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Condorcet methods

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116-416: Condorcet methods Positional voting Cardinal voting Quota-remainder methods Approval-based committees Fractional social choice Semi-proportional representation By ballot type Pathological response Strategic voting Paradoxes of majority rule Positive results The Borda method or order of merit is a positional voting rule that gives each candidate

232-501: A 'cycle'. This situation emerges when, once all votes have been tallied, the preferences of voters with respect to some candidates form a circle in which every candidate is beaten by at least one other candidate ( Intransitivity ). For example, if there are three candidates, Candidate Rock, Candidate Scissors, and Candidate Paper , there will be no Condorcet winner if voters prefer Candidate Rock over Candidate Scissors and Scissors over Paper, but also Candidate Paper over Rock. Depending on

348-400: A 68% majority of 1st choices among the remaining candidates and won as the majority's 1st choice. As noted above, sometimes an election has no Condorcet winner because there is no candidate who is preferred by voters to all other candidates. When this occurs the situation is known as a 'Condorcet cycle', 'majority rule cycle', 'circular ambiguity', 'circular tie', 'Condorcet paradox', or simply

464-552: A biography which spoke fondly of Turgot and advocated Turgot's economic theories. Condorcet continued to receive prestigious appointments: in 1777, he became Permanent Secretary of the Académie des Sciences , holding the post until the abolition of the Académie in 1793; and, in 1782, secretary of the Académie française . In 1785, Condorcet published one of his most important works, Essay on

580-452: A candidate is more likely to be elected if there are similar candidates on the ballot. The Borda count is particularly susceptible to distortion through the presence of candidates who do not themselves come into consideration, even when the voters lie along a spectrum. Voting systems which satisfy the Condorcet criterion are protected against this weakness since they automatically also satisfy

696-493: A candidate preferred by a majority of voters. In 1781, Condorcet anonymously published a pamphlet entitled Reflections on Negro Slavery ( Réflexions sur l'esclavage des nègres ), in which he denounced slavery . In 1786, Condorcet worked on ideas for the differential and integral calculus , giving a new treatment of infinitesimals – a work which apparently was never published. In 1789, he published Vie de Voltaire (1789) , which agreed with Voltaire in his opposition to

812-485: A conservative notion of denying women education and equal rights on account of keeping them tied to the domestic sphere where [according to him] they belonged, Condorcet refused to acquit the inequality between men and women to natural disposition. Instead, he believed that the provision of education to women on par with the education provided to men was the pathway to establishing gender equality. He stated: "I believe that all other differences between men and women are simply

928-483: A contest between candidates A, B and C using the preferential-vote form of Condorcet method, a head-to-head race is conducted between each pair of candidates. A and B, B and C, and C and A. If one candidate is preferred over all others, they are the Condorcet Winner and winner of the election. Because of the possibility of the Condorcet paradox , it is possible, but unlikely, that a Condorcet winner may not exist in

1044-506: A generic Condorcet method , designed to simulate pair-wise elections between all candidates in an election. He disagreed strongly with the alternative method of aggregating preferences put forth by Jean-Charles de Borda (based on summed rankings of alternatives ). Condorcet was one of the first to systematically apply mathematics in the social sciences . He also considered the instant-runoff voting elimination method, as early as 1788, though only to condemn it, for its ability to eliminate

1160-606: A key contribution to the French Enlightenment , particularly his work on the Idea of Progress. Condorcet believed that through the use of our senses and communication with others, knowledge could be compared and contrasted as a way of analyzing our systems of belief and understanding. None of Condorcet's writings refer to a belief in a religion or a god who intervenes in human affairs. Condorcet instead frequently had written of his faith in humanity itself and its ability to progress with

1276-503: A large tie that will be decided semi-randomly. When a voter utilizes compromising , they insincerely raise the position of a second or third choice candidate over their first choice candidate, in order to help the second choice candidate to beat a candidate they like even less. When a voter utilizes burying , voters can help a more-preferred candidate by insincerely lowering the position of a less-preferred candidate on their ballot. Combining both these strategies can be powerful, especially as

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1392-673: A lasting contribution to the pre-feminist debate. Condorcet's Sketch for a Historical Picture of the Progress of the Human Spirit (1795) was perhaps the most influential formulation of the idea of progress ever written. It made the Idea of Progress a central concern of Enlightenment thought. He argued that expanding knowledge in the natural and social sciences would lead to an ever more just world of individual freedom, material affluence, and moral compassion. He argued for three general propositions: that

1508-653: A member of the French Société des Amis des Noirs (Society of the Friends of the Blacks) . He wrote a set of rules for the Society of the Friends of the Blacks which detailed the reasoning and goals behind the organization along with describing the injustice of slavery and put in a statement calling for the abolition of the slave trade as the first step to true abolition. Condorcet was also

1624-421: A number of points equal to the number of candidates ranked below them: the lowest-ranked candidate gets 0 points, the second-lowest gets 1 point, and so on. Once all votes have been counted, the option or candidate or candidates with the most points is/are the winner or winners. The Borda count was developed independently several times, being first proposed in 1435 by Nicholas of Cusa (see History below), but

1740-485: A reaction called a turkey election . The French Academy of Sciences (of which Borda was a member) experimented with Borda's system but abandoned it, in part because "the voters found how to manipulate the Borda rule". In response to the issue of strategic manipulation in the Borda count, M. de Borda said: Mon scrutin n'est fait que pour d'honnêtes gens. My scheme is intended for only honest men. Despite its abandonment,

1856-532: A result of a kind of tie known as a majority rule cycle , described by Condorcet's paradox . The manner in which a winner is then chosen varies from one Condorcet method to another. Some Condorcet methods involve the basic procedure described below, coupled with a Condorcet completion method, which is used to find a winner when there is no Condorcet winner. Other Condorcet methods involve an entirely different system of counting, but are classified as Condorcet methods, or Condorcet consistent, because they will still elect

1972-579: A revised edition between 1847 and 1849. Condorcet's work was mainly focused on a quest for a more egalitarian society. This path led him to think and write about gender equality in the Revolutionary context. In 1790, he published " Sur l'admission des femmes au droit de cité " ("On the Admission of Women to the Rights of Citizenship") in which he strongly advocated for women's suffrage in the new Republic as well as

2088-427: A second preference. Some implementations of Borda voting require voters to truncate their ballots to a certain length: The system invented by 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 recognizing the desired number of candidates with the most points as the winners. In other words, if there are two seats to be filled, then

2204-523: A specific election. This is sometimes called a Condorcet cycle or just cycle and can be thought of as Rock beating Scissors, Scissors beating Paper, and Paper beating Rock . Various Condorcet methods differ in how they resolve such a cycle. (Most elections do not have cycles. See Condorcet paradox#Likelihood of the paradox for estimates.) If there is no cycle, all Condorcet methods elect the same candidate and are operationally equivalent. For most Condorcet methods, those counts usually suffice to determine

2320-446: A strong proponent of women's civil rights. He claimed that women were equal to men in nearly every aspect and asked why then should they be debarred from their fundamental civil rights; the few differences that existed were due to the fact that women were limited by their lack of rights. Condorcet even mentioned several women who were more capable than average men, such as Queen Elizabeth and Maria-Theresa . Furthermore, as he argues for

2436-427: A voter's choice within any given pair can be determined from the ranking. Some elections may not yield a Condorcet winner because voter preferences may be cyclic—that is, it is possible that every candidate has an opponent that defeats them in a two-candidate contest. The possibility of such cyclic preferences is known as the Condorcet paradox . However, a smallest group of candidates that beat all candidates not in

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2552-461: Is a proportional multiwinner variant. The Borda count is a ranked voting system: the voter ranks the list of candidates in order of preference. So, for example, the voter gives a 1 to their most preferred candidate, a 2 to their second most preferred, and so on. In this respect, it is the same as elections under systems such as instant-runoff voting , the single transferable vote or Condorcet methods . The integer-valued ranks for evaluating

2668-407: Is also a Condorcet method, even though the voters do not vote by expressing their orders of preference. There are multiple rounds of voting, and in each round the vote is between two of the alternatives. The loser (by majority rule) of a pairing is eliminated, and the winner of a pairing survives to be paired in a later round against another alternative. Eventually, only one alternative remains, and it

2784-494: Is also referred to collectively as Condorcet's method. A voting system that always elects the Condorcet winner when there is one is described by electoral scientists as a system that satisfies the Condorcet criterion. Additionally, a voting system can be considered to have Condorcet consistency, or be Condorcet consistent, if it elects any Condorcet winner. In certain circumstances, an election has no Condorcet winner. This occurs as

2900-411: Is an election method that elects the candidate who wins a majority of the vote in every head-to-head election against each of the other candidates, whenever there is such a candidate. A candidate with this property, the pairwise champion or beats-all winner , is formally called the Condorcet winner or Pairwise Majority Rule Winner (PMRW). The head-to-head elections need not be done separately;

3016-412: Is an election between four candidates: A, B, C, and D. The first matrix below records the preferences expressed on a single ballot paper, in which the voter's preferences are (B, C, A, D); that is, the voter ranked B first, C second, A third, and D fourth. In the matrix a '1' indicates that the runner is preferred over the 'opponent', while a '0' indicates that the runner is defeated. Using a matrix like

3132-401: Is holding an election on the location of its capital . The population is concentrated around four major cities. All voters want the capital to be as close to them as possible. The options are: The preferences of each region's voters are: To find the Condorcet winner every candidate must be matched against every other candidate in a series of imaginary one-on-one contests. In each pairing

3248-513: Is known as ambiguity resolution, cycle resolution method, or Condorcet completion method . Circular ambiguities arise as a result of the voting paradox —the result of an election can be intransitive (forming a cycle) even though all individual voters expressed a transitive preference. In a Condorcet election it is impossible for the preferences of a single voter to be cyclical, because a voter must rank all candidates in order, from top-choice to bottom-choice, and can only rank each candidate once, but

3364-436: Is more truth in this observation, but it still proves nothing since this difference is caused, not by nature, but by education and society..." His views on rights that must be afforded to women were not limited to education and citizenship but also social freedoms and protections that included the right for women to plan their own pregnancies, provision of access to birth control, and men's obligation to take responsibility for

3480-434: Is named after the 18th-century French mathematician and naval engineer Jean-Charles de Borda , who devised the system in 1770. The Borda count is well-known in social choice theory for both its pleasant theoretical properties and its ease of manipulation. In the absence of strategic voting and strategic nomination , the Borda count tends to elect broadly-acceptable options or candidates (rather than consistently following

3596-440: Is no preference between candidates that were left unranked. Some Condorcet elections permit write-in candidates . The count is conducted by pitting every candidate against every other candidate in a series of hypothetical one-on-one contests. The winner of each pairing is the candidate preferred by a majority of voters. Unless they tie, there is always a majority when there are only two choices. The candidate preferred by each voter

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3712-510: Is taken to be the one in the pair that the voter ranks (or rates) higher on their ballot paper. For example, if Alice is paired against Bob it is necessary to count both the number of voters who have ranked Alice higher than Bob, and the number who have ranked Bob higher than Alice. If Alice is preferred by more voters then she is the winner of that pairing. When all possible pairings of candidates have been considered, if one candidate beats every other candidate in these contests then they are declared

3828-417: Is that his friend Pierre Jean George Cabanis gave him a poison which he eventually used. However, some historians believe that he may have been murdered (perhaps because he was too loved and respected to be executed). Jean-Pierre Brancourt (in his work L'élite, la mort et la révolution ) claims that Condorcet was killed with a mixture of Datura stramonium and opium. Condorcet was symbolically interred in

3944-404: Is the winner. This is analogous to a single-winner or round-robin tournament; the total number of pairings is one less than the number of alternatives. Since a Condorcet winner will win by majority rule in each of its pairings, it will never be eliminated by Robert's Rules. But this method cannot reveal a voting paradox in which there is no Condorcet winner and a majority prefer an early loser over

4060-792: The American Philosophical Society (1775), the Royal Swedish Academy of Sciences (1785), the American Academy of Arts and Sciences (1792) and also in Prussia and Russia. His political ideas, many in congruity with Turgot's, were criticized heavily in the English-speaking world, however, most notably by John Adams who wrote two of his principal works of political philosophy to oppose Turgot's and Condorcet's unicameral legislature and radical democracy. In 1774, Condorcet

4176-570: The Church . In the same year he was elected as president of the Society of the Friends of the Blacks and lived in an apartment at Hôtel des Monnaies, Paris , across the Louvre. In 1791, Condorcet, along with Sophie de Grouchy, Thomas Paine , Etienne Dumont , Jacques-Pierre Brissot , and Achilles Duchastellet published a brief journal titled Le Républicain , its main goal being the promotion of republicanism and

4292-475: The Marquis de Condorcet , who championed such systems. However, Ramon Llull devised the earliest known Condorcet method in 1299. It was equivalent to Copeland's method in cases with no pairwise ties. Condorcet methods may use preferential ranked , rated vote ballots, or explicit votes between all pairs of candidates. Most Condorcet methods employ a single round of preferential voting, in which each voter ranks

4408-575: The Panthéon in 1989, in honour of the bicentennial of the French Revolution and Condorcet's role as a central figure in the Enlightenment. His coffin, however, was empty as his remains, originally interred in the common cemetery of Bourg-la-Reine , were lost during the nineteenth century. In 1786 Condorcet married Sophie de Grouchy , who was more than twenty years his junior. Sophie, reckoned one of

4524-496: The median voter theorem , which says that the winner of an election will be the candidate preferred by the median voter regardless of which other candidates stand. Suppose that there are 11 voters whose positions along the spectrum can be written 0, 1, ..., 10, and suppose that there are 2 candidates, Andrew and Brian, whose positions are as shown: The median voter Marlene is at position 5, and both candidates are to her right, so we would expect A to be elected. We can verify this for

4640-408: The 1790s as the embodiment of the cold, rational Enlightenment. However she suggests his writings on economic policy, voting, and public instruction indicate different views both of Condorcet and of the Enlightenment. Condorcet was concerned with individual diversity; he was opposed to proto-utilitarian theories; he considered individual independence, which he described as the characteristic liberty of

4756-509: The Application of Analysis to the Probability of Majority Decisions ( Essai sur l'application de l'analyse à la probabilité des décisions rendues à la pluralité des voix ). It described several now-famous results, including Condorcet's jury theorem , which states that if each member of a voting group is more likely than not to make a correct decision, the probability that the highest vote of

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4872-579: The Assembly. Condorcet was not affiliated with any political party but counted many friends among the Girondins . He distanced himself from them during the National Convention , however, due to his distaste for their factionalism. In April 1792 Condorcet presented a project for the reformation of the education system, aiming to create a hierarchical system, under the authority of experts, who would work as

4988-535: The Borda count method does not necessarily produce minority representation even if a minority voting block has the equivalent of the Hare quota. This was noticed in 1902 when a similar method was put forward by L.B. Tuckerman of Cleveland. The traditional Borda method is currently used to elect two ethnic minority members of the National Assembly of Slovenia , in modified forms to determine which candidates are elected to

5104-489: The Borda system by constructing a table to illustrate the count. The main part of the table shows the voters who prefer the first to the second candidate, as given by the row and column headings, while the additional column to the right gives the scores for the first candidate. A is indeed elected. But now suppose that two additional candidates, further to the right, enter the election. The counting table expands as follows: The entry of two dummy candidates allows B to win

5220-540: The Condorcet winner if there is one. Not all single winner, ranked voting systems are Condorcet methods. For example, instant-runoff voting and the Borda count are not Condorcet methods. In a Condorcet election the voter ranks the list of candidates in order of preference. If a ranked ballot is used, the voter gives a "1" to their first preference, a "2" to their second preference, and so on. Some Condorcet methods allow voters to rank more than one candidate equally so that

5336-460: The Condorcet winner. As noted above, if there is no Condorcet winner a further method must be used to find the winner of the election, and this mechanism varies from one Condorcet consistent method to another. In any Condorcet method that passes Independence of Smith-dominated alternatives , it can sometimes help to identify the Smith set from the head-to-head matchups, and eliminate all candidates not in

5452-693: The Convention – he proposed to send the king to work as a slave rower on galley ships . Condorcet was on the Constitution Committee and was the main author of the Girondin constitutional project . This constitution was not put to a vote. When the Montagnards gained control of the Convention, they wrote their own, the French Constitution of 1793 . Condorcet criticized the new work, and as a result, he

5568-546: The Copeland winner has the highest possible Copeland score. They can also be found by conducting a series of pairwise comparisons, using the procedure given in Robert's Rules of Order described above. For N candidates, this requires N − 1 pairwise hypothetical elections. For example, with 5 candidates there are 4 pairwise comparisons to be made, since after each comparison, a candidate is eliminated, and after 4 eliminations, only one of

5684-518: The Earth where it has extended its empire; while we will see the genius of science and freedom shine beneath the most absurd superstitions, in the midst of the most barbaric intolerance. China offers us the same phenomenon, although the effects of this stupefying poison have been less fatal." For Condorcet's republicanism the nation needed enlightened citizens and education needed democracy to become truly public. Democracy implied free citizens, and ignorance

5800-588: The Principle of Population (1798) partly in response to Condorcet's views on the " perfectibility of society ." Condorcet took a leading role when the French Revolution swept France in 1789, hoping for a rationalist reconstruction of society, and championed many liberal causes . As a result, in 1791 he was elected as a Paris representative in the Legislative Assembly , and then became the secretary of

5916-635: The Schulze method, use the information contained in the sum matrix to choose a winner. Cells marked '—' in the matrices above have a numerical value of '0', but a dash is used since candidates are never preferred to themselves. The first matrix, that represents a single ballot, is inversely symmetric: (runner, opponent) is ¬(opponent, runner). Or (runner, opponent) + (opponent, runner) = 1. The sum matrix has this property: (runner, opponent) + (opponent, runner) = N for N voters, if all runners were fully ranked by each voter. [REDACTED] Suppose that Tennessee

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6032-414: The absence of strategic voting and with ballots ranking all candidates. Several different methods of handling tied ranks have been suggested. They can be illustrated using the 4-candidate election discussed previously. The modified Borda and tournament Borda methods, as well as methods of Borda that do not allow for equal rankings, are well-known for behaving disastrously in response to tactical voting,

6148-628: The average Borda score is eliminated; in the second, the candidate with lowest score is eliminated. Unlike the Borda count, Nanson and Baldwin are majoritarian and Condorcet methods because they use the fact that a Condorcet winner always has a higher-than-average Borda score relative to other candidates, and the Condorcet loser a lower than average Borda score. However they are not monotonic. Borda counts are vulnerable to manipulation by both tactical voting and strategic nomination. The Dowdall system may be more resistant, based on observations in Kiribati using

6264-411: The basis for defining preference and determined that Memphis voters preferred Chattanooga as a second choice rather than as a third choice, Chattanooga would be the Condorcet winner even though finishing in last place in a first-past-the-post election. An alternative way of thinking about this example if a Smith-efficient Condorcet method that passes ISDA is used to determine the winner is that 58% of

6380-428: The best candidate. His theorem assumes that errors are independent, in other words, that if a voter rates a particular candidate highly, then there is no reason to expect her to rate "similar" candidates highly. If this property is absent – if the voter gives correlated rankings to candidates with shared attributes – then the maximum likelihood property is lost, and the Borda count is highly subject to nomination effects :

6496-458: The candidate with the lowest Borda score; Geller-STV does not recalculate Borda scores after partial vote transfers, meaning partial-transfer of votes affects voting power for election but not for elimination. Nanson's and Baldwin's methods are Condorcet-consistent voting methods based on the Borda score. Both are run as series of elimination rounds analogous to instant-runoff voting . In the first case, in each round every candidate with less than

6612-601: The candidates from most (marked as number 1) to least preferred (marked with a higher number). A voter's ranking is often called their order of preference. Votes can be tallied in many ways to find a winner. All Condorcet methods will elect the Condorcet winner if there is one. If there is no Condorcet winner different Condorcet-compliant methods may elect different winners in the case of a cycle—Condorcet methods differ on which other criteria they satisfy. The procedure given in Robert's Rules of Order for voting on motions and amendments

6728-408: The candidates in the order A-B-C-D while W ranks them B-C-D-A. Thus Brian is elected. A longer example, based on a fictitious election for Tennessee state capital, is shown below . Condorcet looked at an election as an attempt to combine estimators. Suppose that each candidate has a figure of merit and that each voter has a noisy estimate of the value of each candidate. The ballot paper allows

6844-428: The candidates were justified by Laplace , who used a probabilistic model based on the law of large numbers . The Borda count is classified as a positional voting system , that is, all preferences are counted but at different values; the other commonly-used positional system is plurality voting , which only assigns one point to the top candidate. Each candidate is assigned a number of points from each ballot equal to

6960-507: The civil, political, and educational rights of women, Condorcet boldly challenges that unless women's natural inferiority to men could be proven, the denial of the aforementioned rights is an "act of tyranny" constituted by the newly formed French nation. About Islam and China he wrote: "the religion of Mohammed, the simplest in its dogmas, the least absurd in its practices, the most tolerant in its principles, seems to condemn to eternal slavery, to incurable stupidity, this entire vast portion of

7076-496: The complete order of finish (i.e. who won, who came in 2nd place, etc.). They always suffice to determine whether there is a Condorcet winner. Additional information may be needed in the event of ties. Ties can be pairings that have no majority, or they can be majorities that are the same size. Such ties will be rare when there are many voters. Some Condorcet methods may have other kinds of ties. For example, with Copeland's method , it would not be rare for two or more candidates to win

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7192-521: The constitutional drafting process, his convictions did not translate into concrete political action and he made limited efforts to push these issues on the agenda. Some scholars on the other hand, believe that this lack of action is not due to the weakness of his commitment but rather to the political atmosphere at the time and the absence of political appetite for gender equality on the part of decision-makers. Along with authors such as Mary Wollstonecraft , d'Alembert or Olympe de Gouges , Condorcet made

7308-424: The context in which elections are held, circular ambiguities may or may not be common, but there is no known case of a governmental election with ranked-choice voting in which a circular ambiguity is evident from the record of ranked ballots. Nonetheless a cycle is always possible, and so every Condorcet method should be capable of determining a winner when this contingency occurs. A mechanism for resolving an ambiguity

7424-470: The election. Similar examples led the Marquis de Condorcet to argue that the Borda count is "bound to lead to error" because it " relies on irrelevant factors to form its judgments". There are a number of formalised voting system criteria whose results are summarised in the following table. type Simulations show that Borda has a high probability of choosing the Condorcet winner when one exists, in

7540-433: The enlargement of basic political and social rights to include women. One of the most famous Enlightenment thinkers at the time, he was one of the first to make such a radical proposal. 'The rights of men stem exclusively from the fact that they are sentient beings, capable of acquiring moral ideas and of reasoning upon them. Since women have the same qualities, they necessarily also have the same rights. Either no member of

7656-474: The eventual winner (though it will always elect someone in the Smith set ). A considerable portion of the literature on social choice theory is about the properties of this method since it is widely used and is used by important organizations (legislatures, councils, committees, etc.). It is not practical for use in public elections, however, since its multiple rounds of voting would be very expensive for voters, for candidates, and for governments to administer. In

7772-470: The following sum matrix: When the sum matrix is found, the contest between each pair of candidates is considered. The number of votes for runner over opponent (runner, opponent) is compared with the number of votes for opponent over runner (opponent, runner) to find the Condorcet winner. In the sum matrix above, A is the Condorcet winner because A beats every other candidate. When there is no Condorcet winner Condorcet completion methods, such as Ranked Pairs and

7888-403: The foundation of universal values. His difficulties call into question some familiar distinctions, for example between French, German, and English-Scottish thought, and between the Enlightenment and the counter-Enlightenment. There was substantial continuity between Condorcet's criticism of the economic ideas of the 1760s and the liberal thought of the early 19th century. The Lycée Condorcet in

8004-411: The group is the correct decision increases as the number of members of the group increases, and Condorcet's paradox , which shows that majority preferences can become intransitive with three or more options – it is possible for a certain electorate to express a preference for A over B, a preference for B over C, and a preference for C over A , all from the same set of ballots. The paper also outlines

8120-450: The group, known as the Smith set , always exists. The Smith set is guaranteed to have the Condorcet winner in it should one exist. Many Condorcet methods elect a candidate who is in the Smith set absent a Condorcet winner, and is thus said to be "Smith-efficient". Condorcet voting methods are named for the 18th-century French mathematician and philosopher Marie Jean Antoine Nicolas Caritat,

8236-685: The guardians of the Enlightenment and who, independent of power, would be the guarantors of public liberties. The project was judged to be contrary to republican and egalitarian virtues, handing the education of the Nation over to an aristocracy of savants, and Condorcet's proposal was not taken up by the Assembly. Several years later, in 1795, when the Thermidorians had gained in strength, the National Convention would adopt an educational plan based on Condorcet's proposal. He advocated women's suffrage for

8352-405: The help of philosophers such as Aristotle. Through this accumulation and sharing of knowledge he believed it was possible for anybody to comprehend all the known facts of the natural world. The enlightenment of the natural world spurred the desire for enlightenment of the social and political world. Condorcet believed that there was no definition of the perfect human existence and thus believed that

8468-616: The house of Jean-Baptiste Suard , a friend of his with whom he had resided in 1772, but he was refused on the basis that he would be betrayed by one of their residents. Two days later, he was arrested in Clamart and imprisoned in Bourg-la-Reine (or, as it was known during the Revolution, Bourg-l'Égalité , "Equality Borough" rather than "Queen's Borough") where, after another two days, he was found dead in his cell. The most widely accepted theory

8584-418: The human race has any true rights, or else they all have the same ones; and anyone who votes against the rights of another, whatever his religion, colour or sex, automatically forfeits his own.' Like fellow Enlightenment thinker Jean-Jacques Rousseau in his book Emile ou De l'Education (1762), Condorcet identified education as crucial to the emancipation of individuals. However, where Rousseau endorsed

8700-478: The ideals embodied by the newly formed United States, and proposed projects of political, administrative and economic reforms intended to transform France. In 1776, Turgot was dismissed as Controller General. Consequently, Condorcet submitted his resignation as Inspector General of the Monnaie , but the request was refused, and he continued serving in this post until 1791. Condorcet later wrote Vie de M. Turgot (1786),

8816-627: The ideals of the Age of Enlightenment , of which he has been called the "last witness", and Enlightenment rationalism . A critic of the constitution proposed by Marie-Jean Hérault de Séchelles in 1793, the Convention Nationale — and the Jacobin faction in particular — voted to have Condorcet arrested. He died in prison after a period of hiding from the French Revolutionary authorities. Condorcet

8932-440: The loving hopes he has for his daughter as a father, but also for his egalitarian vision of the rights and opportunities for women in society. Condorcet was survived by his widow and four-year-old Eliza. Sophie died in 1822, never having remarried, and having published all her husband's works between 1801 and 1804. Her work was carried on by Eliza, wife of former United Irishman Arthur O'Connor . The Condorcet-O'Connors published

9048-480: The major texts of the Enlightenment and of historical thought. It narrates the history of civilization as one of progress in the sciences, claims an intimate connection between scientific progress and the development of human rights and justice, and outlines the features of a future rational society entirely shaped by scientific knowledge. On 25 March 1794 Condorcet, convinced he was no longer safe, left his hideout and attempted to flee Paris. He went to seek refuge at

9164-406: The moderns, to be of central political importance; and he opposed the imposition of universal and eternal principles. His efforts to reconcile the universality of some values with the diversity of individual opinions are of continuing interest. He emphasizes the institutions of civilized or constitutional conflict, recognizes conflicts or inconsistencies within individuals, and sees moral sentiments as

9280-508: The modified Borda count versus Nauru using the Dowdall system, but little research has been done thus far on the Nauru system. Borda counts are unusually vulnerable to tactical voting , even compared to most other voting systems. Voters who vote tactically, rather than via their true preference, will be more influential; more alarmingly, if everyone starts voting tactically, the result tends to approach

9396-460: The most beautiful women of the day, became an accomplished salon hostess as Madame de Condorcet, and also an accomplished translator of Thomas Paine and Adam Smith . She was intelligent and well educated, fluent in both English and Italian. The marriage was a strong one, and Sophie visited her husband regularly while he remained in hiding. Although she began proceedings for divorce in January 1794, it

9512-551: The new government, writing an article for Journal de la Société de 1789 , and by publishing De l'admission des femmes au droit de cité ("For the Admission to the Rights of Citizenship For Women") in 1790. At the Trial of Louis XVI in December 1792, Condorcet, who opposed the death penalty albeit supporting the trial itself, spoke out against the execution of the King during the public vote at

9628-402: The number of candidates in an election increases. 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,

9744-471: The number of candidates to whom he or she is preferred, so that with n candidates, each one receives n – 1 points for a first preference, n – 2 for a second, and so on. The winner is the candidate with the largest total number of points. For example, in a four-candidate election, the number of points assigned for the preferences expressed by a voter on a single ballot paper might be: Suppose that there are 3 voters, U , V and W , of whom U and V rank

9860-425: The one above, one can find the overall results of an election. Each ballot can be transformed into this style of matrix, and then added to all other ballot matrices using matrix addition . The sum of all ballots in an election is called the sum matrix. Suppose that in the imaginary election there are two other voters. Their preferences are (D, A, C, B) and (A, C, B, D). Added to the first voter, these ballots would give

9976-419: The original 5 candidates will remain. To confirm that a Condorcet winner exists in a given election, first do the Robert's Rules of Order procedure, declare the final remaining candidate the procedure's winner, and then do at most an additional N − 2 pairwise comparisons between the procedure's winner and any candidates they have not been compared against yet (including all previously eliminated candidates). If

10092-584: The paradox of voting means that it is still possible for a circular ambiguity in voter tallies to emerge. Marquis de Condorcet Marie Jean Antoine Nicolas de Caritat, Marquis of Condorcet ( French: [maʁi ʒɑ̃ ɑ̃twan nikɔla də kaʁita maʁki də kɔ̃dɔʁsɛ] ; 17 September 1743 – 29 March 1794), known as Nicolas de Condorcet , was a French political economist and mathematician . His ideas, including support for free markets , public education , constitutional government, and equal rights for women and people of all races, have been said to embody

10208-706: The party list seats in Icelandic parliamentary elections , and for selecting presidential election candidates in Kiribati . A variant known as the Dowdall system is used to elect members of the Parliament of Nauru . Until the early 1970s, another variant was used in Finland to select individual candidates within party lists. It is also widely used throughout the world by various private organizations and competitions. The Quota Borda system

10324-453: The past revealed an order that could be understood in terms of the progressive development of human capabilities, showing that humanity's "present state, and those through which it has passed, are a necessary constitution of the moral composition of humankind"; that the progress of the natural sciences must be followed by progress in the moral and political sciences "no less certain, no less secure from political revolutions"; that social evils are

10440-427: The preferences of a majority); when both voting and nomination patterns are completely random, the Borda count generally has an exceptionally high social utility efficiency . However, the method is highly vulnerable to spoiler effects when there are clusters of similar candidates. In particular, some implementations' treatment of equal-rank or truncated ballots can incentivize turkey-raising strategies. As well,

10556-426: The procedure's winner does not win all pairwise matchups, then no Condorcet winner exists in the election (and thus the Smith set has multiple candidates in it). Computing all pairwise comparisons requires ½ N ( N −1) pairwise comparisons for N candidates. For 10 candidates, this means 0.5*10*9=45 comparisons, which can make elections with many candidates hard to count the votes for. The family of Condorcet methods

10672-404: The progression of the human race would inevitably continue throughout the course of our existence. He envisioned man as continually progressing toward a perfectly utopian society. He believed in the great potential towards growth that man possessed. However, Condorcet stressed that for this to be a possibility man must unify regardless of race, religion, culture or gender. To this end, he became

10788-561: The rejection of constitutional monarchy. The journal's theme was that any sort of monarchy is a threat to freedom no matter who is leading and that liberty is freedom from domination. In 1795, Condorcet's book Sketch for a Historical Picture of the Progress of the Human Mind was published after his death by his wife Sophie de Grouchy. It dealt with theoretical thought on perfecting the human mind and analyzing intellectual history based on social arithmetic. Thomas Malthus wrote An Essay on

10904-450: The result is: Condorcet method Positional voting Cardinal voting Quota-remainder methods Approval-based committees Fractional social choice Semi-proportional representation By ballot type Pathological response Strategic voting Paradoxes of majority rule Positive results A Condorcet method ( English: / k ɒ n d ɔːr ˈ s eɪ / ; French: [kɔ̃dɔʁsɛ] )

11020-413: The result of education". Condorcet's whole plea for gender equality is founded on the belief that the attribution of rights and authority comes from a false assumption that men possess reason and women do not. He even goes on to argue that women possess their own form of reason that is different from their male compatriots but by no means lesser however this is nonetheless an artificial difference: "There

11136-436: The result of ignorance and error rather than an inevitable consequence of human nature. He was innovative in suggesting that scientific medicine might in the future significantly extend the human life span, perhaps even indefinitely, such that future humans only die of accident, murder and suicide rather than simply old age or disease. Nick Bostrom has thus described him as an early transhumanist . Condorcet's writings were

11252-426: The rounded-down Borda rule has a substantially less severe reaction to tactical voting than the traditional or tournament variants. Tactical voting consists of the relatively mild bullet voting , which only causes the race to behave like a cross between a plurality vote and an honest Borda count, rather than producing a potential turkey-election. In Slovenia, which uses this form of the rule, roughly 42% of voters rank

11368-469: The same number of pairings, when there is no Condorcet winner. A Condorcet method is a voting system that will always elect the Condorcet winner (if there is one); this is the candidate whom voters prefer to each other candidate, when compared to them one at a time. This candidate can be found (if they exist; see next paragraph) by checking if there is a candidate who beats all other candidates; this can be done by using Copeland's method and then checking if

11484-426: The set before doing the procedure for that Condorcet method. Condorcet methods use pairwise counting. For each possible pair of candidates, one pairwise count indicates how many voters prefer one of the paired candidates over the other candidate, and another pairwise count indicates how many voters have the opposite preference. The counts for all possible pairs of candidates summarize all the pairwise preferences of all

11600-438: 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 system is a system of proportional representation in multi-seat constituencies that uses the Borda count. Chris Geller's STV-B uses vote count quotas to elect, but eliminates

11716-766: The voter is employing both the compromising and burying tactics at once; if enough voters employ such strategies, then the result will no longer reflect the sincere preferences of the electorate. For an example of how potent tactical voting can be, suppose a trip is being planned by a group of 100 people on the East Coast of North America. They decide to use Borda count to vote on which city they will visit. The three candidates are New York City , Orlando , and Iqaluit . 48 people prefer Orlando / New York / Iqaluit; 44 people prefer New York / Orlando / Iqaluit; 4 people prefer Iqaluit / New York / Orlando; and 4 people prefer Iqaluit / Orlando / New York. If everyone votes their true preference,

11832-482: The voter might express two first preferences rather than just one. If a scored ballot is used, voters rate or score the candidates on a scale, for example as is used in Score voting , with a higher rating indicating a greater preference. When a voter does not give a full list of preferences, it is typically assumed that they prefer the candidates that they have ranked over all the candidates that were not ranked, and that there

11948-453: The voter to rank the candidates in order of estimated merit. The aim of the election is to produce a combined estimate of the best candidate. Such an estimator can be more reliable than any of its individual components. Applying this principle to jury decisions, Condorcet derived his theorem that a large enough jury would always decide correctly. Peyton Young showed that the Borda count gives an approximately maximum likelihood estimator of

12064-420: The voters, a mutual majority , ranked Memphis last (making Memphis the majority loser ) and Nashville, Chattanooga, and Knoxville above Memphis, ruling Memphis out. At that point, the voters who preferred Memphis as their 1st choice could only help to choose a winner among Nashville, Chattanooga, and Knoxville, and because they all preferred Nashville as their 1st choice among those three, Nashville would have had

12180-448: The voters. Pairwise counts are often displayed in a pairwise comparison matrix , or outranking matrix , such as those below. In these matrices , each row represents each candidate as a 'runner', while each column represents each candidate as an 'opponent'. The cells at the intersection of rows and columns each show the result of a particular pairwise comparison. Cells comparing a candidate to themselves are left blank. Imagine there

12296-430: The welfare of children they have fathered, both legitimate and illegitimate and women's right to seek divorce. He also advocated for the criminalization of rape, declaring that it “violates the property which everyone has in her person”. Scholars often disagree on the true impact that Condorcet's work had on pre-modern feminist thinking. His detractors point out that, when he was eventually given some responsibilities in

12412-529: The winner is the candidate preferred by a majority of voters. When results for every possible pairing have been found they are as follows: The results can also be shown in the form of a matrix: ↓ 2 Wins ↓ 1 Win As can be seen from both of the tables above, Nashville beats every other candidate. This means that Nashville is the Condorcet winner. Nashville will thus win an election held under any possible Condorcet method. While any Condorcet method will elect Nashville as

12528-523: The winner, if instead an election based on the same votes were held using first-past-the-post or instant-runoff voting , these systems would select Memphis and Knoxville respectively. This would occur despite the fact that most people would have preferred Nashville to either of those "winners". Condorcet methods make these preferences obvious rather than ignoring or discarding them. On the other hand, in this example Chattanooga also defeats Knoxville and Memphis when paired against those cities. If we changed

12644-464: Was appointed inspector general of the Paris mint by Turgot. From this point on, Condorcet shifted his focus from the purely mathematical to philosophy and political matters. In the following years, he took up the defense of human rights in general, and of women's and Blacks' rights in particular (an abolitionist , he became active in the Society of the Friends of the Blacks in the 1780s). He supported

12760-418: Was at the insistence of Condorcet and Cabanis, who wished to protect their property from expropriation and to provide financially for Sophie and their young daughter, Louise 'Eliza' Alexandrine. During his time in hiding, Condorcet penned a poignant letter to his daughter, who was then a toddler, offering his advice and wisdom to her as she grows to become an adult. The letter stands as a testament, not only for

12876-832: Was born in Ribemont (in present-day Aisne ), descended from the ancient family of Caritat, who took their title from the town of Condorcet in Dauphiné , of which they were long-time residents. Fatherless at a young age, he was taken care of by his devoutly religious mother who dressed him as a girl till age eight. He was educated at the Jesuit College in Reims and at the Collège de Navarre in Paris, where he quickly showed his intellectual ability and gained his first public distinctions in mathematics . When he

12992-414: Was branded a traitor. On 3 October 1793, a warrant was issued for Condorcet's arrest. The warrant forced Condorcet into hiding. He hid for some months in the house of Mme. Vernet in Paris, where he wrote Esquisse d'un tableau historique des progrès de l'esprit humain ( Sketch for a Historical Picture of the Progress of the Human Spirit ), which was published posthumously in 1795 and is considered one of

13108-540: Was elected to the Académie royale des Sciences . In 1772, he published another paper on integral calculus . Soon after, he met Jacques Turgot , a French economist, and the two became friends. Turgot became an administrator under King Louis XV in 1772 and Controller-General of Finance under Louis XVI in 1774. Condorcet worked with Leonhard Euler and Benjamin Franklin . He soon became an honorary member of many foreign academies and philosophic societies, including

13224-426: Was not made to last and that revolutionary institutions were not intended to prolong the revolutionary experience but to establish political rules and legal mechanisms that would insure future changes without revolution. In a democratic city there would be no Bastille to be seized. Public education would form free and responsible citizens, not revolutionaries. Rothschild (2001) argues that Condorcet has been seen since

13340-422: Was sixteen, his analytical abilities gained the praise of Jean le Rond d'Alembert and Alexis Clairaut ; soon, Condorcet would study under d'Alembert. From 1765 to 1774, he focused on science. In 1765, he published his first work on mathematics, entitled Essai sur le calcul intégral , which was well received, launching his career as a mathematician. He went on to publish more papers, and on 25 February 1769, he

13456-430: Was the source of servitude. Citizens had to be provided with the necessary knowledge to exercise their freedom and understand the rights and laws that guaranteed their enjoyment. Although education could not eliminate disparities in talent, all citizens, including women, had the right to free education. In opposition to those who relied on revolutionary enthusiasm to form the new citizens, Condorcet maintained that revolution

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