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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] |
Mathematic
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics with the major subdisciplines of number theory, algebra, geometry, and analysis, respectively. There is no general consensus among mathematicians about a common definition for their academic discipline. Most mathematical activity involves the discovery of properties of abstract objects and the use of pure reason to prove them. These objects consist of either abstractions from nature orin modern mathematicsentities that are stipulated to have certain properties, called axioms. A ''proof'' consists of a succession of applications of deductive rules to already established results. These results include previously proved theorems, axioms, andin case of abstraction from naturesome basic properties that are considered true starting points of ... [...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, and the analysis of political activities, political thought, political behavior, and associated constitutions and laws. Modern political science can generally be divided into the three subdisciplines of comparative politics, international relations, and political theory. Other notable subdisciplines are public policy and administration, domestic politics and government, political economy, and political methodology. Furthermore, political science is related to, and draws upon, the fields of economics, law, sociology, history, philosophy, human geography, political anthropology, and psychology. Political science is methodologically diverse and appropriates many methods originating in psychology, social research, and political philosophy. Approaches include positivism, interpretivism, rational choice theory, behaviouralism, structuralism, pos ... [...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 m ... [...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 governi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Electoral System
An electoral system or voting system is a set of rules that determine how elections and referendums are conducted and how their results are determined. Electoral systems are used in politics to elect governments, while non-political elections may take place in business, non-profit organisations and informal organisations. These rules govern all aspects of the voting process: when elections occur, who is allowed to vote, who can stand as a candidate, how ballots are marked and cast, how the ballots are counted, how votes translate into the election outcome, limits on campaign spending, and other factors that can affect the result. Political electoral systems are defined by constitutions and electoral laws, are typically conducted by election commissions, and can use multiple types of elections for different offices. Some electoral systems elect a single winner to a unique position, such as prime minister, president or governor, while others elect multiple winners, such as me ... [...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] |
Integer
An integer is the number zero (), a positive natural number (, , , etc.) or a negative integer with a minus sign ( −1, −2, −3, etc.). The negative numbers are the additive inverses of the corresponding positive numbers. In the language of mathematics, the set of integers is often denoted by the boldface or blackboard bold \mathbb. 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 natural numbers, \mathbb is countably infinite. An integer may be regarded as a real number that can be written without a fractional component. For example, 21, 4, 0, and −2048 are integers, while 9.75, , and are not. The integers form the smallest group and the smallest ring containing the natural numbers. In algebraic number theory, the integers are sometimes qualified as rational integers to distinguish them from the more general algebraic in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Apportionment 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] |
Apportionment 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] |
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] |
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] |
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] |
