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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] |
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] |
Parliament
In modern politics, and history, a parliament is a legislative body of government. Generally, a modern parliament has three functions: representing the electorate, making laws, and overseeing the government via hearings and inquiries. The term is similar to the idea of a senate, synod or congress and is commonly used in countries that are current or former monarchies. Some contexts restrict the use of the word ''parliament'' to parliamentary systems, although it is also used to describe the legislature in some presidential systems (e.g., the Parliament of Ghana), even where it is not in the official name. Historically, parliaments included various kinds of deliberative, consultative, and judicial assemblies, an example being the French medieval and early modern parlements. Etymology The English term is derived from Anglo-Norman and dates to the 14th century, coming from the 11th century Old French , "discussion, discourse", from , meaning "to talk". The meaning evo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Federal States
A federation (also known as a federal state) is a political entity characterized by a union of partially self-governing provinces, states, or other regions under a central federal government (federalism). In a federation, the self-governing status of the component states, as well as the division of power between them and the central government, is typically constitutionally entrenched and may not be altered by a unilateral decision, neither by the component states nor the federal political body. Alternatively, a federation is a form of government in which sovereign power is formally divided between a central authority and a number of constituent regions so that each region retains some degree of control over its internal affairs. It is often argued that federal states where the central government has overriding powers are not truly federal states. For example, such overriding powers may include: the constitutional authority to suspend a constituent state's government by in ... [...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] |
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] |
Agner Krarup Erlang
Agner Krarup Erlang (1 January 1878 – 3 February 1929) was a Danish mathematician, statistician and engineer, who invented the fields of traffic engineering and queueing theory. By the time of his relatively early death at the age of 51, Erlang had created the field of telephone networks analysis. His early work in scrutinizing the use of local, exchange and trunk telephone line usage in a small community to understand the theoretical requirements of an efficient network led to the creation of the Erlang formula, which became a foundational element of modern telecommunication network studies. Life Erlang was born at Lønborg, near Tarm, in Jutland. He was the son of a schoolmaster, and a descendant of Thomas Fincke on his mother's side. At age 14, he passed the Preliminary Examination of the University of Copenhagen with distinction, after receiving dispensation to take it because he was younger than the usual minimum age. For the next two years he taught alongside h ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Aanund Hylland
Aanund Hylland (born 19 October 1949) is a Norwegian economist. He completed a master's degree in mathematical logic at the University of Oslo in 1974, and a Ph.D. at the John F. Kennedy School of Government, Harvard University in 1980. He worked at the University of Oslo and BI Norwegian Business School from 1983, and in 1991, he was promoted to professor at the University of Oslo. He was the dean of the Faculty of Social Sciences from 1996 to 1998. He is a member of the Norwegian Academy of Science and Letters. He was the vice chairman of the board of the Norwegian Institute for Social Research The Norwegian Institute for Social Research ( no, Institutt for samfunnsforskning, ISF) is a private social science research institute based in Oslo, Norway. It was founded in 1950 by Vilhelm Aubert, Arne Næss, Eirik Rinde, and Stein Rokkan ... from 2005 to 2008, and was re-elected for the term 2009 to 2012. [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Harvard University
Harvard University is a private Ivy League research university in Cambridge, Massachusetts. Founded in 1636 as Harvard College and named for its first benefactor, the Puritan clergyman John Harvard, it is the oldest institution of higher learning in the United States and one of the most prestigious and highly ranked universities in the world. The university is composed of ten academic faculties plus Harvard Radcliffe Institute. The Faculty of Arts and Sciences offers study in a wide range of undergraduate and graduate academic disciplines, and other faculties offer only graduate degrees, including professional degrees. Harvard has three main campuses: the Cambridge campus centered on Harvard Yard; an adjoining campus immediately across Charles River in the Allston neighborhood of Boston; and the medical campus in Boston's Longwood Medical Area. Harvard's endowment is valued at $50.9 billion, making it the wealthiest academic institution in the world. Endow ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vote-ratio Monotonicity
Vote-ratio monotonicity (VRM) is a property of apportionment methods, which are methods of allocating seats in a parliament among political parties. The property says that, if the ratio between the number of votes won by party A to the number of votes won by party B increases, then it should NOT happen that party A loses a seat while party B gains a seat. The property was first presented in the context of apportionment of seats in a parliament among federal states. In this context, it is called population monotonicity or population-pair monotonicity. The property says that, if the population of state A increases faster than that of state B, then state A should not lose a seat while state B gains a seat. An apportionment method that fails to satisfy this property is said to have a population paradox. Note the term "population monotonicity" is more commonly used to denote a very different property of resource-allocation rules; see population monotonicity. Therefore, we prefer to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
No Show Paradox
The participation criterion is a voting system criterion. Voting systems that fail the participation criterion are said to exhibit the no show paradox and allow a particularly unusual strategy of tactical voting: abstaining from an election can help a voter's preferred choice win. The criterion has been defined as follows: * In a deterministic framework, the participation criterion says that the addition of a ballot, where candidate A is strictly preferred to candidate B, to an existing tally of votes should not change the winner from candidate A to candidate B. * In a probabilistic framework, the participation criterion says that the addition of a ballot, where each candidate of the set X is strictly preferred to each other candidate, to an existing tally of votes should not reduce the probability that the winner is chosen from the set X. Plurality voting, approval voting, range voting, and the Borda count all satisfy the participation criterion. All Condorcet methods, Bucklin ... [...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 t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Largest Remainder Method
The largest remainder method (also known as Hare–Niemeyer method, Hamilton method or as Vinton's method) is one way of allocating seats proportionally for representative assemblies with party list voting systems. It contrasts with various highest averages methods (also known as divisor methods). Method The ''largest remainder method'' requires the numbers of votes for each party to be divided by a quota representing the number of votes ''required'' for a seat (i.e. usually the total number of votes cast divided by the number of seats, or some similar formula). The result for each party will usually consist of an integer part plus a fractional remainder. Each party is first allocated a number of seats equal to their integer. This will generally leave some remainder seats unallocated: the parties are then ranked on the basis of the fractional remainders, and the parties with the largest remainders are each allocated one additional seat until all the seats have been alloc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
