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Borda count: Difference between revisions
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The Borda count is also vulnerable to [[tactical voting|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
==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 in elections with a small number of voters. As the electorate increases, the teaming or "clone" effects decrease towards zero.
==Criteria passed and failed==
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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
The Borda count also does not satisfy the [[majority criterion]],
[[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.
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*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,
**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]], the [[Favorite
**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.
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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]].
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]].
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*[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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