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Balinski–Young Theorem
An apportionment paradox is a situation where an apportionment—a rule for dividing discrete objects according to some proportional relationship—produces results that violate notions of common sense or fairness. Certain quantities, like milk, can be divided in any proportion whatsoever; others, such as horses, cannot—only whole numbers will do. In the latter case, there is an inherent tension between the desire to obey the rule of proportion as closely as possible and the constraint restricting the size of each portion to discrete values. Several paradoxes related to apportionment and fair division have been identified. In some cases, simple adjustments to an apportionment methodology can resolve observed paradoxes. However, as shown by the Balinski–Young theorem, it is not always possible to provide a perfectly fair resolution that satisfies all competing fairness criteria. History An example of the apportionment paradox known as "the Alabama paradox" was discovered in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quota Rule
In mathematics and political science, the quota rule describes a desired property of proportional apportionment methods. It says that the number of seats allocated to a party should be equal to their entitlement plus or minus one.Michael J. Caulfield"Apportioning Representatives in the United States Congress - The Quota Rule". MAA Publications. Retrieved October 22, 2018 The ideal number of seats for a party, called their seat entitlement, is calculated by multiplying each party's share of the vote by the total number of seats. Equivalently, it is equal to the number of votes divided by the Hare quota. For example, if a party receives 10.56% of the vote, and there are 100 seats in a parliament, the quota rule says that when all seats are allotted, the party may get either 10 or 11 seats. The most common apportionment methods (the highest averages methods) violate the quota rule in situations where upholding it would cause a population paradox, although unbiased apportionment ru ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Apportionment (politics)
Apportionment is the process by which seats in a Legislature, legislative body are distributed among administrative divisions, such as states or parties, entitled to Representation (politics), representation. This page presents the general principles and issues related to apportionment. The apportionment by country page describes the specific practices used around the world. The Mathematics of apportionment page describes mathematical formulations and properties of apportionment rules. The simplest and most universal principle is that elections should One man, one vote, give each vote an equal weight. This is both intuitive and stated in laws such as the Fourteenth Amendment to the United States Constitution (the Equal Protection Clause). One example of deliberate malapportionment is seen in bicameral legislatures: while one house, often called a house of commons or representatives, is based on proportional representation, the other is based on regional representation. This is mod ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
United States Census Bureau
The United States Census Bureau, officially the Bureau of the Census, is a principal agency of the Federal statistical system, U.S. federal statistical system, responsible for producing data about the American people and American economy, economy. The U.S. Census Bureau is part of the United States Department of Commerce, U.S. Department of Commerce and its Director of the United States Census Bureau, director is appointed by the president of the United States. Currently, Ron S. Jarmin is the acting director of the U.S. Census Bureau. The Census Bureau's primary mission is conducting the United States census, U.S. census every ten years, which allocates the seats of the United States House of Representatives, U.S. House of Representatives to the U.S. state, states based on their population. The bureau's various censuses and surveys help allocate over $675 billion in federal funds every year and it assists states, local communities, and businesses in making informed decisions. T ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rutherford Hayes
Rutherford may refer to: Places Australia * Rutherford, New South Wales, a suburb of Maitland * Rutherford (Parish), New South Wales, a civil parish of Yungnulgra County Canada * Mount Rutherford, Jasper National Park * Rutherford, Edmonton, neighbourhood * Rutherford House, in Edmonton, Alberta * Rutherford Library, University of Alberta United Kingdom * Rutherford Appleton Laboratory, Oxfordshire United States * Rutherford, California, in Napa County * East Rutherford, New Jersey * Rutherford, New Jersey * Rutherford, Pennsylvania * Rutherford, West Virginia * Rutherford County, North Carolina * Rutherford County, Tennessee People * Rutherford (name), people with the surname or given name Fiction * Rutherford the Brave, a character from Gamehendge, the fictional setting for a number of songs by the rock band Phish * Rutherford, Ohio, fictional setting of the television series '' 3rd Rock from the Sun'' * Cullen Stanton Rutherford, a character from the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1876 United States Presidential Election
United States presidential election, Presidential elections were held in the United States on November 7, 1876. Republican Party (United States), Republican Governor Rutherford B. Hayes of Ohio very narrowly defeated Democratic Party (United States), Democratic Governor Samuel J. Tilden of New York. Following President Ulysses S. Grant's decision to retire after his second term, U.S. Representative James G. Blaine emerged as frontrunner for the Republican nomination; however, Blaine was unable to win a majority at the 1876 Republican National Convention, which settled on Hayes as a compromise candidate. The 1876 Democratic National Convention nominated Tilden on the second ballot. The election was among the most contentious in American history, and was only resolved by the Compromise of 1877, in which Hayes agreed to end Reconstruction era, Reconstruction in exchange for recognition of his presidency. In the first count, Tilden had 184 Electoral College (United States), electoral ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Highest Averages Method
The highest averages, divisor, or divide-and-round methods are a family of Apportionment (politics), apportionment rules, i.e. algorithms for fair division of seats in a legislature between several groups (like Political party, political parties or State (sub-national), states). More generally, divisor methods are used to round shares of a total to a Ratio, fraction with a fixed denominator (e.g. percentage points, which must add up to 100). The methods aim to treat voters equally by ensuring legislators One man, one vote, represent an equal number of voters by ensuring every party has the same seats-to-votes ratio (or ''divisor''). Such methods divide the number of votes by the number of votes needed to win a seat. The final apportionment. In doing so, the method approximately maintains proportional representation, meaning that a party with e.g. twice as many votes will win about twice as many seats. The divisor methods are generally preferred by Social choice theory, social ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Proof Of Impossibility
In mathematics, an impossibility theorem is a theorem that demonstrates a problem or general set of problems cannot be solved. These are also known as proofs of impossibility, negative proofs, or negative results. Impossibility theorems often resolve decades or centuries of work spent looking for a solution by proving there ''is'' no solution. Proving that something is impossible is usually much harder than the opposite task, as it is often necessary to develop a proof that works in general, rather than to just show a particular example. Impossibility theorems are usually expressible as negative existential propositions or universal propositions in logic. The irrationality of the square root of 2 is one of the oldest proofs of impossibility. It shows that it is impossible to express the square root of 2 as a ratio of two integers. Another consequential proof of impossibility was Ferdinand von Lindemann's proof in 1882, which showed that the problem of squaring the circle cannot ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Proportional Representation
Proportional representation (PR) refers to any electoral system under which subgroups of an electorate are reflected proportionately in the elected body. The concept applies mainly to political divisions (Political party, political parties) among voters. The aim of such systems is that all votes cast contribute to the result so that each representative in an assembly is mandated by a roughly equal number of voters, and therefore all votes have equal weight. Under other election systems, a bare Plurality (voting), plurality or a scant majority in a district are all that are used to elect a member or group of members. PR systems provide balanced representation to different factions, usually defined by parties, reflecting how votes were cast. Where only a choice of parties is allowed, the seats are allocated to parties in proportion to the vote tally or ''vote share'' each party receives. Exact proportionality is never achieved under PR systems, except by chance. The use of elector ... [...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 to 2008. 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 represe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Michel Balinski
Michel Louis Balinski (born Michał Ludwik Baliński; October 6, 1933 – February 4, 2019) was an American and French applied mathematician, economist, operations research analyst and political scientist. Educated in the United States, from 1980 he lived and worked in France. He was known for his work in optimisation (combinatorial, linear, nonlinear), convex polyhedra, stable matching, and the theory and practice of electoral systems, jury decision, and social choice. He was Directeur de Recherche de classe exceptionnelle (emeritus) of the C.N.R.S. at the École Polytechnique (Paris). He was awarded the John von Neumann Theory Prize by INFORMS in 2013. Michel Louis Balinski died in Bayonne, France. He maintained an active involvement in research and public appearances, his last public engagement took place in January 2019. Early life Michel Balinski was born in Geneva, Switzerland, the grandson of the Polish bacteriologist and founder of UNICEF, Ludwik Rajchman. Brought up ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Coherence (fairness)
Coherence, also called uniformity or consistency, is a criterion for evaluating rules for fair division. Coherence requires that the outcome of a fairness rule is fair not only for the overall problem, but also for each sub-problem. Every part of a fair division should be fair. The coherence requirement was first studied in the context of Mathematics of apportionment, apportionment. In this context, failure to satisfy coherence is called the new states paradox: when a new U.S. state Admission to the Union, enters the union, and the number of seats in the United States House of Representatives, House of Representatives is enlarged to accommodate the number of seats allocated to this new state, some other unrelated states are affected. Coherence is also relevant to other fair division problems, such as bankruptcy problems. Definition There is a ''resource'' to allocate, denoted by h. For example, it can be an integer representing the number of seats in a ''h''ouse of representati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
House Monotonicity
House monotonicity (also called house-size monotonicity) is a property of apportionment methods. These are methods for allocating seats in a parliament among federal states (or among political parties). The property says that, if the number of seats in the "house" (the parliament) increases, and the method is re-activated, then no state (or party) should have fewer seats than it previously had. A method that fails to satisfy house-monotonicity is said to have the Alabama paradox. In the context of committee elections, house monotonicity is often called committee monotonicity. It says that, if the size of the committee increases, then all the candidate that were previously elected, are still elected. House monotonicity is the special case of ''resource monotonicity'' for the setting in which the resource consists of identical discrete items (the seats). Methods violating house-monotonicity An example of a method violating house-monotonicity is the largest remainder method (= H ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
