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Alabama Paradox
An apportionment paradox exists when the rules for apportionment in a political system produce results which are unexpected or seem to violate common sense. To apportion is to divide into parts according to some rule, the rule typically being one of proportion. 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. This results, at times, in unintuitive observations, or paradoxes. Several paradoxes related to apportionment, also called ''fair division'', have been identified. In some cases, simple ''post facto'' adjustments, if allowed, to an apportionment methodology can resolve observed paradoxes. However, as shown by examples relating to the United States House of Representatives, and subsequently proven ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Apportionment (politics)
Apportionment is the process by which seats in a legislative body are distributed among administrative divisions, such as states or parties, entitled to representation. This page presents the general principles and issues related to apportionment. The page Apportionment by country describes specific practices used around the world. The page Mathematics of apportionment describes mathematical formulations and properties of apportionment rules. The simplest and most universal principle is that elections should give each voter's intentions equal weight. This is both intuitive and stated in laws such as the Fourteenth Amendment to the United States Constitution (the Equal Protection Clause). However, there are a variety of historical and technical reasons why this principle is not followed absolutely or, in some cases, as a first priority. Common problems Fundamentally, the representation of a population in the thousands or millions by a reasonable size, thus accountable govern ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
United States Congressional Apportionment
United States congressional apportionment is the process by which seats in the United States House of Representatives are distributed among the 50 states according to the most recent decennial census mandated by the United States Constitution. Each state is apportioned a number of seats which approximately corresponds to its share of the aggregate population of the 50 states. Every state is constitutionally guaranteed at least one seat in the House and two seats in the Senate, regardless of population. The number of voting seats in the House of Representatives has been 435 since 1913, capped at that number by the Reapportionment Act of 1929—except for a temporary (1959–1962) increase to 437 when Alaska and Hawaii were admitted into the Union.Public Law 62-5 of 1911. The Huntington–Hill method of equal proportions has been used to distribute the seats among the states since the 1940 census reapportionment. Federal law requires the Clerk of the United States House of Rep ... [...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, Virginia * Rutherford, West Virginia * Rutherford County, North Carolina * Rutherford County, Tennessee People * Rutherford (name), people with the surname or given name ** Ernest Rutherford (1871–1937), 1st Baron Rutherford of Nelson, known as the father of nuclear physics ** Rutherford B. Hayes (1822–1893), 19th president of the United States (1877–1881) Fiction * Rutherford the Brave, a character from Gamehen ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1876 United States Presidential Election
The 1876 United States presidential election was the 23rd quadrennial presidential election, held on Tuesday, November 7, 1876, in which Republican nominee Rutherford B. Hayes faced Democrat Samuel J. Tilden. It was one of the most contentious presidential elections in American history. Its resolution involved negotiations between the Republicans and Democrats, resulting in the Compromise of 1877, and on March 2, 1877, the counting of electoral votes by the House and Senate occurred, confirming Hayes as President. It was the second of five U.S. presidential elections in which the winner did not win a plurality of the national popular vote. This is the only time both major party nominees were incumbent US governors. After U.S. President Ulysses S. Grant declined to seek a third term despite previously being expected to do so, U.S. Representative James G. Blaine emerged as the frontrunner for the Republican nomination. However, Blaine was unable to win a majority at the 1876 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Highest Averages Method
A highest-averages method, also called a divisor method, is a class of methods for allocating seats in a parliament among agents such as political parties or federal states. A divisor method is an iterative method: at each iteration, the number of votes of each party is divided by its ''divisor'', which is a function of the number of seats (initially 0) currently allocated to that party. The next seat is allocated to the party whose resulting ratio is largest. Definitions The inputs to a divisor method are the number of seats to allocate, denoted by ''h'', and the vector of parties' entitlements, where the entitlement of party i is denoted by t_i (a number between 0 and 1 determining the fraction of seats to which i is entitled). Assuming all votes are counted, t_i is simply the number of votes received by i, divided by the total number of votes. Procedural definition A divisor method is parametrized by a function d(k), mapping each integer k to a real number (usually in th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Proof Of Impossibility
In mathematics, a proof of impossibility is a proof that demonstrates that a particular problem cannot be solved as described in the claim, or that a particular set of problems cannot be solved in general. Such a case is also known as a negative proof, proof of an impossibility theorem, or negative result. Because they show that something cannot be done, proofs of impossibility can be the resolutions to decades or centuries of work attempting to find a 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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Proportional Representation
Proportional representation (PR) refers to a type of electoral system under which subgroups of an electorate are reflected proportionately in the elected body. The concept applies mainly to geographical (e.g. states, regions) and political divisions (political parties) of the electorate. The essence of such systems is that all votes cast - or almost all votes cast - contribute to the result and are actually used to help elect someone—not just a plurality, or a bare majority—and that the system produces mixed, balanced representation reflecting how votes are cast. "Proportional" electoral systems mean proportional to ''vote share'' and ''not'' proportional to population size. For example, the US House of Representatives has 435 districts which are drawn so roughly equal or "proportional" numbers of people live within each district, yet members of the House are elected in first-past-the-post elections: first-past-the-post is ''not'' proportional by vote share. The ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quota Rule
In mathematics and political science, the quota rule describes a desired property of a proportional apportionment or election method. It states that the number of seats that should be allocated to a given party should be between the upper or lower roundings (called upper and lower quotas) of its fractional proportional share (called natural quota).Michael J. Caulfield"Apportioning Representatives in the United States Congress - The Quota Rule" MAA Publications. Retrieved October 22, 2018 As an example, if a party deserves 10.56 seats out of 15, the quota rule states that when the seats are allotted, the party may get 10 or 11 seats, but not lower or higher. Many common election methods, such as all highest averages methods, violate the quota rule. Mathematics If P is the population of the party, T is the total population, and S is the number of available seats, then the natural quota for that party (the number of seats the party would ideally get) is : \frac P T \cdot S The lower ... [...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 representati ... [...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 applied mathematician, economist, operations research analyst and political scientist. As a Polish-American, educated in the United States, he lived and worked primarily in the United States and 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, Lu ... [...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 apportionment. In this context, failure to satisfy coherence is called the new states paradox: when a new state enters the union, and the house size 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 representatives. The resource should be allocated between some n ''agents''. For example, these can be federal states or political parties. The agent ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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