||173273
|-
!Knoxville
|17||15||26||42||107207
|}
</div>
Nashville is the winner in this election, as it has the most points. Nashville also happens to be the [[Condorcet winner]] in this case., Whilebut 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.
Like most voting methods, The Borda count is vulnerable to compromising. That is, voters can help avoid the election of a less-preferred candidate by insincerely raising the position of a more-preferred candidate on their ballot.
The Borda count is also vulnerable to burying. That is, voters can help a more-preferred candidate by insincerely lowering the position of a less-preferred candidate on their ballot.
For example, if there are two candidates whom a voter considers to be the most likely to win, the voter can maximize their impact on the contest between these candidates by ranking the candidate whom they like more in first place, and ranking the candidate whom they like less in last place. If neither candidate is their sincere first or last choice, the voter is employing both the compromising and burying strategies at once. If many voters employ such strategies, then the result will no longer reflect the sincere preferences of the electorate.
In response to the issue of strategic manipulation in the Borda count, M. de Borda said "My scheme is only intended for honest men."
==Potential for tactical voting==
Like most voting methods, The Borda count is vulnerable to compromising. That is, voters can help avoid the election of a less-preferred candidate by insincerely raising the position of a more-preferred candidate on their ballot.
The Borda count is also vulnerable to burying. That is, voters can help a more-preferred candidate by insincerely lowering the position of a less-preferred candidate on their ballot.
For example, if there are two candidates whom a voter considers to be the most likely to win, the voter can maximize their impact on the contest between these candidates by ranking the candidate whom they like more in first place, and ranking the candidate whom they like less in last place. If neither candidate is their sincere first or last choice, the voter is employing both the compromising and burying strategies at once. If many voters employ such strategies, then the result will no longer reflect the sincere preferences of the electorate.
In response to the issue of strategic manipulation in the Borda count, M. de Borda said "My scheme is only intended for honest men."
==Effect on factions and candidates==
The Borda count is vulnerable to [[Strategic nomination|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 can, creating the opposite of the [[spoiler effect]]. The teaming or "clone" effect is significant only where restrictions are placed on the candidate set.
==Criteria passed and failed==
Voting systems are often compared using mathematically-defined criteria. See [[voting system criterion]] for a list of such criteria.
The Borda count satisfies the [[monotonicity criterion]], the [[summability criterion]], the [[consistency criterion]], the [[participation criterion]], the [[Plurality criterion]] (trivially), [[Reversal symmetry]], [[Intensity of Binary Independence]] and the [[Condorcet loser criterion]].
It does not satisfy the [[Condorcet criterion]], the [[Independence of irrelevant alternatives]] criterion, or the [[Strategic nomination|Independence of Clones criterion]].
The Borda count also does not satisfy the [[majority criterion]], i.e. if a majority of voters rank one candidate in first place, that candidate is not guaranteed to win. This could be considered a disadvantage for Borda count in political elections, but it also could be considered an advantage if the favorite of a slight majority is strongly disliked by most voters outside the majority, in which case the Borda winner could have a higher overall utility than the majority winner.
[[Donald G. Saari]] created a mathematical framework for evaluating positional methods in which he showed that Borda count has fewer opportunities for strategic voting than other positional methods, such as [[plurality voting]] or [[anti-plurality voting]], e.g.; "vote for two", "vote for three", etc.
==Variants==
*The Borda count method can be extended to include tie-breaking methods.
*Ballots that do not rank all the candidates can be allowed in three 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, allows 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. This variant would satisfy the [[Plurality criterion]] and the [[Non-compulsory support criterion]].
**Another way, called the ''modified Borda count'', is to assign the points up to ''k'', 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. This variant would ''not'' satisfy the [[Plurality criterion]] or the [[Non-compulsory support criterion]].
**The third way is to employ a uniformly truncated ballot obliging the voter to rank a certain number of candidates, while not ranking the remainder, who all receive 0 points. This variant would satisfy the same criteria as the Borda count.
*A proportional election requires a different variant of the Borda count called the [[quota Borda system]].
*A voting system based on the Borda count that allows for change only when it is compelling, is called the [[Borda fixed point]] system.
*A procedure for finding the [[Condorcet winner]] of a Borda count tally is called [[Nanson's method]] or [[Instant Borda runoff]].
==Current Uses of the Borda count==
The Borda count is popular in determining awards for sports in the [[United States]]. It is used in determining the [[MLB Most Valuable Player Award|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. It is used for [[wine]] trophy judging by the [[Australian Society of Viticulture and Oenology]]. Borda count is used by the [[RoboCup]] [[robot]] competition at the Center for Computing Technologies, [[University of Bremen]] in [[Germany]].
The Borda count has historical precedent in political usage as it was one of the voting methods employed in the [[Roman Senate]] beginning around the year [[105]]. The Borda count is presently used for the election of ethnic minority members of parliament in [[Slovenia]]. In modified versions it is also used to elect members of parliament for the central Pacific island of [[Nauru]] (using a different positional point system) and for the selection of Presidential election candidates from among members of parliament in neighbouring [[Kiribati]]. The Borda count and variations have been used in [[Northern Ireland]] for non-electoral purposes, such as to achieve a consensus between participants including members of [[Sinn Féin]], the [[Ulster Unionists]], and the political wing of the [[UDA]].
== Potential for Tactical Voting ==
In educational institutions, the Borda count is used at the [[University of Michigan]] College of Literature, Science and the Arts to elect the Student Government, to elect the Michigan Student Assembly for the university at large, at the [[University of Missouri]] Graduate-Professional Council to elect its officers, at the [[University of California Los Angeles]] Graduate Student Association to elect its officers, the Civil Liberties Union of [[Harvard University]] to elect its officers, at [[Southern Illinois University]] at [[Carbondale, Illinois|Carbondale]] to elect officers to the Faculty Senate, and at [[Arizona State University]] to elect officers to the Department of Mathematics and Statistics assembly. Borda count is used to break ties for member elections of the faculty personnel committee of the School of Business Administration at the [[College of William and Mary]]. All these universities are located in the [[United States]].
The Borda count encourages [[tactical voting]] in many ways. Voters can be encouraged to "bury their favorite" candidate if they have no chance of winning. In the above example, voters from Memphis and Knoxville are encouraged to compromise because their first choices are unlikely to win.
In professional societies, the Borda count is used to elect the Board of Governors of the [[International Society for Cryobiology]], the management committee of [[Tempo sustainable design network]], located in [[Cornwall]], [[United Kingdom]], and to elect members to Research Area Committees of the [[U.S. Wheat and Barley Scab Initiative]].
In addition, voters are also encouraged to "bury" likely opponents by insincerely ranking them lower or not at all. In the above example, voters from both Memphis and Nashville are encouraged to insincerely "bury" Chattanooga, the candidate most likely to challenge Nashville, while voters from Chattanooga and Knoxville are encouraged to insincerely rank Nashville lower for the same reason.
Borda count is one of the feature selection methods used by the [[OpenGL]] Architecture Review Board.
In an extreme example of burying likely rivals, voters may "bullet vote": vote for a single choice only, thus allocating no points to other choices. One variation of Borda addresses this by allocating a number of points for the first choice equal to the number of choices made. In the above example, a partisan for Memphis who listed only Memphis on her ballot would give one point to Memphis, while a voter who listed Memphis first and listed second, third, and fourth choices on the ballot would allocate four points to Memphis. If there were more choices, this form of Borda encourages voters to vote for "push-overs", candidates absolutely unlikely to win the election, in order to get more points for their preferred candidate.
Borda count is one of the voting methods used and advocated by the [[Florida]] affiliate of the [[American Patriot Party]]. See [http://www.patriotparty.us/state/fl/platform.htm here] and [http://www.patriotparty.us/state/fl/bylaws.htm here].
In addition to tactical voting, [[strategic nomination]] considerations reign supreme in the Borda count. Running multiple, similar candidates may enhance a party's chance of winning the election by increasing the point differences with opposing candidates, if the party is allowed to advance more than one candidate for consideration.
==See also==
* [[Correlated Instant Borda Runoff]]
==FurtherExternal readinglink==
*[http://www.deborda.org The de Borda Institute, Northern Ireland]
* ''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.
*[http://fc.antioch.edu/~james_green-armytage/vm/antiborda.htm Critique] of the Borda count
==External links==
*[http://www.deborda.org The de Borda Institute, Northern Ireland]
*[http://www.colorado.edu/education/DMP/voting_b.html The Symmetry and Complexity of Elections] Article by mathematician [[Donald G. Saari]] shows that the Borda Count has relatively few paradoxes compared to certain other voting methods.
*[http://tinyurl.com/4wly9 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?
*[http://apseg.anu.edu.au/staff/pub_highlights/ReillyB_05.pdf Article by Benjamin Reilly] Social Choice in the South Seas: Electoral Innovation and the Borda Count in the Pacific Island Countries.
*[http://www.colorado.edu/education/DMP/voting_c.html A Fourth Grade Experience] Article by [[Donald G. Saari]] observing the choice intuition of young children.
*[http://hypatia.ss.uci.edu/imbs/tr/Final1.pdf Consequences of Reversing Preferences] An article by Donald G. Saari and Steven Barney.
*[http://www2.hmc.edu/~dym/PairwiseComparisons.pdf Rank Ordering Engineering Designs: Pairwise Comparison Charts and Borda Counts] Article by Clive L. Dym, William H. Wood and Michael J. Scott.
*[http://mason.gmu.edu/~atabarro/arrowstheorem.pdf Arrow's Impossibility Theorem] This is an article by Alexander Tabarrok on analysis of the Borda Count under Arrow's Theorem.
*[http://www.kfunigraz.ac.at/fwiwww/home-eng/activities/pdfs/2003-5.pdf Article by Daniel Eckert, Christian Klamler, and Johann Mitlöhner] On the superiority of the Borda rule in a distance-based perspective on Condorcet efficiency.
*[http://www.math.auckland.ac.nz/~slinko/Research/Borda3.pdf On Asymptotic Strategy-Proofness of Classical Social Choice Rules] An article by Arkadii Slinko.
*[http://www.bgse.uni-bonn.de/fileadmin/Fachbereich_Wirtschaft/Einrichtungen/BGSE/Discussion_Papers/2003/bgse13_2003.pdf Non-Manipulable Domains for the Borda Count] Article by Martin Barbie, Clemens Puppe, and Attila Tasnadi.
*[http://www.math.union.edu/~dpvc/papers/2001-01.DC-BG-BZ/DC-BG-BZ.pdf Which scoring rule maximizes Condorcet Efficiency?] Article by Davide P. Cervone, William V. Gehrlein, and William S. Zwicker.
*[http://pareto.uab.es/wp/2004/61704.pdf Scoring Rules on Dichotomous Preferences] Article mathematically comparing the Borda count to Approval voting under specific conditions by Marc Vorsatz.
*[http://www.eco.fundp.ac.be/cahiers/filepdf/c224.pdf Condorcet Efficiency: A Preference for Indifference] Article by William V. Gehrlein and Fabrice Valognes.
*[http://www.hss.caltech.edu/Events/SCW/Papers/seraj.pdf Cloning manipulation of the Borda rule] An article by Jérôme Serais.
*[http://ksgnotes1.harvard.edu/research/wpaper.nsf/rwp/RWP03-023/$File/rwp03_023_risse.pdf Democracy and Social Choice: A Response to Saari] Article by Mathias Risse.
*[http://allserv.rug.ac.be/~tmarchan/Crystals.pdf Cooperative phenomena in crystals and social choice theory] Article by Thierry Marchant.
*[http://tinyurl.com/7tadt A program to implement the Condorcet and Borda rules in a small-n election] Article by Iain McLean and Neil Shephard.
*[http://tinyurl.com/aeloj The Reasonableness of Independence] Article by Iain McLean.
*[http://proceedings.eldoc.ub.rug.nl/FILES/HOME/IAPR_IWFHR_2000/3D/43/paper-072-vanerp.pdf Variants of the Borda Count Method for Combining Ranked Classifier Hypotheses] Article by Merijn Van Erp and Lambert Schomaker
*[http://ola4.aacc.edu/kehays/umbc/MVP/Modified_BC.html Flash animation by Kathy Hays] An example of how the Borda count is used to determine the Most Valuable Player in Major League Baseball.
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[[Category:VotingSingle-winner voting systems]]
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