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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] |
Mathematic
Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many areas of mathematics, which include number theory (the study of numbers), algebra (the study of formulas and related structures), geometry (the study of shapes and spaces that contain them), Mathematical analysis, analysis (the study of continuous changes), and set theory (presently used as a foundation for all mathematics). Mathematics involves the description and manipulation of mathematical object, abstract objects that consist of either abstraction (mathematics), abstractions from nature orin modern mathematicspurely abstract entities that are stipulated to have certain properties, called axioms. Mathematics uses pure reason to proof (mathematics), prove properties of objects, a ''proof'' consisting of a succession of applications of in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Seat Bias
Seat bias is a property describing methods of apportionment. These are methods used to allocate seats in a parliament among federal states or among political parties. A method is ''biased'' if it systematically favors small parties over large parties, or vice versa. There are several mathematical measures of bias, which can disagree slightly, but all measures broadly agree that rules based on Droop's quota or Jefferson's method are strongly biased in favor of large parties, while rules based on Webster's method, Hill's method, or Hare's quota have low levels of bias, with the differences being sufficiently small that different definitions of bias produce different results. Notation There is a positive integer h (=house size), representing the total number of seats to allocate. There is a positive integer n representing the number of parties to which seats should be allocated. There is a vector of fractions (t_1,\ldots,t_n) with \sum_^n t_i = 1, representing ''entitlements' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
D'Hondt Method
The D'Hondt method, also called the Jefferson method or the greatest divisors method, is an apportionment method for allocating seats in parliaments among federal states, or in proportional representation among political parties. It belongs to the class of highest-averages methods. Compared to ideal proportional representation, the D'Hondt method reduces somewhat the political fragmentation for smaller electoral district sizes, where it favors larger political parties over small parties. The method was first described in 1792 by American Secretary of State and later President of the United States Thomas Jefferson. It was re-invented independently in 1878 by Belgian mathematician Victor D'Hondt, which is the reason for its two different names. Motivation Proportional representation systems aim to allocate seats to parties approximately in proportion to the number of votes received. For example, if a party wins one-third of the votes then it should gain about one-third of th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Alabama Paradox
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] |
Largest Remainder Method
Party-list proportional representation Apportionment methods The quota or divide-and-rank methods make up a category of apportionment rules, i.e. algorithms for allocating seats in a legislative body among multiple groups (e.g. parties or federal states). The quota methods begin by calculating an entitlement (basic number of seats) for each party, by dividing their vote totals by an electoral quota (a fixed number of votes needed to win a seat, as a unit). Then, leftover seats, if any are allocated by rounding up the apportionment for some parties. These rules are typically contrasted with the more popular highest averages methods (also called divisor methods). By far the most common quota method are the largest remainders or quota-shift methods, which assign any leftover seats to the "plurality" winners (the parties with the largest remainders, i.e. most leftover votes). When using the Hare quota, this rule is called Hamilton's method, and is the third-most common ap ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Apportionment Paradox
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] |
Integer
An integer is the number zero (0), a positive natural number (1, 2, 3, ...), or the negation of a positive natural number (−1, −2, −3, ...). The negations or additive inverses of the positive natural numbers are referred to as negative integers. The set (mathematics), set of all integers is often denoted by the boldface or blackboard bold The set of natural numbers \mathbb is a subset of \mathbb, which in turn is a subset of the set of all rational numbers \mathbb, itself a subset of the real numbers \mathbb. Like the set of natural numbers, the set of integers \mathbb is Countable set, countably infinite. An integer may be regarded as a real number that can be written without a fraction, fractional component. For example, 21, 4, 0, and −2048 are integers, while 9.75, , 5/4, and Square root of 2, are not. The integers form the smallest Group (mathematics), group and the smallest ring (mathematics), ring containing the natural numbers. In algebraic number theory, the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Webster's Method
''Webster's Dictionary'' is any of the US English language dictionaries edited in the early 19th century by Noah Webster (1758–1843), a US lexicographer, as well as numerous related or unrelated dictionaries that have adopted the Webster's name in his honor. "''Webster's''" has since become a genericized trademark in the United States for US English dictionaries, and is widely used in dictionary titles. Merriam-Webster is the corporate heir to Noah Webster's original works, which are in the public domain. Noah Webster's ''American Dictionary of the English Language'' Noah Webster (1758–1843), the author of the readers and spelling books which dominated the American market at the time, spent decades of research in compiling his dictionaries. His first dictionary, ''A Compendious Dictionary of the English Language'', appeared in 1806. In it, he popularized features which would become a hallmark of American English spelling (''center'' rather than ''centre'', ''honor'' rat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Population Paradox
Vote-ratio, weight-ratio, or population-ratio monotonicity is a property of some apportionment methods. It says that if the entitlement for A grows at a faster rate than B (i.e. A grows proportionally more than B), A should not lose a seat to B. More formally, if the ratio of votes or populations A / B increases, then A should not lose a seat while B gains a seat. An apportionment method violating this rule may encounter population paradoxes. A particularly severe variant, where voting ''for'' a party causes it to ''lose'' seats, is called a no-show paradox. The largest remainders method exhibits both population and no-show paradoxes. Population-pair monotonicity Pairwise monotonicity says that if the ''ratio'' between the entitlements of two states i, j increases, then state j should not gain seats at the expense of state i. In other words, a shrinking state should not "steal" a seat from a growing state. Some earlier apportionment rules, such as Hamilton's method, do not sa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Political Science
Political science is the scientific study of politics. It is a social science dealing with systems of governance and Power (social and political), power, and the analysis of political activities, political philosophy, political thought, political behavior, and associated constitutions and laws. Specialists in the field are political scientists. History Origin Political science is a social science dealing with systems of governance and power, and the analysis of political activities, political institutions, political thought and behavior, and associated constitutions and laws. As a social science, contemporary political science started to take shape in the latter half of the 19th century and began to separate itself from political philosophy and history. Into the late 19th century, it was still uncommon for political science to be considered a distinct field from history. The term "political science" was not always distinguished from political philosophy, and the modern dis ... [...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] |
