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Optimal Apportionment
Optimal apportionment is an approach to apportionment that is based on mathematical optimization. In a problem of apportionment, 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 agents have different ''entitlements'', denoted by a vector of fractions t_1,\ldots,t_n with a sum of 1. For example, ''ti'' can be the fraction of votes won by party ''i''. The goal is to find ''allocation'' - a vector a_1,\ldots,a_n with \sum_^n a_i = h. The ideal share for agent ''i'' is his/her ''quota'', defined as q_i := t_i\cdot h. If it is possible to give each agent his/her quota, then the allocation is maximally fair. However, exact fairness is usually unattainable, since the quotas are not integers and the allocations must be integers. There are various approaches to ... [...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 econo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Egalitarian Rule
In social choice and operations research, the egalitarian rule (also called the max-min rule or the Rawlsian rule) is a rule saying that, among all possible alternatives, society should pick the alternative which maximizes the ''minimum utility'' of all individuals in society. It is a formal mathematical representation of the egalitarian philosophy. It also corresponds to John Rawls' principle of maximizing the welfare of the worst-off individual. Definition Let X be a set of possible `states of the world' or `alternatives'. Society wishes to choose a single state from X. For example, in a single-winner election, X may represent the set of candidates; in a resource allocation setting, X may represent all possible allocations. Let I be a finite set, representing a collection of individuals. For each i \in I, let u_i:X\longrightarrow\mathbb be a ''utility function'', describing the amount of happiness an individual ''i'' derives from each possible state. A '' social choice rule' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Optimization
Mathematical optimization (alternatively spelled ''optimisation'') or mathematical programming is the selection of a best element, with regard to some criterion, from some set of available alternatives. It is generally divided into two subfields: discrete optimization and continuous optimization. Optimization problems of sorts arise in all quantitative disciplines from computer science and engineering to operations research and economics, and the development of solution methods has been of interest in mathematics for centuries. In the more general approach, an optimization problem consists of maxima and minima, maximizing or minimizing a Function of a real variable, real function by systematically choosing Argument of a function, input values from within an allowed set and computing the Value (mathematics), value of the function. The generalization of optimization theory and techniques to other formulations constitutes a large area of applied mathematics. More generally, op ... [...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 gove ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Apportionment Method Criteria
The legal term apportionment (french: apportionement; Mediaeval Latin: , derived from la, portio, share), also called delimitation, is in general the distribution or allotment of proper shares, though may have different meanings in different contexts. Apportionment can refer to estate, the amount of compensation received by a worker and in respect of time. This term may be employed roughly and sometimes has no technical meaning; this indicates the distribution of a benefit (''e.g.'' salvage or damages under the Fatal Accidents Act 1846, § 2), or liability (''e.g.'' general average contributions, or tithe rent-charge), or the incidence of a duty (''e.g.'' obligations as to the maintenance of highways). Apportionment in respect of estate Apportionment in respect of estate may result either from the act of the parties or from the operation of law. Apportionment by act of the parties Where a lessee is evicted from, or surrenders or forfeits possession of part of the property le ... [...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] |
Venice Commission
The Venice Commission, officially European Commission for Democracy through Law, is an advisory body of the Council of Europe, composed of independent experts in the field of constitutional law. It was created in 1990 after the fall of the Berlin Wall, at a time of urgent need for constitutional assistance in Central and Eastern Europe. Creation The idea to create a Commission for Democracy through Law as a group of experts in constitutional law was conceived by the then Minister for Community Policies of Italy, Antonio Mario La Pergola. The election of the name was based on the theory of La Pergola that expressed that sustainable democracies could only be built in a constitutional framework based on the rule of law. The formal proposal for the creation of the commission was made by the Italian Minister of Foreign Affairs, Gianni De Michelis, who invited the other Foreign Affairs ministers of the Council of Europe to the ''Conference for the Creation of the European Commiss ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Leximin Order
In mathematics, leximin order is a total preorder on finite-dimensional vectors. A more accurate, but less common term is leximin preorder. The leximin order is particularly important in social choice theory and fair division. Definition A vector x = (''x''1, ..., ''x''''n'') is ''leximin-larger'' than a vector y = (''y''1, ..., ''y''''n'') if one of the following holds: * The smallest element of x is larger than the smallest element of y; * The smallest elements of both vectors are equal, and the second-smallest element of x is larger than the second-smallest element of y; * ... * The ''k'' smallest elements of both vectors are equal, and the (''k''+1)-smallest element of x is larger than the (''k''+1)-smallest element of y. Examples The vector (3,5,3) is leximin-larger than (4,2,4), since the smallest element in the former is 3 and in the latter is 2. The vector (4,2,4) is leximin-larger than (5,3,2), since the smallest elements in both are 2, but the second-smallest elem ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hill's Method
Hill's Pet Nutrition, Inc., marketed simply as "Hill's", is an American pet food company that produces dog and cat foods. The company is a subsidiary of Colgate-Palmolive. History Hill's Pet Nutrition was founded in the spring of 1907 by Burton Hill and started operation as Hill Rendering Works. Hill Rendering Works provided rendering services to Shawnee County, Kansas, and had a contract with Topeka, Kansas, to dispose of dead and lame animals. Hill Rendering Works produced tallow, hides, tankage, meat scraps and farm animal feed including hogs and chicken feed. By the 1930s, the name had changed to Hill Packing Company, which included a milling division, Hill Milling company. At this time the company produced farm animal feed, dog food and horse meat for human consumption, processing 500 head of horse per week. The meat was shipped to markets in Norway, Sweden, Finland and the Netherlands. Much of the horse meat was sold to the east coast as a product called Chopped and Cu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Optimization
Mathematical optimization (alternatively spelled ''optimisation'') or mathematical programming is the selection of a best element, with regard to some criterion, from some set of available alternatives. It is generally divided into two subfields: discrete optimization and continuous optimization. Optimization problems of sorts arise in all quantitative disciplines from computer science and engineering to operations research and economics, and the development of solution methods has been of interest in mathematics for centuries. In the more general approach, an optimization problem consists of maxima and minima, maximizing or minimizing a Function of a real variable, real function by systematically choosing Argument of a function, input values from within an allowed set and computing the Value (mathematics), value of the function. The generalization of optimization theory and techniques to other formulations constitutes a large area of applied mathematics. More generally, op ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Webster/Sainte-Laguë Method
The Webster method, also called the Sainte-Laguë method () or the major fractions method, is a method for allocating seats in a parliament among federal states, or among parties in a party-list proportional representation system. The method was first described in 1832 by the American statesman and senator Daniel Webster. In 1842 the method was adopted for proportional allocation of seats in United States congressional apportionment (Act of 25 June 1842, ch 46, 5 Stat. 491). It was then replaced by Hamilton method and in 1911 the Webster method was reintroduced. The method was again replaced in 1940, this time by the Huntington–Hill method. The same method was independently invented in 1910 by the French mathematician André Sainte-Laguë. It seems that French and European literature was unaware of Webster until after World War II. This is the reason for the double name. Description After all the votes have been tallied, successive quotients are calculated for each p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hamilton's 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 allocated ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
