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House Monotonicity
House monotonicity (also called house-size monotonicity) is a property of apportionment methods. These are methods for allocating seats in a parliament among federal states (or among political parties). The property says that, if the number of seats in the "house" (the parliament) increases, and the method is re-activated, then no state (or party) should have fewer seats than it previously had. A method that fails to satisfy house-monotonicity is said to have the Alabama paradox. In the context of committee elections, house monotonicity is often called committee monotonicity. It says that, if the size of the committee increases, then all the candidate that were previously elected, are still elected. House monotonicity is the special case of ''resource monotonicity'' for the setting in which the resource consists of identical discrete items (the seats). Methods violating house-monotonicity An example of a method violating house-monotonicity is the largest remainder method (= H ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics Of Apportionment
In mathematics and fair division, apportionment problems involve dividing (''apportioning'') a whole number of identical goods fairly across several parties with real-valued entitlements. The original, and best-known, example of an apportionment problem involves distributing seats in a legislature between different federal states or political parties. However, apportionment methods can be applied to other situations as well, including bankruptcy problems, inheritance law (e.g. dividing animals), manpower planning (e.g. demographic quotas), and rounding percentages. Mathematically, an apportionment method is just a method of rounding real numbers to natural numbers. Despite the simplicity of this problem, every method of rounding suffers one or more paradoxes, as proven by the Balinski–Young theorem. The mathematical theory of apportionment identifies what properties can be expected from an apportionment method. The mathematical theory of apportionment was studied as early ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rank-index Methods
In apportionment theory, rank-index methods are a set of apportionment methods that generalize the divisor method. These have also been called Huntington methods, since they generalize an idea by Edward Vermilye Huntington. Input and output Like all apportionment methods, the inputs of any rank-index method are: * A positive integer h representing the total number of items to allocate. It is also called the ''house size.'' * A positive integer n representing the number of ''agents'' to which items should be allocated. For example, these can be federal states or political parties. * A vector of fractions (t_1,\ldots,t_n) with \sum_^n t_i = 1, representing ''entitlements'' - t_i represents the entitlement of agent i, that is, the fraction of items to which i is entitled (out of the total of h). Its output is a vector of integers a_1,\ldots,a_n with \sum_^n a_i = h, called an apportionment of h, where a_i is the number of items allocated to agent ''i''. Iterative procedu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Monotonicity Criterion
Electoral system criteria In social choice, the negative response, perversity, or additional support paradox is a pathological behavior of some voting rules where a candidate loses as a result of having too much support (or wins because of increased opposition). In other words, increasing (decreasing) a candidate's ranking or rating causes that candidate to lose (win), respectively. Electoral systems that do not exhibit perversity are sometimes said to satisfy the monotonicity criterion.D R Woodall"Monotonicity and Single-Seat Election Rules" '' Voting matters'', Issue 6, 1996 Perversity is often described by social choice theorists as an exceptionally severe kind of electoral pathology, as such rules can have "backwards" responses to voters' opinions, where popularity causes defeat while unpopularity leads to a win. Similar rules treat the well-being of some voters as "less than worthless". These issues have led to constitutional prohibitions on such systems as violating ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Resource Monotonicity
Resource monotonicity (RM; aka aggregate monotonicity) is a principle of fair division. It says that, if there are more resources to share, then all agents should be weakly better off; no agent should lose from the increase in resources. The RM principle has been studied in various division problems. Allocating divisible resources Single homogeneous resource, general utilities Suppose society has m units of some homogeneous divisible resource, such as water or flour. The resource should be divided among n agents with different utilities. The utility of agent i is represented by a function u_i; when agent i receives y_i units of resource, he derives from it a utility of u_i(y_i). Society has to decide how to divide the resource among the agents, i.e, to find a vector y_1,\dots,y_n such that: y_1+\cdots+y_n = m. Two classic allocation rules are the egalitarian rule - aiming to equalize the utilities of all agents (equivalently: maximize the minimum utility), and the utilitari ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Phragmen's Voting Rules
Phragmén's voting rules are rules for multiwinner voting. They allow voters to vote for individual candidates rather than parties, but still guarantee proportional representation. They were published by Lars Edvard Phragmén in French and Swedish between 1893 and 1899, and translated to English by Svante Janson in 2016. Background In multiwinner approval voting, each voter can vote for one or more candidates, and the goal is to select a fixed number ''k'' of winners (where ''k'' may be, for example, the number of parliament members). The question is how to determine the set of winners? * The simplest method is ''multiple non-transferable vote'', in which the ''k'' candidates with the largest number of approvals are elected. But this method tends to select ''k'' candidates of the largest party, leaving the smaller parties with no representation at all. * In the 19th century, there was much discussion regarding election systems that could guarantee proportional representatio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Coherency (apportionment)
Coherence, also called uniformity or consistency, is a criterion for evaluating rules for fair division. Coherence requires that the outcome of a fairness rule is fair not only for the overall problem, but also for each sub-problem. Every part of a fair division should be fair. The coherence requirement was first studied in the context of apportionment. In this context, failure to satisfy coherence is called the new states paradox: when a new U.S. state enters the union, and the number of seats in the House of Representatives is enlarged to accommodate the number of seats allocated to this new state, some other unrelated states are affected. Coherence is also relevant to other fair division problems, such as bankruptcy problems. Definition 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 f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics Of Apportionment
In mathematics and fair division, apportionment problems involve dividing (''apportioning'') a whole number of identical goods fairly across several parties with real-valued entitlements. The original, and best-known, example of an apportionment problem involves distributing seats in a legislature between different federal states or political parties. However, apportionment methods can be applied to other situations as well, including bankruptcy problems, inheritance law (e.g. dividing animals), manpower planning (e.g. demographic quotas), and rounding percentages. Mathematically, an apportionment method is just a method of rounding real numbers to natural numbers. Despite the simplicity of this problem, every method of rounding suffers one or more paradoxes, as proven by the Balinski–Young theorem. The mathematical theory of apportionment identifies what properties can be expected from an apportionment method. The mathematical theory of apportionment was studied as early ... [...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 to 2008. 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 represe ... [...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 American and French applied mathematician, economist, operations research analyst and political scientist. Educated in the United States, from 1980 he lived and worked in 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, Ludwik Rajchman. Brought up ... [...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] |
Parliament
In modern politics and history, a parliament is a legislative body of government. Generally, a modern parliament has three functions: Representation (politics), representing the Election#Suffrage, 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 Legal name, official name. Historically, parliaments included various kinds of deliberative, consultative, and judicial assemblies. What is considered to be the first modern parliament, was the Cortes of León, held in the Kingdom of León in 1188. According to the UNESCO, the Decreta of Leon of 1188 is the oldest documentary manifestation ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Alabama
Alabama ( ) is a U.S. state, state in the Southeastern United States, Southeastern and Deep South, Deep Southern regions of the United States. It borders Tennessee to the north, Georgia (U.S. state), Georgia to the east, Florida and the Gulf of Mexico to the south, and Mississippi to the west. Alabama is the List of U.S. states and territories by area, 30th largest by area, and the List of U.S. states and territories by population, 24th-most populous of the List of states and territories of the United States, 50 U.S. states. Alabama is nicknamed the ''Northern flicker, Yellowhammer State'', after the List of U.S. state birds, state bird. Alabama is also known as the "Heart of Dixie" and the "Cotton State". The state has diverse geography, with the north dominated by the mountainous Tennessee Valley and the south by Mobile Bay, a historically significant port. Alabama's capital is Montgomery, Alabama, Montgomery, and its largest city by population and area is Huntsville, Ala ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
