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Condorcet Methods
A Condorcet method (; ) 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, that is, a candidate preferred by more voters than any others, whenever there is such a candidate. A candidate with this property, the ''pairwise champion'' or ''beats-all winner'', is formally called the ''Condorcet winner''. The head-to-head elections need not be done separately; 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 (but rare) that every candidate has an opponent that defeats them in a two-candidate contest.(This is similar to the game rock paper scissors, where each hand shape wins against one opponent and loses to another one). The possibility of such cyclic preferences is known as the Condorcet paradox. However, a smallest group of candidates that beat a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Preferential Ballot
The term ranked voting (also known as preferential voting or ranked choice voting) refers to any voting system in which voters rank their candidates (or options) in a sequence of first or second (or third, etc.) on their respective ballots. Ranked voting systems differ on the basis of how the ballots are marked, how the preferences are tabulated and counted, how many seats are filled, and whether voters are allowed to rank candidates equally. An electoral system that uses ranked voting uses one of the many available counting methods to select the winning candidate or candidates. There is also variation among ranked voting electoral systems in that in some ranked voting systems, officials require voters to rank a set number of candidates, sometimes all of them; in others, citizens may rank as many candidates as they see fit. Election of single members using ranked votes is often instant-runoff voting. Election of multiple members using ranked votes is usually single transferabl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Voting Paradox
The Condorcet paradox (also known as the voting paradox or the paradox of voting) in social choice theory is a situation noted by the Marquis de Condorcet in the late 18th century, in which collective preferences can be cyclic, even if the preferences of individual voters are not cyclic. This is paradoxical, because it means that majority wishes can be in conflict with each other: Suppose majorities prefer, for example, candidate A over B, B over C, and yet C over A. When this occurs, it is because the conflicting majorities are each made up of different groups of individuals. Thus an expectation that transitivity on the part of all individuals' preferences should result in transitivity of societal preferences is an example of a fallacy of composition. The paradox was independently discovered by Lewis Carroll and Edward J. Nanson, but its significance was not recognized until popularized by Duncan Black in the 1940s. Example Suppose we have three candidates, A, B, and C, and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Matrix Addition
In mathematics, matrix addition is the operation of adding two matrices by adding the corresponding entries together. However, there are other operations which could also be considered addition for matrices, such as the direct sum and the Kronecker sum. Entrywise sum Two matrices must have an equal number of rows and columns to be added. In which case, the sum of two matrices A and B will be a matrix which has the same number of rows and columns as A and B. The sum of A and B, denoted , is computed by adding corresponding elements of A and B: :\begin \mathbf+\mathbf & = \begin a_ & a_ & \cdots & a_ \\ a_ & a_ & \cdots & a_ \\ \vdots & \vdots & \ddots & \vdots \\ a_ & a_ & \cdots & a_ \\ \end + \begin b_ & b_ & \cdots & b_ \\ b_ & b_ & \cdots & b_ \\ \vdots & \vdots & \ddots & \vdots \\ b_ & b_ & \cdots & b_ \\ \end \\ & = \begin a_ + b_ & a_ + b_ & \cdots & a_ + b_ \\ a_ + b_ & a_ + b_ & \cdots & a_ + b_ \\ \vdots & \vdots & \ddots & \vdots \\ a_ + b_ & a_ + b_ & \cd ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Matrix (mathematics)
In mathematics, a matrix (plural matrices) is a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns, which is used to represent a mathematical object or a property of such an object. For example, \begin1 & 9 & -13 \\20 & 5 & -6 \end is a matrix with two rows and three columns. This is often referred to as a "two by three matrix", a "-matrix", or a matrix of dimension . Without further specifications, matrices represent linear maps, and allow explicit computations in linear algebra. Therefore, the study of matrices is a large part of linear algebra, and most properties and operations of abstract linear algebra can be expressed in terms of matrices. For example, matrix multiplication represents composition of linear maps. Not all matrices are related to linear algebra. This is, in particular, the case in graph theory, of incidence matrices, and adjacency matrices. ''This article focuses on matrices related to linear algebra, and, un ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Independence Of Smith-dominated Alternatives
Independence of Smith-dominated alternatives (ISDA, also known as Smith- IIA or Weak independence of irrelevant alternatives) is a voting system criterion defined such that its satisfaction by a voting system occurs when the selection of the winner is independent of candidates who are not within the Smith set. A simple way to describe it is that if a voting system is ISDA, then whenever you can partition the candidates into group ''A'' and group ''B'' such that each candidate in group ''A'' is preferred over each candidate in group ''B'', you can eliminate all candidates of group ''B'' without changing the outcome of the election. Any election method that is independent of Smith-dominated alternatives automatically satisfies the Smith criterion (because all candidates not in the Smith set can be eliminated without changing the result, implying that the winner was someone in the Smith set), and all criteria implied by it, notably the Condorcet criterion and the mutual majority ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Write-in Candidate
A write-in candidate is a candidate whose name does not appear on the ballot but seeks election by asking voters to cast a vote for the candidate by physically writing in the person's name on the ballot. Depending on electoral law it may be possible to win an election by winning a sufficient number of such write-in votes, which count equally as if the person was formally listed on the ballot. Writing in a name that is not already on the election ballot is considered a practice of the United States. However, some other jurisdictions have allowed this practice. In the United States, there are variations in laws governing write-in candidates, depending on the office (federal or local) and whether the election is a primary election or the general election; general practice is an empty field close by annotated to explain its purpose on the ballot if it applies. In five U.S. states there are no elections to which it can apply, under their present laws. Election laws are enacted by each ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Score Voting
Score voting or range voting is an electoral system for single-seat elections, in which voters give each candidate a score, the scores are added (or averaged), and the candidate with the highest total is elected. It has been described by various other names including evaluative voting, utilitarian voting, interval measure voting, the point system, ratings summation, 0-99 voting, average voting and utility voting. It is a type of cardinal voting electoral system, and aims to implement the utilitarian social choice rule. Score voting should be distinguished from positional voting systems, such as the Borda count: in score voting, each voter is free to give any score to any candidate; in positional voting, the score that each voter gives to each candidate is uniquely determined by the candidate's rank in the voter's ballot. Usage Political use Combined approval voting, a 3-rank form of score voting, is used to determine which candidates represent the parties in Latvia's S ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Andranik Tangian
Andranik Semovich Tangian (Melik-Tangyan) (Russian: Андраник Семович Тангян (Мелик-Тангян)); born March 29, 1952) is a Soviet Armenian-German mathematician, political economist and music theorist. Tangian is known for the mathematical theory of democracy, the Third Vote election method, criticism of flexicurity employment strategy and models of artificial perception of music. He is professor of the Institute for Economics (ECON) of the Karlsruhe Institute of Technology. Biography Andranik Tangian was born in Moscow, Soviet Union, on March 29, 1952. After the graduation from the Faculty of Mechanics and Mathematics of the Moscow State University in 1974, he has worked at the Gubkin Russian State University of Oil and Gas and the Central Economic Mathematical Institute of the Academy of Sciences of the Soviet Union, where he got his PhD in mathematics in 1979. From 1980 to 1983 he worked as assistant professor at the Academy of National Econo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Peyton Young
Hobart Peyton Young (born March 9, 1945) is an American game theorist and economist known for his contributions to evolutionary game theory and its application to the study of institutional and technological change, as well as the theory of learning in games. He is currently centennial professor at the London School of Economics, James Meade Professor of Economics Emeritus at the University of Oxford, professorial fellow at Nuffield College Oxford, and research principal at the Office of Financial Research at the U.S. Department of the Treasury. Peyton Young was named a fellow of the Econometric Society in 1995, a fellow of the British Academy in 2007, and a fellow of the American Academy of Arts and Sciences in 2018. He served as president of the Game Theory Society from 2006–08. He has published widely on learning in games, the evolution of social norms and institutions, cooperative game theory, bargaining and negotiation, taxation and cost allocation, political represent ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bernard Grofman
Bernard Norman Grofman (born December 2, 1944) is a political scientist at the University of California, Irvine. He is an expert on redistricting and has been a special master on several district map redrawings. From the University of Chicago he received a B.S. (1966) in mathematics and an M.A. (1968) and Ph.D. (1972) in political science. He began teaching at the University of California, Irvine, in 1976, becoming a full professor in 1980. His works include ''Quiet Revolution in the South: The Impact of the Voting Rights Act, 1965-1990'' (with Chandler Davidson, eds., 1994), ''Legacies of the 1964 Civil Rights Act'' (ed., 2000), ''Political Science as Puzzle Solving'' (ed., 2001), ''A Unified Theory of Voting'' (with Samuel Merrill III, 1999), and ''A Unified Theory of Party Competition'' (with James Adams and Samuel Merrill III, 2005), among many others. He also published over 200 articles in periodicals. He has published several articles under the pseudonym "A. Wuffle" or " ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Borda Count
The Borda count is a family of positional voting rules which gives each candidate, for each ballot, a number of points corresponding to the number of candidates ranked lower. In the original variant, the lowest-ranked candidate gets 0 points, the next-lowest gets 1 point, etc., and the highest-ranked candidate gets ''n'' − 1 points, where ''n'' is the number of candidates. Once all votes have been counted, the option or candidate with the most points is the winner. The Borda count is intended to elect broadly acceptable options or candidates, rather than those preferred by a majority, and so is often described as a consensus-based voting system rather than a majoritarian one. The Borda count was developed independently several times, being first proposed in 1435 by Nicholas of Cusa (see History below), but is named for the 18th-century French mathematician and naval engineer Jean-Charles de Borda, who devised the system in 1770. It is currently used to elect two ethnic minority ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Instant-runoff Voting
Instant-runoff voting (IRV) is a type of Ranked voting, ranked preferential Electoral system, voting method. It uses a Majority rule, majority voting rule in single-winner elections where there are more than two candidates. It is commonly referred to as ranked-choice voting (RCV) Ranked-choice voting in the United States, in the United States (although there are other forms of ranked voting), preferential voting in Australia, where it has seen the widest adoption; in the United Kingdom, it is generally called alternative vote (AV), whereas in some other countries it is referred to as the single transferable vote, which usually means only its multi-winner variant. All these names are often used inconsistently. Voters in IRV elections rank the candidates in order of preference. Ballots are initially counted for each voter's top choice. If a candidate has Majority, more than half of the first-choice votes, that candidate wins. If not, then the candidate with the fewest votes is elim ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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