Borda count: Difference between revisions
Added link to FBC compliant version of the Borda count.
(Added an example of an MBC decision.) |
(Added link to FBC compliant version of the Borda count.) |
||
| (4 intermediate revisions by 2 users not shown) | |||
Line 1:
{{Wikipedia}}
The '''Borda count''' BC and the Modified Borda count MBC are two [[voting system]] used mainly for decision-making and in election systems like the [[Quota Borda system]] QBS and the matrix vote.
The Borda count BC was devised by Nicholas Cusanus in 1433, while the Modified Borda Count MBC was proposed 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 for decision-making, but mainly for elections, by M. de 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.
Line 13:
The points are added up across all the ballots, and the candidate with the most points is the winner.
The MBC procedure is similar, but the difference can be huge.
he who casts just one preference gets his favourite only 1 point;
Line 23:
those who cast all 5 preferences get their favourite 5 points, (their 2nd choice 4 points, etc.).
In a BC, he who truncates his ballot and casts only 1 point, gets his favourite an (''n-1'') points advantage over all the other options/candidates.
== An example of a BC election==
Line 47:
</div>
Nashville is the winner in this election, as it has the most points.
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.
Line 60:
<u><big>An Example of an MBC decision</big></u>
In 2023 in a seminar Queen's University Belfast, the subject was the (forthcoming) border poll.
the max possible MBC score
Line 90:
|}
==Potential for BC tactical voting==
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.
Line 99:
In response to the issue of strategic manipulation in the Borda count, M. de Borda said "My scheme is only intended for honest men."
In majority voting, the two options listed are (regarded as being) mutually exclusive. So it is that, for example, in the Balkans, the 1991 referendum - "Are you Serb or Croat?" - disenfranchised any partner in, or adult child of, a mixed relationship... or anyone who wanted to vote for a compromise, or more importantly, for peace.
In an MBC of, say, five options, not every option will be totally mutually exclusive of all the other options. If, then, the two winning options are 'neck-and-neck', a composite may be formed based on the most popular option, as amended by those parts of the runner-up which are compatible with the winning option. The voter's 2nd preference should therefore best be his/her actual desire. As the old saying goes, "be careful what you wish for."
==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]].
==Criteria passed and failed==
Line 108 ⟶ 112:
Voting systems are often compared using mathematically-defined criteria. See [[voting system criterion]] for a list of such criteria.
The Borda count BC and Modified Borda Count MBC satisfy the [[monotonicity criterion]], the [[summability criterion]], the [[consistency criterion]], the [[participation criterion]],
It does not satisfy the [[Condorcet criterion]], the [[Independence of irrelevant alternatives]] criterion, or the [[Strategic nomination|Independence of Clones criterion]].
Line 114 ⟶ 118:
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. However, Borda does satisfy the majority criterion in the two-candidate case, meaning that it has a [[spoiler effect]] when it doesn't elect the [[Condorcet winner]] (because the CW would guaranteeably win when it's just them and any other candidate).
[[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]]
==Variants==
*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]].
Line 134 ⟶ 135:
==Current Uses of the Borda count==
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 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]].
Line 188 ⟶ 189:
*[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
*[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.
| |||