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Banzhaf Power Index
The Banzhaf power index, named after John F. Banzhaf III (originally invented by Lionel Penrose in 1946 and sometimes called Penrose–Banzhaf index; also known as the Banzhaf–Coleman index after James Samuel Coleman), is a power index defined by the probability of changing an outcome of a vote where voting rights are not necessarily equally divided among the voters or shareholders. To calculate the power of a voter using the Banzhaf index, list all the winning coalitions, then count the critical voters. A ''critical voter'' is a voter who, if he changed his vote from yes to no, would cause the measure to fail. A voter's power is measured as the fraction of all swing votes that he could cast. There are some algorithms for calculating the power index, e.g., dynamic programming techniques, enumeration methods and Monte Carlo methods. Examples Voting game Simple voting game A simple voting game, taken from ''Game Theory and Strategy'' by Philip D. Straffin: ; 4, 3, 2, 1 T ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Republican Party (United States)
The Republican Party, also referred to as the GOP ("Grand Old Party"), is one of the two major contemporary political parties in the United States. The GOP was founded in 1854 by anti-slavery activists who opposed the Kansas–Nebraska Act, which allowed for the potential expansion of chattel slavery into the western territories. Since Ronald Reagan's presidency in the 1980s, conservatism has been the dominant ideology of the GOP. It has been the main political rival of the Democratic Party since the mid-1850s. The Republican Party's intellectual predecessor is considered to be Northern members of the Whig Party, with Republican presidents Abraham Lincoln, Rutherford B. Hayes, Chester A. Arthur, and Benjamin Harrison all being Whigs before switching to the party, from which they were elected. The collapse of the Whigs, which had previously been one of the two major parties in the country, strengthened the party's electoral success. Upon its founding, it supported c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
R (programming Language)
R is a programming language for statistical computing and graphics supported by the R Core Team and the R Foundation for Statistical Computing. Created by statisticians Ross Ihaka and Robert Gentleman, R is used among data miners, bioinformaticians and statisticians for data analysis and developing statistical software. Users have created packages to augment the functions of the R language. According to user surveys and studies of scholarly literature databases, R is one of the most commonly used programming languages used in data mining. R ranks 12th in the TIOBE index, a measure of programming language popularity, in which the language peaked in 8th place in August 2020. The official R software environment is an open-source free software environment within the GNU package, available under the GNU General Public License. It is written primarily in C, Fortran, and R itself (partially self-hosting). Precompiled executables are provided for various operating systems. R ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Python (programming Language)
Python is a high-level, general-purpose programming language. Its design philosophy emphasizes code readability with the use of significant indentation. Python is dynamically-typed and garbage-collected. It supports multiple programming paradigms, including structured (particularly procedural), object-oriented and functional programming. It is often described as a "batteries included" language due to its comprehensive standard library. Guido van Rossum began working on Python in the late 1980s as a successor to the ABC programming language and first released it in 1991 as Python 0.9.0. Python 2.0 was released in 2000 and introduced new features such as list comprehensions, cycle-detecting garbage collection, reference counting, and Unicode support. Python 3.0, released in 2008, was a major revision that is not completely backward-compatible with earlier versions. Python 2 was discontinued with version 2.7.18 in 2020. Python consistently ranks as ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Penrose Square Root Law
In the mathematical theory of games, the Penrose square root law, originally formulated by Lionel Penrose, concerns the distribution of the voting power in a voting body consisting of ''N'' members. It states that the ''a priori'' voting power of any voter, measured by the Penrose–Banzhaf index \psi scales like 1/\sqrt . This result was used to design the Penrose method for allocating the voting weights of representatives in a decision-making bodies proportional to the square root of the population represented. Short derivation To estimate the voting index of any player one needs to estimate the number of the possible winning coalitions in which his vote is decisive. Assume for simplicity that the number of voters is odd, ''N'' = 2''j'' + 1, and the body votes according to the standard majority rule. Following Penrose one concludes that a given voter will be able to effectively influence the outcome of the voting only if the votes split half and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Penrose Method
The Penrose method (or square-root method) is a method devised in 1946 by Professor Lionel Penrose for allocating the voting weights of delegations (possibly a single representative) in decision-making bodies proportional to the square root of the population represented by this delegation. This is justified by the fact that, due to the square root law of Penrose, the ''a priori'' voting power (as defined by the Penrose–Banzhaf index) of a member of a voting body is inversely proportional to the square root of its size. Under certain conditions, this allocation achieves equal voting powers for all people represented, independent of the size of their constituency. Proportional allocation would result in excessive voting powers for the electorates of larger constituencies. A precondition for the appropriateness of the method is ''en bloc'' voting of the delegations in the decision-making body: a delegation cannot split its votes; rather, each delegation has just a single vote to wh ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Game Theory
Game theory is the study of mathematical models of strategic interactions among rational agents. Myerson, Roger B. (1991). ''Game Theory: Analysis of Conflict,'' Harvard University Press, p.&nbs1 Chapter-preview links, ppvii–xi It has applications in all fields of social science, as well as in logic, systems science and computer science. Originally, it addressed two-person zero-sum games, in which each participant's gains or losses are exactly balanced by those of other participants. In the 21st century, game theory applies to a wide range of behavioral relations; it is now an umbrella term for the science of logical decision making in humans, animals, as well as computers. Modern game theory began with the idea of mixed-strategy equilibria in two-person zero-sum game and its proof by John von Neumann. Von Neumann's original proof used the Brouwer fixed-point theorem on continuous mappings into compact convex sets, which became a standard method in game theory and mathema ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Council Of The European Union
The Council of the European Union, often referred to in the treaties and other official documents simply as the Council, and informally known as the Council of Ministers, is the third of the seven Institutions of the European Union (EU) as listed in the Treaty on European Union. It is one of two legislative bodies and together with the European Parliament serves to amend and approve or veto the proposals of the European Commission, which holds the right of initiative. The Council of the European Union and the European Council are the only EU institutions that are explicitly intergovernmental, that is, forums whose attendees express and represent the position of their Member State's executive, be they ambassadors, ministers or heads of state/government. The Council meets in 10 different configurations of national ministers (one per state). The precise membership of these configurations varies according to the topic under consideration; for example, when discussing agri ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Shapley–Shubik Power Index
The Shapley–Shubik power index was formulated by Lloyd Shapley and Martin Shubik in 1954 to measure the powers of players in a voting game. The index often reveals surprising power distribution that is not obvious on the surface. The constituents of a voting system, such as legislative bodies, executives, shareholders, individual legislators, and so forth, can be viewed as players in an ''n''-player game. Players with the same preferences form coalitions. Any coalition that has enough votes to pass a bill or elect a candidate is called winning, and the others are called losing. Based on Shapley value, Shapley and Shubik concluded that the power of a coalition was not simply proportional to its size. The power of a coalition (or a player) is measured by the fraction of the possible voting sequences in which that coalition casts the deciding vote, that is, the vote that first guarantees passage or failure. The power index is normalized between 0 and 1. A power of 0 means that a c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nassau County, New York
Nassau County ( ) is a county in the U.S. state of New York. At the 2020 U.S. census, Nassau County's population is 1,395,774. The county seat is Mineola and the largest town is Hempstead. Nassau County is situated on western Long Island, bordering New York City's borough of Queens to the west, and Suffolk County to the east. It is the most densely populated and second-most populous county in the State of New York outside of New York City, with which it maintains extensive rail and highway connectivity, and is considered one of the central counties within the New York metropolitan area. Nassau County contains two cities, three towns, 64 incorporated villages, and more than 60 unincorporated hamlets. Nassau County has a designated police department, fire commission, and elected executive and legislative bodies. A 2012 ''Forbes'' article based on the American Community Survey reported Nassau County as the most expensive county and one of the highest income counties in th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Shapley Value
The Shapley value is a solution concept in cooperative game theory. It was named in honor of Lloyd Shapley, who introduced it in 1951 and won the Nobel Memorial Prize in Economic Sciences for it in 2012. To each cooperative game it assigns a unique distribution (among the players) of a total surplus generated by the coalition of all players. The Shapley value is characterized by a collection of desirable properties. Hart (1989) provides a survey of the subject. The setup is as follows: a coalition of players cooperates, and obtains a certain overall gain from that cooperation. Since some players may contribute more to the coalition than others or may possess different bargaining power (for example threatening to destroy the whole surplus), what final distribution of generated surplus among the players should arise in any particular game? Or phrased differently: how important is each player to the overall cooperation, and what payoff can he or she reasonably expect? The Shapley val ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Monopoly
A monopoly (from Greek language, Greek el, μόνος, mónos, single, alone, label=none and el, πωλεῖν, pōleîn, to sell, label=none), as described by Irving Fisher, is a market with the "absence of competition", creating a situation where a specific person or company, enterprise is the only supplier of a particular thing. This contrasts with a monopsony which relates to a single entity's control of a Market (economics), market to purchase a good or service, and with oligopoly and duopoly which consists of a few sellers dominating a market. Monopolies are thus characterized by a lack of economic Competition (economics), competition to produce the good (economics), good or Service (economics), service, a lack of viable substitute goods, and the possibility of a high monopoly price well above the seller's marginal cost that leads to a high monopoly profit. The verb ''monopolise'' or ''monopolize'' refers to the ''process'' by which a company gains the ability to raise ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
