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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 t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Political Party
A political party is an organization that coordinates candidates to compete in a particular country's elections. It is common for the members of a party to hold similar ideas about politics, and parties may promote specific ideological or policy goals. Political parties have become a major part of the politics of almost every country, as modern party organizations developed and spread around the world over the last few centuries. It is extremely rare for a country to have no political parties. Some countries have only one political party while others have several. Parties are important in the politics of autocracies as well as democracies, though usually democracies have more political parties than autocracies. Autocracies often have a single party that governs the country, and some political scientists consider competition between two or more parties to be an essential part of democracy. Parties can develop from existing divisions in society, like the divisions betwee ... [...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 lowe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Entitlement (fair Division)
Entitlement in fair division describes that proportion of the resources or goods to be divided that a player can expect to receive. In many fair division settings, all agents have ''equal entitlements'', which means that each agent is entitled to 1/''n'' of the resource. But there are practical settings in which agents have ''different entitlements''. Some examples are: * In partnership resolution settings, each partner is entitled to a fraction of the common assets in proportion to his/her investment in the partnership. * In inheritance settings, the law in some jurisdictions prescribes a different share to each heir according to his/her proximity to the deceased person. For example, according to the Bible, the firstborn son must receive twice as much as every other son. In contrast, according to the Italian law, when there are three heirs - parent, brother and spouse - they are entitled to 1/4, 1/12 and 2/3 respectively. * In parliamentary democracies, each party is entitled to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Edward Vermilye Huntington
Edward Vermilye Huntington (April 26, 1874November 25, 1952) was an American mathematician. Biography Huntington was awarded the B.A. and the M.A. by Harvard University in 1895 and 1897, respectively. After two years' teaching at Williams College, he began a doctorate at the University of Strasbourg, which was awarded in 1901. He then spent his entire career at Harvard, retiring in 1941. He taught in the engineering school, becoming Professor of Mechanics in 1919. Although Huntington's research was mainly in pure mathematics, he valued teaching mathematics to engineering students. He advocated mechanical calculators and had one in his office. He had an interest in statistics, unusual for the time, and worked on statistical problems for the USA military during World War I. Huntington's primary research interest was the foundations of mathematics. He was one of the "American postulate theorists" (according to Michael Scanlan, the expression is due to John Corcoran), American mathem ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Divisor 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 t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
State-population Monotonicity
State-population monotonicity is a property of apportionment methods, which are methods of allocating seats in a parliament among federal states. The property says that, if the population of a state increases faster than that of other states, then it should not lose a seat. An apportionment method that fails to satisfy this property is said to have a population paradox. In the apportionment literature, this property is simply called population monotonicity. However, the term "population monotonicity" is more commonly used to denote a very different property of resource-allocation rules: * In resource allocation, the property relates to the set of agents participating in the division process. A population-increase means that the previously-present agents are entitled to fewer items, as there are more mouths to feed. See population monotonicity for more information. * In apportionment, the property relates to the population of an individual state, which determines the state's ''e ... [...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] |
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, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics Of Apportionment
Mathematics of apportionment describes mathematical principles and algorithms for fair allocation of identical items among parties with different entitlements. Such principles are used to apportion seats in parliaments among federal states or political parties. See apportionment (politics) for the more concrete principles and issues related to apportionment, and apportionment by country for practical methods used around the world. Mathematically, an apportionment method is just a method of rounding fractions to integers. As simple as it may sound, each and every method for rounding suffers from one or more paradoxes. The mathematical theory of apportionment aims to decide what paradoxes can be avoided, or in other words, what properties can be expected from an apportionment method. The mathematical theory of apportionment was studied as early as 1907 by the mathematician Agner Krarup Erlang. It was later developed to a great detail by the mathematician Michel Balinsky and the ec ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Population Paradox
State-population monotonicity is a property of apportionment methods, which are methods of allocating seats in a parliament among federal states. The property says that, if the population of a state increases faster than that of other states, then it should not lose a seat. An apportionment method that fails to satisfy this property is said to have a population paradox. In the apportionment literature, this property is simply called population monotonicity. However, the term "population monotonicity" is more commonly used to denote a very different property of resource-allocation rules: * In resource allocation, the property relates to the set of agents participating in the division process. A population-increase means that the previously-present agents are entitled to fewer items, as there are more mouths to feed. See population monotonicity for more information. * In apportionment, the property relates to the population of an individual state, which determines the state's ''e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Population Monotonicity
Population monotonicity (PM) is a principle of consistency in allocation problems. It says that, when the set of agents participating in the allocation changes, the utility of all agents should change in the same direction. For example, if the resource is good, and an agent leaves, then all remaining agents should receive at least as much utility as in the original allocation. The term "population monotonicity" is used in an unrelated meaning in the context of apportionment of seats in the congress among states. There, the property relates to the population of an individual state, which determines the state's ''entitlement.'' A population-increase means that a state is entitled to more seats. This different property is described in the page ''state-population monotonicity''. In fair cake cutting In the fair cake-cutting problem, classic allocation rules such as divide and choose are not PM. Several rules are known to be PM: * When the pieces may be ''disconnected'', any function ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 prov ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
