Borda count
Encyclopedia
The Borda count is a single-winner election method
in which voters rank candidates in order of preference. The Borda count determines the winner of an election by giving each candidate a certain number of points corresponding to the position in which he or she is ranked by each voter. Once all votes have been counted the candidate with the most points is the winner. Because it sometimes elects broadly acceptable candidates, rather than those preferred by the majority, the Borda count is often described as a consensus-based electoral system, rather than a majoritarian one.
The Borda count was developed independently several times, but is named for the 18th-century French mathematician
and political scientist Jean-Charles de Borda
, who devised the system in 1770. It is currently used for the election of two ethnic minority members of the National Assembly of Slovenia, and, in modified forms, to select presidential election candidates in Kiribati
and to elect members of the Parliament of Nauru
. It is also used throughout the world by various private organisations and competitions.
systems, such as instant-runoff voting
, the Single Transferable Vote
or Condorcet's method
.
The number of points given to candidates for each ranking is determined by the number of candidates standing in the election. Thus, under the simplest form of the Borda count, if there are five candidates in an election then a candidate will receive five points each time they are ranked first, four for being ranked second, and so on, with a candidate receiving 1 point for being ranked last (or left unranked). In other words, where there are n candidates a candidate will receive n points for a first preference, n – 1 points for a second preference, n – 2 for a third, and so on, as shown in the following example:
Alternatively, votes can be counted by giving each candidate a number of points equal to the number of candidates ranked lower than them, so that a candidate receives n – 1 points for a first preference, n – 2 for a second, and so on, with zero points for being ranked last (or left unranked). Another way to express this is that a candidate ranked in ith place receives n – i points. For example, in a five-candidate election, the number of points assigned for the preferences expressed by a voter on a single ballot paper might be:
While the first of the above two formulae is used in the Slovenian parliamentary elections (as mentioned, for two out of 90 seats only), Nauru uses a sort of modified Borda count: the voter awards the first-ranked candidate with one point, while the second-ranked candidate receives half of the point, the third-ranked candidate receives one-third of the point, etc. (A similar system of weighting lower-preference votes is used in the Oklahoma primary electoral system
.) Using the above example, in Nauru the point distribution among the five candidates would be this:
When all votes have been counted, and the points added up, the candidate with most points wins. We have already noted that the Borda count is a preferential voting system; because, from each voter, candidates receive a certain number of points, the Borda count is also classified as a positional voting system
. Other positional methods include the 'first-past-the-post
' (plurality) system, bloc voting
, approval voting
and the limited vote
.
It can be seen above, for example, that Chattanooga is ranked first by 15% of voters, second by 43%, third by 42%, and last by no voters at all. To give points to each candidate for these rankings this example will use the formula, explained above, whereby a candidate receives one point for each time a candidate is ranked lower than them (or n – i points). Thus when Chattanooga's votes are added up the results are calculated as: (15*3) + (43*2) + (42*1) + (0*0) = 173. When the points of all candidates are added up, the results are as follows:
Result: The winner of the election is Nashville, as it has 194 points, which is more than any other candidate. Since this example was worked purely according to geographical distance, we would expect the "most acceptable" city to be the most central; a glance at the map above confirms that this is indeed the case. However, if voters in both Knoxville and Chattanooga were to put Chattanooga first and Nashville last, the winner would be Chattanooga, a preferable outcome for voters in both those cities. This is an example of tactical voting.
In Kiribati, a variant is employed which uses a traditional Borda formula, but in which voters rank only four candidates, irrespective of how many are standing – an example of a truncated ballot.
Thus he who votes for only one option/candidate exercises only 1 point; while she who casts two preferences will exercise 3 (2 plus 1) points.
In more general terms, an 'x'th preference, if cast, gets one more point than an 'x+1'th preference (whether cast or not). The MBC involves no special weighting: the difference is always just one point.
It is also possible, if specifically stipulated by the body using the MBC as its voting method, that candidates voted for by someone who does not cast preferences for all candidates get even less points than described above. For example, the first preference listed may receive m – 1 points instead of m points, the second preference will then receive m – 2 points, and so on.
The modified Borda count differs from a Borda count only in the preferences of those who submit partial ballots. In a BC on five options, he who votes for all five options gives his first preference 5 points, his second preference 4 points, and so on and she who votes for only one option still gives her first preference 5 points. In effect, therefore, a modified Borda count encourages the voter to submit only a first preference, in which case it degenerates into a plurality vote.
In a five-option MBC, by contrast, she who votes for only one option thus gives her favourite just 1 point; he who votes for two options gives his first preference 2 points (and his second preference 1 point). To ensure your favourite gets the maximum 5 points, therefore, you should cast all five preferences, then your favourite gets 5 points, your second preference gets 4 points, and so on, just like in a Borda count. The MBC thus encourages voters to submit a fully marked ballot.
The modified Borda count has been used by the Irish Green Party to elect its chairperson.
is a system of proportional representation
in multi-seat constituencies that uses the Borda count.
and Baldwin methods are single-winner voting systems that combine elements of the Borda count and instant-runoff voting. Unlike the Borda count, Nanson and Baldwin are majoritarian and Condorcet method
s.
and Condorcet's method. The Borda count tends to favour candidates supported by a broad consensus among voters, rather than the candidate who is necessarily the favourite of a majority; for this reason, some of its supporters see the Borda count as a method that promotes consensus and avoids the 'tyranny of the majority
'. Advocates argue, for example, that where the majority candidate is strongly opposed by a large minority of the electorate, the Borda winner may have higher overall utility than the majority winner. On grounds such as these, the de Borda Institute of Northern Ireland
advocates the use of a form of referendum
based on the Borda count in divided societies such as Northern Ireland, the Balkans
and Kashmir
.
Because it will not necessarily elect a candidate who is the first preference of a majority of voters, the Borda count is said by scholars to fail the majority criterion
. It is also theoretically possible for such a candidate to fail to be elected under approval voting
.
The Borda scores of the candidates are:
Under most single-winner voting systems – including 'first-past-the-post
' (plurality), instant-runoff and Condorcet's method – Andrew would have been the winning candidate; however, under the Borda count, Catherine has the highest Borda score and so is elected instead. Favouring Andrew as the winner is the fact that he is supported by an unambiguous absolute majority of voters. On the other hand, he is the last preference of 49 voters, which suggests that he may be strongly opposed by almost one-half of the electorate. Catherine, though she receives only a handful of first-preference votes, is at least the second choice of all voters; this seems to suggest that she is broadly acceptable to all voters.
. In particular, it is highly vulnerable to the tactics of compromising and burying. Compromising: voters can help avoid the election of a less-preferred candidate by insincerely raising the position of a more-preferred candidate on their ballot. Burying: voters can help a more-preferred candidate by insincerely lowering the position of a less-preferred candidate on their ballot.
An effective tactic is to combine these two strategies. For example, if there are two candidates whom a voter considers to be the most likely to win, the voter can maximise his impact on the contest between these front runners by ranking the candidate whom he likes more in first place, and ranking the candidate whom he likes less in last place. If neither front runner is his sincere first or last choice, the voter is employing both the compromising and burying tactics at once; if many voters employ such strategies, then the result will no longer reflect the sincere preferences of the electorate.
Using the above example based on choosing the capital of Tennessee, if polls suggest a toss-up between Nashville and Chattanooga, citizens of Knoxville might change their ranking to
If many Knoxville voters voted in this way, it would result in the election of Chattanooga. Citizens of Chattanooga could also increase the likelihood of the election of their city by voting tactically, but would require the assistance of some tactical voters from Knoxville to be successful.
In response to the issue of strategic manipulation in the Borda count, M. de Borda said, "My scheme is intended for only honest men". The academic Donald G. Saari
has created a mathematical framework for evaluating positional methods in which he claims to show that the Borda count has fewer opportunities for tactical voting than other positional methods such as plurality voting.
called teaming or cloning. This means that 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. For example, even in a single-seat election, it would be to the advantage of a political party to stand as many candidates as possible in an election. In this respect, the Borda count differs from many other single-winner systems, such as the 'first past the post
' plurality system, in which a political faction is disadvantaged by running too many candidates. Under systems such as plurality, 'splitting
' a party's vote in this way can lead to the spoiler effect
, which harms the chances of any of a faction's candidates being elected.
In 1980, William Gehrlein
and Peter Fishburn compared the Borda count to other positional methods, such as plurality and approval voting
. They investigated the likelihood of a positional method choosing the same candidate when the set of candidates was modified by eliminating one losing candidate from a three-candidate election, and two losing candidates from a four-candidate election. They found that the Borda count was the positional rule which maximises the probability of electing the same candidate after this modification of the choice set.
The variant of the Borda count that permits bullet voting satisfies the plurality criterion
, but the 'modified Borda count' does not. Variants that oblige voters to rank only a certain specified number of candidates satisfy the same criteria as the conventional Borda count.
and the tiny Micronesia
n nations of Kiribati
and Nauru
. In Slovenia, the Borda count is used to elect two of the ninety members of the National Assembly: one member represents a constituency of ethnic Italians, the other a constituency of the Hungarian minority. As noted above, members of the Parliament of Nauru are elected based on a variant of the Borda count that involves two departures from the normal practice: (1) multi-seat constituencies, of either two or four seats, and (2) a point-allocation formula that involves increasingly small fractions of points for each ranking, rather than whole points. In Kiribati, the president (or Beretitenti) is elected by the plurality system, but a variant of the Borda count is used to select either three or four candidates to stand in the election. The constituency consists of members of the legislature (Maneaba). Voters in the legislature rank only four candidates, with all other candidates receiving zero points. Since at least 1991, tactical voting has been an important feature of the nominating process.
The Republic of Nauru became independent from Australia
in 1968. Before independence, and for three years afterwards, Nauru used instant-runoff voting, importing the system from Australia, but since 1971, a variant of the Borda count has been used.
The Borda count has been used for non-governmental purposes at certain peace conferences in Northern Ireland, where it has been used to help achieve consensus between participants including members of Sinn Féin
, the Ulster Unionists, and the political wing of the UDA
.
, and is used in determining the Most Valuable Player
in Major League Baseball
, by the Associated Press
and United Press International
to rank teams in NCAA
sports, to determine the winner of the Heisman Trophy
, and so on. The Eurovision Song Contest
also uses a positional voting method similar to the Borda count, with a different distribution of points: only the top ten entries are considered in each ballot, the favourite entry receiving 12 points, the second-placed entry receiving 10 points, and the other eight entries getting points from 8 to 1. Although designed to favour a clear winner, it has produced very close races and even a tie. The Borda count is used for wine trophy judging by the Australian Society of Viticulture and Oenology
, and by the RoboCup
autonomous robot soccer competition at the Center for Computing Technologies, in the University of Bremen
in Germany
. The People's Remix Competition uses a Borda variant where each voter ranks only the top three contestants.
The Borda count is used in a number of educational institutions in the United States, such as 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, in the Civil Liberties Union of Harvard University
to elect its officers, at Southern Illinois University
at Carbondale
to elect officers to the Faculty Senate, and at Arizona State University
to elect officers to the Department of Mathematics and Statistics assembly. It is also used to elect faculty members to committees at Wheaton College, Massachusetts. 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
.
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
. The Borda count is one of the feature-selection methods used by the OpenGL
Architecture Review Board. The Borda count is used to elect the Board of Directors of the X.Org Foundation
.
The Borda count is used to determine winners for Toastmasters International
speech contests. Judges offer a ranking of their top-three speakers, awarding them three points, two points, and one point, respectively. All unranked candidates receive zero points.
The modified Borda count is used to elect the President for the United States member committee of AIESEC
.
The Finnish Associations Act lists three different modifications of the Borda count for holding a proportional election. All the modifications use fractions, like in Nauru. A Finnish assoction may choose to use other methods of election, as well.
An example is the case of the voting to determine the winner of the Heisman Trophy: judges vote 3,2,1 for their top three choices – the vote weights are thus (3,2,1,0,0,0, ..., 0,0,0). By contrast, the Borda vote weights in, say, a fifty-candidate election would be (49,48,47, ..., 2,1,0), which is markedly different. Heisman-style voting, when there are more than a handful of candidates, is thus more similar to plurality voting, which has weights (1,0,0,0, ..., 0,0,0), than it is to Borda.
beginning around the year 105. However, in its modern, mathematical form, the system is thought have been discovered independently by at least three men:
Voting system
A voting system or electoral system is a method by which voters make a choice between options, often in an election or on a policy referendum....
in which voters rank candidates in order of preference. The Borda count determines the winner of an election by giving each candidate a certain number of points corresponding to the position in which he or she is ranked by each voter. Once all votes have been counted the candidate with the most points is the winner. Because it sometimes elects broadly acceptable candidates, rather than those preferred by the majority, the Borda count is often described as a consensus-based electoral system, rather than a majoritarian one.
The Borda count was developed independently several times, but is named for the 18th-century French mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
and political scientist Jean-Charles de Borda
Jean-Charles de Borda
Jean-Charles, chevalier de Borda was a French mathematician, physicist, political scientist, and sailor.-Life history:...
, who devised the system in 1770. It is currently used for the election of two ethnic minority members of the National Assembly of Slovenia, and, in modified forms, to select presidential election candidates in Kiribati
Kiribati
Kiribati , officially the Republic of Kiribati, is an island nation located in the central tropical Pacific Ocean. The permanent population exceeds just over 100,000 , and is composed of 32 atolls and one raised coral island, dispersed over 3.5 million square kilometres, straddling the...
and to elect members of the Parliament of Nauru
Parliament of Nauru
The Parliament of Nauru has 18 members, elected for a three year term in multi-seat constituencies. The President of Nauru is elected by the members of the Parliament.The members of the Parliament of Nauru are elected by a positional voting system....
. It is also used throughout the world by various private organisations and competitions.
Voting and counting
Under the Borda count the voter ranks the list of candidates in order of preference. So, for example, the voter gives a '1' to their first preference, a '2' to their second preference, and so on. In this respect, a Borda count election is the same as elections under other preferential votingPreferential voting
Preferential voting is a type of ballot structure used in several electoral systems in which voters rank candidates in order of relative preference. For example, the voter may select their first choice as '1', their second preference a '2', and so on...
systems, such as instant-runoff voting
Instant-runoff voting
Instant-runoff voting , also known as preferential voting, the alternative vote and ranked choice voting, is a voting system used to elect one winner. Voters rank candidates in order of preference, and their ballots are counted as one vote for their first choice candidate. If a candidate secures a...
, the Single Transferable Vote
Single transferable vote
The single transferable vote is a voting system designed to achieve proportional representation through preferential voting. Under STV, an elector's vote is initially allocated to his or her most preferred candidate, and then, after candidates have been either elected or eliminated, any surplus or...
or Condorcet's method
Condorcet method
A Condorcet method is any single-winner election method that meets the Condorcet criterion, which means the method always selects the Condorcet winner if such a candidate exists. The Condorcet winner is the candidate who would beat each of the other candidates in a run-off election.In modern...
.
The number of points given to candidates for each ranking is determined by the number of candidates standing in the election. Thus, under the simplest form of the Borda count, if there are five candidates in an election then a candidate will receive five points each time they are ranked first, four for being ranked second, and so on, with a candidate receiving 1 point for being ranked last (or left unranked). In other words, where there are n candidates a candidate will receive n points for a first preference, n – 1 points for a second preference, n – 2 for a third, and so on, as shown in the following example:
Alternatively, votes can be counted by giving each candidate a number of points equal to the number of candidates ranked lower than them, so that a candidate receives n – 1 points for a first preference, n – 2 for a second, and so on, with zero points for being ranked last (or left unranked). Another way to express this is that a candidate ranked in ith place receives n – i points. For example, in a five-candidate election, the number of points assigned for the preferences expressed by a voter on a single ballot paper might be:
While the first of the above two formulae is used in the Slovenian parliamentary elections (as mentioned, for two out of 90 seats only), Nauru uses a sort of modified Borda count: the voter awards the first-ranked candidate with one point, while the second-ranked candidate receives half of the point, the third-ranked candidate receives one-third of the point, etc. (A similar system of weighting lower-preference votes is used in the Oklahoma primary electoral system
Oklahoma primary electoral system
The Oklahoma primary electoral system is a voting system used to elect one winner from a pool of candidates using preferential voting. Voters rank candidates in order of preference, and their votes are initially allocated to their first-choice candidate. If, after this initial count, no candidate...
.) Using the above example, in Nauru the point distribution among the five candidates would be this:
When all votes have been counted, and the points added up, the candidate with most points wins. We have already noted that the Borda count is a preferential voting system; because, from each voter, candidates receive a certain number of points, the Borda count is also classified as a positional voting system
Positional voting system
A positional voting system is a ranked voting method in which the options receive points based on their position on each ballot, and the option with the most points wins....
. Other positional methods include the 'first-past-the-post
Plurality voting system
The plurality voting system is a single-winner voting system often used to elect executive officers or to elect members of a legislative assembly which is based on single-member constituencies...
' (plurality) system, bloc voting
Plurality-at-large voting
Plurality-at-large voting is a non-proportional voting system for electing several representatives from a single multimember electoral district using a series of check boxes and tallying votes similar to a plurality election...
, approval voting
Approval voting
Approval voting is a single-winner voting system used for elections. Each voter may vote for as many of the candidates as the voter wishes. The winner is the candidate receiving the most votes. Each voter may vote for any combination of candidates and may give each candidate at most one vote.The...
and the limited vote
Limited Voting
Limited voting is a voting system in which electors have fewer votes than there are positions available. The positions are awarded to the candidates who receive the most votes absolutely...
.
An example
If the various rankings given to each candidate are added up they are as follows.It can be seen above, for example, that Chattanooga is ranked first by 15% of voters, second by 43%, third by 42%, and last by no voters at all. To give points to each candidate for these rankings this example will use the formula, explained above, whereby a candidate receives one point for each time a candidate is ranked lower than them (or n – i points). Thus when Chattanooga's votes are added up the results are calculated as: (15*3) + (43*2) + (42*1) + (0*0) = 173. When the points of all candidates are added up, the results are as follows:
Result: The winner of the election is Nashville, as it has 194 points, which is more than any other candidate. Since this example was worked purely according to geographical distance, we would expect the "most acceptable" city to be the most central; a glance at the map above confirms that this is indeed the case. However, if voters in both Knoxville and Chattanooga were to put Chattanooga first and Nashville last, the winner would be Chattanooga, a preferable outcome for voters in both those cities. This is an example of tactical voting.
Variants
As noted above, there is more than one formula for assigning points for each ranking of a candidate. In Nauru, a distinctive formula is used based on increasingly small fractions of points. Under the system a candidate receives 1 point for a first preference, ½ a point for a second preference, ⅓ for third preference, and so on. This method is far more favourable to candidates with many first preferences than the conventional Borda count; it also substantially reduces the impact of electors indicating late preferences at random because they have to complete the full ballot.In Kiribati, a variant is employed which uses a traditional Borda formula, but in which voters rank only four candidates, irrespective of how many are standing – an example of a truncated ballot.
Truncated ballots
A common way in which versions of the Borda count differ is the method for dealing with truncated ballots, that is, ballots on which a voter has not expressed a full list of preferences. There are several methods:- The simplest method is to allow voters to rank as many or as few candidates as they wish, but simply give every unranked candidate the minimum number of 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 or 10 points (depending on the formula used), candidate B receives 8 or 9 points, and all other candidates receive either zero or 1. However, this method allows strategic voting in the form of bullet votingBullet votingBullet voting is a tactic in which the voter only selects one candidate, despite the option to indicate a preference for other candidates. They might do this either because it is easier than evaluating all the candidates, or as a form of tactical voting.If enough voters bullet vote, almost any...
: voting for only one candidate and leaving every other candidate unranked. This variant makes a bullet vote more effective than a fully ranked ballot.
- Voters can simply be obliged to rank all candidates. This is the method used in Nauru.
- Voters can be permitted to rank only a subset of the total number of candidates but obliged to rank all of those, with all unranked candidates being given zero points. This is the system used in Kiribati.
- In Slovenia legislation does not mention the truncated ballots. Consequently, in the past election bodies dealed with them differently from district to district and from election to election. In 2004 parliamentary election, for instance, in one district unranked candidates received one point while in the other district they received zero points. In 2008, unranked candidates in both districts that use Borda Count received one point.
Modified Borda count
In a modified Borda count (MBC), the number of points given for a voter's first and subsequent preferences is determined by the total number of candidates they have actually ranked, rather than the total number standing. This is to say, typically, on a ballot of n options/candidates, if a voter casts preferences for only m options (where m is smaller than n), a first preference gets m points, a second preference m – 1 points, and so on. This means, in other words, that if there are ten candidates but a voter ranks only five, then their first preference will receive only five points; their second preference will receive 4 points, their next 3, and so on. This method effectively penalises voters who do not rank a full ballot, by diminishing the number of points their vote distributes among candidates.Thus he who votes for only one option/candidate exercises only 1 point; while she who casts two preferences will exercise 3 (2 plus 1) points.
In more general terms, an 'x'th preference, if cast, gets one more point than an 'x+1'th preference (whether cast or not). The MBC involves no special weighting: the difference is always just one point.
It is also possible, if specifically stipulated by the body using the MBC as its voting method, that candidates voted for by someone who does not cast preferences for all candidates get even less points than described above. For example, the first preference listed may receive m – 1 points instead of m points, the second preference will then receive m – 2 points, and so on.
The modified Borda count differs from a Borda count only in the preferences of those who submit partial ballots. In a BC on five options, he who votes for all five options gives his first preference 5 points, his second preference 4 points, and so on and she who votes for only one option still gives her first preference 5 points. In effect, therefore, a modified Borda count encourages the voter to submit only a first preference, in which case it degenerates into a plurality vote.
In a five-option MBC, by contrast, she who votes for only one option thus gives her favourite just 1 point; he who votes for two options gives his first preference 2 points (and his second preference 1 point). To ensure your favourite gets the maximum 5 points, therefore, you should cast all five preferences, then your favourite gets 5 points, your second preference gets 4 points, and so on, just like in a Borda count. The MBC thus encourages voters to submit a fully marked ballot.
The modified Borda count has been used by the Irish Green Party to elect its chairperson.
Multiple winners
The system invented by Jean-Charles de Borda was intended for use in elections with a single winner, but it is also possible to conduct a Borda count with more than one winner, by electing those candidates with the most points. In other words, if there are two seats to be filled, then the two candidates with most points win; in a three-seat election, the three candidates with most points, and so on. In Nauru, which uses the multi-seat variant of the Borda count, parliamentary constituencies of two and four seats are used. The Quota Borda SystemQuota Borda system
The Quota Borda System or Quota Preference Score is a voting system that was devised by the British philosopher Michael Dummett and first published in 1984 in his book, Voting Procedures, and again in his Principles of Electoral Reform....
is a system of proportional representation
Proportional representation
Proportional representation is a concept in voting systems used to elect an assembly or council. PR means that the number of seats won by a party or group of candidates is proportionate to the number of votes received. For example, under a PR voting system if 30% of voters support a particular...
in multi-seat constituencies that uses the Borda count.
Other systems
A number of voting systems other than the Borda count employ its system of assigning points for rankings. The NansonNanson's method
The Borda count can be combined with an Instant Runoff procedure to create hybrid election methods that are called Nanson method and Baldwin method.- Nanson method :The Nanson method is based on the original work of the mathematician Edward J...
and Baldwin methods are single-winner voting systems that combine elements of the Borda count and instant-runoff voting. Unlike the Borda count, Nanson and Baldwin are majoritarian and Condorcet method
Condorcet method
A Condorcet method is any single-winner election method that meets the Condorcet criterion, which means the method always selects the Condorcet winner if such a candidate exists. The Condorcet winner is the candidate who would beat each of the other candidates in a run-off election.In modern...
s.
As a consensual method
Unlike most other voting systems, in the Borda count it is possible for a candidate who is the first preference of an absolute majority of voters to fail to be elected; this is because the Borda count affords greater importance to a voter's lower preferences than most other systems, including other preferential methods such as instant-runoff votingInstant-runoff voting
Instant-runoff voting , also known as preferential voting, the alternative vote and ranked choice voting, is a voting system used to elect one winner. Voters rank candidates in order of preference, and their ballots are counted as one vote for their first choice candidate. If a candidate secures a...
and Condorcet's method. The Borda count tends to favour candidates supported by a broad consensus among voters, rather than the candidate who is necessarily the favourite of a majority; for this reason, some of its supporters see the Borda count as a method that promotes consensus and avoids the 'tyranny of the majority
On Liberty
On Liberty is a philosophical work by British philosopher John Stuart Mill. It was a radical work to the Victorian readers of the time because it supported individuals' moral and economic freedom from the state....
'. Advocates argue, for example, that where the majority candidate is strongly opposed by a large minority of the electorate, the Borda winner may have higher overall utility than the majority winner. On grounds such as these, the de Borda Institute of Northern Ireland
Northern Ireland
Northern Ireland is one of the four countries of the United Kingdom. Situated in the north-east of the island of Ireland, it shares a border with the Republic of Ireland to the south and west...
advocates the use of a form of referendum
Referendum
A referendum is a direct vote in which an entire electorate is asked to either accept or reject a particular proposal. This may result in the adoption of a new constitution, a constitutional amendment, a law, the recall of an elected official or simply a specific government policy. It is a form of...
based on the Borda count in divided societies such as Northern Ireland, the Balkans
Balkans
The Balkans is a geopolitical and cultural region of southeastern Europe...
and Kashmir
Kashmir
Kashmir is the northwestern region of the Indian subcontinent. Until the mid-19th century, the term Kashmir geographically denoted only the valley between the Great Himalayas and the Pir Panjal mountain range...
.
Because it will not necessarily elect a candidate who is the first preference of a majority of voters, the Borda count is said by scholars to fail the majority criterion
Majority criterion
The majority criterion is a single-winner voting system criterion, used to compare such systems. The criterion states that "if one candidate is preferred by a majority of voters, then that candidate must win"....
. It is also theoretically possible for such a candidate to fail to be elected under approval voting
Approval voting
Approval voting is a single-winner voting system used for elections. Each voter may vote for as many of the candidates as the voter wishes. The winner is the candidate receiving the most votes. Each voter may vote for any combination of candidates and may give each candidate at most one vote.The...
.
An example
Imagine an election in which 100 voters express the following preferences:| # | 51 voters | 5 voters | 23 voters | 21 voters |
|---|---|---|---|---|
| 1st | Andrew | Catherine | Brian | David |
| 2nd | Catherine | Brian | Catherine | Catherine |
| 3rd | Brian | David | David | Brian |
| 4th | David | Andrew | Andrew | Andrew |
The Borda scores of the candidates are:
- Andrew: 153
- Catherine: 205
- Brian: 151
- David: 91
Under most single-winner voting systems – including 'first-past-the-post
Plurality voting system
The plurality voting system is a single-winner voting system often used to elect executive officers or to elect members of a legislative assembly which is based on single-member constituencies...
' (plurality), instant-runoff and Condorcet's method – Andrew would have been the winning candidate; however, under the Borda count, Catherine has the highest Borda score and so is elected instead. Favouring Andrew as the winner is the fact that he is supported by an unambiguous absolute majority of voters. On the other hand, he is the last preference of 49 voters, which suggests that he may be strongly opposed by almost one-half of the electorate. Catherine, though she receives only a handful of first-preference votes, is at least the second choice of all voters; this seems to suggest that she is broadly acceptable to all voters.
Tactical voting
Like all voting systems, the Borda count is vulnerable to tactical votingTactical voting
In voting systems, tactical voting occurs, in elections with more than two viable candidates, when a voter supports a candidate other than his or her sincere preference in order to prevent an undesirable outcome.It has been shown by the Gibbard-Satterthwaite theorem that any voting method which is...
. In particular, it is highly vulnerable to the tactics of compromising and burying. Compromising: voters can help avoid the election of a less-preferred candidate by insincerely raising the position of a more-preferred candidate on their ballot. Burying: voters can help a more-preferred candidate by insincerely lowering the position of a less-preferred candidate on their ballot.
An effective tactic is to combine these two strategies. For example, if there are two candidates whom a voter considers to be the most likely to win, the voter can maximise his impact on the contest between these front runners by ranking the candidate whom he likes more in first place, and ranking the candidate whom he likes less in last place. If neither front runner is his sincere first or last choice, the voter is employing both the compromising and burying tactics at once; if many voters employ such strategies, then the result will no longer reflect the sincere preferences of the electorate.
Using the above example based on choosing the capital of Tennessee, if polls suggest a toss-up between Nashville and Chattanooga, citizens of Knoxville might change their ranking to
- Chattanooga (compromising their sincere first choice, Knoxville)
- Knoxville
- Memphis (burying their sincere third choice, Nashville)
- Nashville
If many Knoxville voters voted in this way, it would result in the election of Chattanooga. Citizens of Chattanooga could also increase the likelihood of the election of their city by voting tactically, but would require the assistance of some tactical voters from Knoxville to be successful.
In response to the issue of strategic manipulation in the Borda count, M. de Borda said, "My scheme is intended for only honest men". The academic Donald G. Saari
Donald G. Saari
Donald Gene Saari is the Distinguished Professor of Mathematics and Economics and director of the Institute for Mathematical Behavioral Sciences at the University of California Irvine...
has created a mathematical framework for evaluating positional methods in which he claims to show that the Borda count has fewer opportunities for tactical voting than other positional methods such as plurality voting.
Strategic nomination
The Borda count is highly vulnerable to a form of strategic nominationStrategic nomination
Strategic nomination is the manipulation of an election through its candidate set...
called teaming or cloning. This means that 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. For example, even in a single-seat election, it would be to the advantage of a political party to stand as many candidates as possible in an election. In this respect, the Borda count differs from many other single-winner systems, such as the 'first past the post
Plurality voting system
The plurality voting system is a single-winner voting system often used to elect executive officers or to elect members of a legislative assembly which is based on single-member constituencies...
' plurality system, in which a political faction is disadvantaged by running too many candidates. Under systems such as plurality, 'splitting
Vote splitting
Vote splitting is an electoral effect in which the distribution of votes among multiple similar candidates reduces the chance of winning for any of the similar candidates, and increases the chance of winning for a dissimilar candidate....
' a party's vote in this way can lead to the spoiler effect
Spoiler effect
The spoiler effect describes the effect a minor party candidate with little chance of winning has in a close election, when that candidate's presence in the election draws votes from a major candidate similar to them, thereby causing a candidate dissimilar to them to win the election...
, which harms the chances of any of a faction's candidates being elected.
In 1980, William Gehrlein
William Gehrlein
William V. Gehrlein is a notable researcher in the areas of social choice theory, decision theory and graph theory. He received his B.S. in Physics from Gannon College in Erie, Pennsylvania in 1968, his M.S. in Physics from Pennsylvania State University in 1972, and his Ph.D. in Business...
and Peter Fishburn compared the Borda count to other positional methods, such as plurality and approval voting
Approval voting
Approval voting is a single-winner voting system used for elections. Each voter may vote for as many of the candidates as the voter wishes. The winner is the candidate receiving the most votes. Each voter may vote for any combination of candidates and may give each candidate at most one vote.The...
. They investigated the likelihood of a positional method choosing the same candidate when the set of candidates was modified by eliminating one losing candidate from a three-candidate election, and two losing candidates from a four-candidate election. They found that the Borda count was the positional rule which maximises the probability of electing the same candidate after this modification of the choice set.
Evaluation by criteria
Scholars of electoral systems often compare them using mathematically defined voting system criteria. From among these:- The Borda count satisfies the monotonicity criterionMonotonicity criterionThe monotonicity criterion is a voting system criterion used to analyze both single and multiple winner voting systems. A voting system is monotonic if it satisfies one of the definitions of the monotonicity criterion, given below.Douglas R...
, the consistency criterionConsistency criterionA voting system is consistent if, when the electorate is divided arbitrarily into two parts and separate elections in each part result in the same choice being selected, an election of the entire electorate also selects that alternative...
, the participation criterionParticipation criterionThe participation criterion is a voting system criterion. It is also known as the "no show paradox". It has been defined as follows:* In a deterministic framework, the participation criterion says that the addition of a ballot, where candidate A is strictly preferred to candidate B, to an existing...
, the resolvability criterionResolvability criterionResolvability criterion can refer to any voting system criterion that ensures a low possibility of tie votes.#Nicolaus Tideman's version of the criterion demands that if and only if for every winner in a result, a vote exists, such that when added, makes that winner unique.#Douglas R...
, the plurality criterionPlurality criterionPlurality criterion is a voting system criterion devised by Douglas R. Woodall for ranked voting methods with incomplete ballots. It is stated as follows:...
(trivially), reversal symmetryReversal symmetryReversal symmetry is a voting system criterion which requires that if candidate A is the unique winner, and each voter's individual preferences are inverted, then A must not be elected. Methods that satisfy reversal symmetry include Borda count, the Kemeny-Young method, and the Schulze method...
, and the Condorcet loser criterionCondorcet loser criterionIn single-winner voting system theory, the Condorcet loser criterion is a measure for differentiating voting systems. It implies the majority loser criterion.... - The Borda count does not satisfy the Condorcet criterionCondorcet criterionThe Condorcet candidate or Condorcet winner of an election is the candidate who, when compared with every other candidate, is preferred by more voters. Informally, the Condorcet winner is the person who would win a two-candidate election against each of the other candidates...
, the independence of irrelevant alternativesIndependence of irrelevant alternativesIndependence of irrelevant alternatives is an axiom of decision theory and various social sciences.The word is used in different meanings in different contexts....
criterion, the independence of clones criterionIndependence of clones criterionIn voting systems theory, the independence of clones criterion measures an election method's robustness to strategic nomination. Nicolaus Tideman first formulated the criterion, which states that the addition of a candidate identical to one already present in an election will not cause the winner...
, the later-no-harm criterionLater-no-harm criterionThe later-no-harm criterion is a voting system criterion formulated by Douglas Woodall. The criterion is satisfied if, in any election, a voter giving an additional ranking or positive rating to a less preferred candidate cannot cause a more preferred candidate to lose.- Complying methods :Single...
, or the majority criterionMajority criterionThe majority criterion is a single-winner voting system criterion, used to compare such systems. The criterion states that "if one candidate is preferred by a majority of voters, then that candidate must win"....
.
The variant of the Borda count that permits bullet voting satisfies the plurality criterion
Plurality criterion
Plurality criterion is a voting system criterion devised by Douglas R. Woodall for ranked voting methods with incomplete ballots. It is stated as follows:...
, but the 'modified Borda count' does not. Variants that oblige voters to rank only a certain specified number of candidates satisfy the same criteria as the conventional Borda count.
Political uses
The Borda count is used for certain political elections in at least three countries, SloveniaSlovenia
Slovenia , officially the Republic of Slovenia , is a country in Central and Southeastern Europe touching the Alps and bordering the Mediterranean. Slovenia borders Italy to the west, Croatia to the south and east, Hungary to the northeast, and Austria to the north, and also has a small portion of...
and the tiny Micronesia
Micronesia
Micronesia is a subregion of Oceania, comprising thousands of small islands in the western Pacific Ocean. It is distinct from Melanesia to the south, and Polynesia to the east. The Philippines lie to the west, and Indonesia to the southwest....
n nations of Kiribati
Kiribati
Kiribati , officially the Republic of Kiribati, is an island nation located in the central tropical Pacific Ocean. The permanent population exceeds just over 100,000 , and is composed of 32 atolls and one raised coral island, dispersed over 3.5 million square kilometres, straddling the...
and Nauru
Nauru
Nauru , officially the Republic of Nauru and formerly known as Pleasant Island, is an island country in Micronesia in the South Pacific. Its nearest neighbour is Banaba Island in Kiribati, to the east. Nauru is the world's smallest republic, covering just...
. In Slovenia, the Borda count is used to elect two of the ninety members of the National Assembly: one member represents a constituency of ethnic Italians, the other a constituency of the Hungarian minority. As noted above, members of the Parliament of Nauru are elected based on a variant of the Borda count that involves two departures from the normal practice: (1) multi-seat constituencies, of either two or four seats, and (2) a point-allocation formula that involves increasingly small fractions of points for each ranking, rather than whole points. In Kiribati, the president (or Beretitenti) is elected by the plurality system, but a variant of the Borda count is used to select either three or four candidates to stand in the election. The constituency consists of members of the legislature (Maneaba). Voters in the legislature rank only four candidates, with all other candidates receiving zero points. Since at least 1991, tactical voting has been an important feature of the nominating process.
The Republic of Nauru became independent from Australia
Australia
Australia , officially the Commonwealth of Australia, is a country in the Southern Hemisphere comprising the mainland of the Australian continent, the island of Tasmania, and numerous smaller islands in the Indian and Pacific Oceans. It is the world's sixth-largest country by total area...
in 1968. Before independence, and for three years afterwards, Nauru used instant-runoff voting, importing the system from Australia, but since 1971, a variant of the Borda count has been used.
The Borda count has been used for non-governmental purposes at certain peace conferences in Northern Ireland, where it has been used to help achieve consensus between participants including members of Sinn Féin
Sinn Féin
Sinn Féin is a left wing, Irish republican political party in Ireland. The name is Irish for "ourselves" or "we ourselves", although it is frequently mistranslated as "ourselves alone". Originating in the Sinn Féin organisation founded in 1905 by Arthur Griffith, it took its current form in 1970...
, the Ulster Unionists, and the political wing of the UDA
Ulster Defence Association
The Ulster Defence Association is the largest although not the deadliest loyalist paramilitary and vigilante group in Northern Ireland. It was formed in September 1971 and undertook a campaign of almost twenty-four years during "The Troubles"...
.
Other uses
The Borda count, and points-based systems similar to it, are often used to determine awards in competitions. The Borda count is a popular method for granting awards for sports in the United StatesUnited States
The United States of America is a federal constitutional republic comprising fifty states and a federal district...
, and is used in determining the Most Valuable Player
MLB Most Valuable Player Award
The Major League Baseball Most Valuable Player Award is an annual Major League Baseball award, given to one outstanding player in the American League and one in the National League. Since 1931, it has been awarded by the Baseball Writers Association of America...
in Major League Baseball
Major League Baseball
Major League Baseball is the highest level of professional baseball in the United States and Canada, consisting of teams that play in the National League and the American League...
, by the Associated Press
Associated Press
The Associated Press is an American news agency. The AP is a cooperative owned by its contributing newspapers, radio and television stations in the United States, which both contribute stories to the AP and use material written by its staff journalists...
and United Press International
United Press International
United Press International is a once-major international news agency, whose newswires, photo, news film and audio services provided news material to thousands of newspapers, magazines and radio and television stations for most of the twentieth century...
to rank teams in NCAA
National Collegiate Athletic Association
The National Collegiate Athletic Association is a semi-voluntary association of 1,281 institutions, conferences, organizations and individuals that organizes the athletic programs of many colleges and universities in the United States...
sports, to determine the winner of the Heisman Trophy
Heisman Trophy
The Heisman Memorial Trophy Award , is awarded annually to the player deemed the most outstanding player in collegiate football. It was created in 1935 as the Downtown Athletic Club trophy and renamed in 1936 following the death of the Club's athletic director, John Heisman The Heisman Memorial...
, and so on. The Eurovision Song Contest
Eurovision Song Contest
The Eurovision Song Contest is an annual competition held among active member countries of the European Broadcasting Union .Each member country submits a song to be performed on live television and then casts votes for the other countries' songs to determine the most popular song in the competition...
also uses a positional voting method similar to the Borda count, with a different distribution of points: only the top ten entries are considered in each ballot, the favourite entry receiving 12 points, the second-placed entry receiving 10 points, and the other eight entries getting points from 8 to 1. Although designed to favour a clear winner, it has produced very close races and even a tie. The Borda count is used for wine trophy judging by the Australian Society of Viticulture and Oenology
Australian Society of Viticulture and Oenology
Based in Glen Osmond, South Australia, the Australian Society of Viticulture and Oenology is a non-political organization that was founded in 1980 to serve the interests of practicing winemakers and viticulturists by encouraging the exchange of technical information...
, and by the RoboCup
RoboCup
RoboCup is an international robotics competition founded in 1997. The aim is to develop autonomous soccer robots with the intention of promoting research and education in the field of artificial intelligence...
autonomous robot soccer competition at the Center for Computing Technologies, in the University of Bremen
University of Bremen
The University of Bremen is a university of approximately 23,500 people from 126 countries that are studying, teaching, researching, and working in Bremen, Germany...
in Germany
Germany
Germany , officially the Federal Republic of Germany , is a federal parliamentary republic in Europe. The country consists of 16 states while the capital and largest city is Berlin. Germany covers an area of 357,021 km2 and has a largely temperate seasonal climate...
. The People's Remix Competition uses a Borda variant where each voter ranks only the top three contestants.
The Borda count is used in a number of educational institutions in the United States, such as at the University of Michigan
University of Michigan
The University of Michigan is a public research university located in Ann Arbor, Michigan in the United States. It is the state's oldest university and the flagship campus of 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
University of Missouri
The University of Missouri System is a state university system providing centralized administration for four universities, a health care system, an extension program, five research and technology parks, and a publishing press. More than 64,000 students are currently enrolled at its four campuses...
Graduate-Professional Council to elect its officers, at the University of California Los Angeles Graduate Student Association to elect its officers, in the Civil Liberties Union of Harvard University
Harvard University
Harvard University is a private Ivy League university located in Cambridge, Massachusetts, United States, established in 1636 by the Massachusetts legislature. Harvard is the oldest institution of higher learning in the United States and the first corporation chartered in the country...
to elect its officers, at Southern Illinois University
Southern Illinois University
Southern Illinois University is a state university system based in Carbondale, Illinois, in the Southern Illinois region of the state, with multiple campuses...
at Carbondale
Carbondale, Illinois
Carbondale is a city in Jackson County, in the state of Illinois, within the Southern Illinois region. It is located at the junction of Illinois Route 13 and U.S. Route 51, southeast of St. Louis, Missouri, on the northern edge of the Shawnee National Forest...
to elect officers to the Faculty Senate, and at Arizona State University
Arizona State University
Arizona State University is a public research university located in the Phoenix Metropolitan Area of the State of Arizona...
to elect officers to the Department of Mathematics and Statistics assembly. It is also used to elect faculty members to committees at Wheaton College, Massachusetts. 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
College of William and Mary
The College of William & Mary in Virginia is a public research university located in Williamsburg, Virginia, United States...
.
In professional societies, the Borda count is used to elect the Board of Governors of the International Society for Cryobiology
International Society for Cryobiology
The Society for Cryobiology is an international scientific society that was founded in 1964. Its objectives are to promote research in low temperature biology, to improve scientific understanding in this field, and to disseminate and aid in the application of this knowledge...
, the management committee of Tempo sustainable design network, located in Cornwall
Cornwall
Cornwall is a unitary authority and ceremonial county of England, within the United Kingdom. It is bordered to the north and west by the Celtic Sea, to the south by the English Channel, and to the east by the county of Devon, over the River Tamar. Cornwall has a population of , and covers an area of...
, United Kingdom
United Kingdom
The United Kingdom of Great Britain and Northern IrelandIn the United Kingdom and Dependencies, other languages have been officially recognised as legitimate autochthonous languages under the European Charter for Regional or Minority Languages...
, and to elect members to Research Area Committees of the U.S. Wheat and Barley Scab Initiative
U.S. Wheat and Barley Scab Initiative
The U.S. Wheat and Barley Scab Initiative was founded in 1998. The Initiative's goal is to develop as quickly as possible effective control measures that minimize the threat of Fusarium head blight , including the reduction of mycotoxins, to the producers, processors, and consumers of wheat and...
. The Borda count is one of the feature-selection methods used by the OpenGL
OpenGL
OpenGL is a standard specification defining a cross-language, cross-platform API for writing applications that produce 2D and 3D computer graphics. The interface consists of over 250 different function calls which can be used to draw complex three-dimensional scenes from simple primitives. OpenGL...
Architecture Review Board. The Borda count is used to elect the Board of Directors of the X.Org Foundation
X.Org Foundation
The X.Org Foundation is the organization holding the stewardship for the development of the X Window System. It was founded on 22 January 2004....
.
The Borda count is used to determine winners for Toastmasters International
Toastmasters International
Toastmasters International is a nonprofit educational organization that operates clubs worldwide for the purpose of helping members improve their communication, public speaking and leadership skills...
speech contests. Judges offer a ranking of their top-three speakers, awarding them three points, two points, and one point, respectively. All unranked candidates receive zero points.
The modified Borda count is used to elect the President for the United States member committee of AIESEC
AIESEC
AIESEC is a global youth organisation that develops leadership capabilities through their internal leadership programmes and engaging students and graduates in international student exchange and internship programmes for profit and non-profit organisations. Its international office is in...
.
The Finnish Associations Act lists three different modifications of the Borda count for holding a proportional election. All the modifications use fractions, like in Nauru. A Finnish assoction may choose to use other methods of election, as well.
Application of the term
It is debatable whether or not some of the systems explained above are accurately described as "variants" of the Borda count; the scores candidates receive in some of those systems are significantly different from those they would receive using a strict Borda count.An example is the case of the voting to determine the winner of the Heisman Trophy: judges vote 3,2,1 for their top three choices – the vote weights are thus (3,2,1,0,0,0, ..., 0,0,0). By contrast, the Borda vote weights in, say, a fifty-candidate election would be (49,48,47, ..., 2,1,0), which is markedly different. Heisman-style voting, when there are more than a handful of candidates, is thus more similar to plurality voting, which has weights (1,0,0,0, ..., 0,0,0), than it is to Borda.
History
A form of the Borda count was one of the voting methods employed in the Roman SenateRoman Senate
The Senate of the Roman Republic was a political institution in the ancient Roman Republic, however, it was not an elected body, but one whose members were appointed by the consuls, and later by the censors. After a magistrate served his term in office, it usually was followed with automatic...
beginning around the year 105. However, in its modern, mathematical form, the system is thought have been discovered independently by at least three men:
- Ramon LlullRamon LlullRamon Llull was a Majorcan writer and philosopher, logician and tertiary Franciscan. He wrote the first major work of Catalan literature. Recently-surfaced manuscripts show him to have anticipated by several centuries prominent work on elections theory...
(1232–1315), who with the 2001 discovery of his lost manuscripts Ars notandi, Ars eleccionis, and Alia ars eleccionis, was given credit for discovering the Borda count and Condorcet criterion (Llull winner) in the 13th century - Nicholas of CusaNicholas of CusaNicholas of Kues , also referred to as Nicolaus Cusanus and Nicholas of Cusa, was a cardinal of the Catholic Church from Germany , a philosopher, theologian, jurist, mathematician, and an astronomer. He is widely considered one of the great geniuses and polymaths of the 15th century...
(1401–1464), who in 1433 unsuccessfully suggested the method as a way of electing the Holy Roman EmperorHoly Roman EmperorThe Holy Roman Emperor is a term used by historians to denote a medieval ruler who, as German King, had also received the title of "Emperor of the Romans" from the Pope... - Jean-Charles de BordaJean-Charles de BordaJean-Charles, chevalier de Borda was a French mathematician, physicist, political scientist, and sailor.-Life history:...
, who devised the system in June of 1770, invented his system as a fair way to elect members to the French Academy of SciencesFrench Academy of SciencesThe French Academy of Sciences is a learned society, founded in 1666 by Louis XIV at the suggestion of Jean-Baptiste Colbert, to encourage and protect the spirit of French scientific research...
, and first published his method in 1781 as Mémoire sur les élections au scrutin in the Histoire de l'Académie Royale des Sciences, Paris. The method was used by the Academy from 1784 until being quashed by Napoleon in 1800.
See also
- Portal:Politics
- Quota Borda systemQuota Borda systemThe Quota Borda System or Quota Preference Score is a voting system that was devised by the British philosopher Michael Dummett and first published in 1984 in his book, Voting Procedures, and again in his Principles of Electoral Reform....
- Nanson's methodNanson's methodThe Borda count can be combined with an Instant Runoff procedure to create hybrid election methods that are called Nanson method and Baldwin method.- Nanson method :The Nanson method is based on the original work of the mathematician Edward J...
- Arrow's impossibility theoremArrow's impossibility theoremIn social choice theory, Arrow’s impossibility theorem, the General Possibility Theorem, or Arrow’s paradox, states that, when voters have three or more distinct alternatives , no voting system can convert the ranked preferences of individuals into a community-wide ranking while also meeting a...
- Oklahoma primary electoral systemOklahoma primary electoral systemThe Oklahoma primary electoral system is a voting system used to elect one winner from a pool of candidates using preferential voting. Voters rank candidates in order of preference, and their votes are initially allocated to their first-choice candidate. If, after this initial count, no candidate...
Further reading
- Economic Theory, Vol. 15, Issue 1, 2000: Mathematical Structure of Voting Paradoxes: II. Positional Voting, Donald G. Saari
- Chaotic Elections!, by Donald G. SaariDonald G. SaariDonald Gene Saari is the Distinguished Professor of Mathematics and Economics and director of the Institute for Mathematical Behavioral Sciences at the University of California Irvine...
(ISBN 0-8218-2847-9) describes various voting systems using a mathematical model, and supports the use of the Borda count. - Toplak, Jurij. The parliamentary election in Slovenia, October 2004. Electoral Studies 25 (2006) 825-831.
- Benjamin Reilly. Social Choice in the South Seas: Electoral Innovation and the Borda Count in the Pacific Island Countries. International Political Science Review (2002), Vol 23, No. 4, 355–372.
- Peter Emerson, Designing an All-Inclusive Democracy - Consensual Voting Procedures for use in Parliaments, Councils and Committees. Springer-Verlag, 2007. ISBN 978-3-540-33163-6 (Print) 978-3-540-33164-3 (online)
External links
- The de Borda Institute, Northern Ireland
- Cloning manipulation of the Borda rule: article by Jérôme Serais.
- The Symmetry and Complexity of Elections: article by mathematician Donald G. SaariDonald G. SaariDonald Gene Saari is the Distinguished Professor of Mathematics and Economics and director of the Institute for Mathematical Behavioral Sciences at the University of California Irvine...
explaining paradoxes not suffered by the Borda count. - Complexity of Control of Borda Count Elections: thesis by Nathan F. Russell
- 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?
- Consequences of Reversing Preferences: 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: 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.
- Non-Manipulable Domains for the Borda Count: article by Martin Barbie, Clemens Puppe, and Attila Tasnadi.
- Which scoring rule maximizes Condorcet Efficiency?: article by Davide P. Cervone, William V. Gehrlein, and William S. Zwicker.
- Scoring Rules on Dichotomous Preferences: article by Marc Vorsatz, mathematically comparing the Borda count to approval votingApproval votingApproval voting is a single-winner voting system used for elections. Each voter may vote for as many of the candidates as the voter wishes. The winner is the candidate receiving the most votes. Each voter may vote for any combination of candidates and may give each candidate at most one vote.The...
under specific conditions. - Condorcet Efficiency: A Preference for Indifference: article by William V. Gehrlein and Fabrice Valognes.
- Why the Count de Borda Cannot Beat the Marquis de Condorcet: article by Mathias Risse, published in Social Choice and Welfare. (older version)
- Cooperative phenomena in crystals and social choice theory: article by Thierry Marchant.
- A program to implement the Condorcet and Borda rules in a small-n election: article by Iain McLean and Neil Shephard.
- The Reasonableness of Independence: article by Iain McLean.
- Variants of the Borda Count Method for Combining Ranked Classifier Hypotheses: article by Merijn Van Erp and Lambert Schomaker
- Selecting Committees: article by Thomas C. Ratliff.
- Flash animation by Kathy Hays: an example of how the Borda count is used to determine the Most Valuable Player in Major League Baseball.
- Range Voting: article by Warren D. Smith. The author finds deficiencies in the Borda count based on various analysis.
- Against the Borda Count: A concise summary of some of the major flaws of the Borda count, with examples. Élections au scrutin: Borda's original French text (1781) in a high definition PDF file.