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Penrose–Banzhaf Index
The Banzhaf power index, named after John Banzhaf (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 The nu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
United States Presidential Election
The election of the president of the United States, president and Vice President of the United States, vice president of the United States is an indirect election in which citizens of the United States who are Voter registration in the United States, registered to vote in one of the fifty U.S. states or in Washington, D.C., cast ballots not directly for those offices, but instead for members of the United States Electoral College, Electoral College. These electors then cast direct votes, known as electoral votes, for president and for vice president. The candidate who receives an absolute majority of electoral votes (at least 270 out of 538, since the Twenty-third Amendment to the United States Constitution, Twenty-third Amendment granted voting rights to citizens of D.C.) is then elected to that office. If no candidate receives an absolute majority of the votes for president, the United States House of Representatives, House of Representatives elects the president; likewise if ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Political Science Theories
Politics () is the set of activities that are associated with making decisions in groups, or other forms of power relations among individuals, such as the distribution of status or resources. The branch of social science that studies politics and government is referred to as political science. Politics may be used positively in the context of a "political solution" which is compromising and non-violent, or descriptively as "the art or science of government", but the word often also carries a negative connotation.. The concept has been defined in various ways, and different approaches have fundamentally differing views on whether it should be used extensively or in a limited way, empirically or normatively, and on whether conflict or co-operation is more essential to it. A variety of methods are deployed in politics, which include promoting one's own political views among people, negotiation with other political subjects, making laws, and exercising internal and external f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cooperative Games , a video game that allows players to work together as teammates
{{disambiguation ...
Cooperative game may refer to: * Cooperative board game, board games in which players work together to achieve a common goal * Cooperative game theory, in game theory, a game with competition between groups of players and the possibility of cooperative behavior * Cooperative video game A cooperative video game, often abbreviated as co-op, is a video game that allows players to work together as teammates, usually against one or more non-player character opponents ( PvE). Co-op games can be played locally using one or multiple i ... [...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 h ... [...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. It has applications in many fields of social science, and is used extensively in economics, logic, systems science and computer science. Initially, game theory addressed two-person zero-sum games, in which a participant's gains or losses are exactly balanced by the losses and gains of the other participant. In the 1950s, it was extended to the study of non zero-sum games, and was eventually applied to a wide range of Human behavior, behavioral relations. It is now an umbrella term for the science of rational Decision-making, decision making in humans, animals, and computers. Modern game theory began with the idea of mixed-strategy equilibria in two-person zero-sum games 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 mathematical economics. His paper was f ... [...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 less formally 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 discussin ... [...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 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. 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 coalition has no effect at all on the outcome of the game; and a power of 1 means a coalition determines the outcome by its vote. Also the sum of the powers of all the players is always equal to 1. There are some algorithms for calculating the power ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nassau County, New York
Nassau County ( ) is a suburban County (United States), county located on Long Island, immediately to the east of New York City, bordering the Long Island Sound on the north and the open Atlantic Ocean to the south. As of the 2020 United States census, Nassau County's population was 1,395,774, making it the sixth-most populous county in the State of New York, and reflecting an increase of 56,242 (+4.2%) from the 1,339,532 residents enumerated at the 2010 United States census, 2010 census. Its county seat is Mineola, New York, Mineola, while the county's largest and most populous town is Hempstead, New York, Hempstead. Situated on western Long Island, the County of Nassau borders New York City's Boroughs of New York City, borough of Queens to its west, and Long Island's Suffolk County, New York, Suffolk County to its 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 commu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
John F
John is a common English name and surname: * John (given name) * John (surname) John may also refer to: New Testament Works * Gospel of John, a title often shortened to John * First Epistle of John, often shortened to 1 John * Second Epistle of John, often shortened to 2 John * Third Epistle of John, often shortened to 3 John People * John the Baptist (died ), regarded as a prophet and the forerunner of Jesus Christ * John the Apostle (died ), one of the twelve apostles of Jesus Christ * John the Evangelist, assigned author of the Fourth Gospel, once identified with the Apostle * John of Patmos, also known as John the Divine or John the Revelator, the author of the Book of Revelation, once identified with the Apostle * John the Presbyter, a figure either identified with or distinguished from the Apostle, the Evangelist and John of Patmos Other people with the given name Religious figures * John, father of Andrew the Apostle and Saint Peter * Pope Jo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
New York (state)
New York, also called New York State, is a U.S. state, state in the northeastern United States. Bordered by New England to the east, Canada to the north, and Pennsylvania and New Jersey to the south, its territory extends into both the Atlantic Ocean and the Great Lakes. New York is the List of U.S. states and territories by population, fourth-most populous state in the United States, with nearly 20 million residents, and the List of U.S. states and territories by area, 27th-largest state by area, with a total area of . New York has Geography of New York (state), a varied geography. The southeastern part of the state, known as Downstate New York, Downstate, encompasses New York City, the List of U.S. cities by population, most populous city in the United States; Long Island, with approximately 40% of the state's population, the nation's most populous island; and the cities, suburbs, and wealthy enclaves of the lower Hudson Valley. These areas are the center of the expansive New ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
