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House Monotonicity
House monotonicity (also called house-size monotonicity) is a property of apportionment methods and multiwinner voting systems. These are methods for allocating seats in a parliament among federal states (or among political party). The property says that, if the number of seats in the "house" (the parliament) increases, and the method is re-activated, then no state should have less seats than it previously had. A method that fails to satisfy house-monotonicity is said to have the Alabama paradox. 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 (= Hamilton's method). Consider the following instance with three states: When one seat is added to the house, the share of state C decreases from 2 to 1. This occurs because increasing the number of seats increas ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics Of Apportionment
Mathematics of apportionment describes Mathematics, 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 party, 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 Apportionment paradox, 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 detai ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Monotonicity Criterion
The monotonicity criterion is a voting system criterion used to evaluate both single and multiple winner ranked voting systems. A ranked voting system is monotonic if it is neither possible to prevent the election of a candidate by ranking them higher on some of the ballots, nor possible to elect an otherwise unelected candidate by ranking them lower on some of the ballots (while nothing else is altered on any ballot).D R Woodall"Monotonicity and Single-Seat Election Rules" ''Voting matters'', Issue 6, 1996 That is to say, in single winner elections no winner is harmed by up-ranking and no loser is helped by down-ranking. Douglas Woodall called the criterion mono-raise. Raising a candidate on some ballots ''while changing'' the orders of other candidates does ''not'' constitute a failure of monotonicity. E.g., harming candidate by changing some ballots from to would violate the monotonicity criterion, while harming candidate by changing some ballots from to would not. The ... [...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 multiwinner voting methods that 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. There are two kinds of Phragmén rules: rules using approval ballots (that is, multiwinner approval voting), and rules using ranked ballots (that is, multiwinner ranked voting). 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 m ... [...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 state enters the union, and the house size 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 federal states or political parties. The agent ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics Of Apportionment
Mathematics of apportionment describes Mathematics, 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 party, 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 Apportionment paradox, 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 detai ... [...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 2006–08. 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 representati ... [...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 applied mathematician, economist, operations research analyst and political scientist. As a Polish-American, educated in the United States, he lived and worked primarily in the United States and 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, Lu ... [...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 th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Multiwinner Voting
Multiwinner voting, also called multiple-winner elections or committee voting or committee elections, is an electoral system in which multiple candidates are elected. The number of elected candidates is usually fixed in advance. For example, it can be the number of seats in a country's parliament, or the required number of members in a committee. There are many scenarios in which multiwinner voting is useful. They can be broadly classified into three classes, based on the main objective in electing the committee: # Excellence. Here, each voter is an expert, and each vote expresses his/her opinion about which candidate/s is "better" for a certain task. The goal is to find the "best" candidates. An example application is shortlisting: selecting, from a list of candidate employees, a small set of finalists, who will proceed to the final stage of evaluation (e.g. using an interview). Here, each candidate is evaluated independently of the other candidates. If two candidates are simila ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Alabama
(We dare defend our rights) , anthem = "Alabama (state song), Alabama" , image_map = Alabama in United States.svg , seat = Montgomery, Alabama, Montgomery , LargestCity = Huntsville, Alabama, Huntsville , LargestCounty = Baldwin County, Alabama, Baldwin County , LargestMetro = Birmingham metropolitan area, Alabama, Greater Birmingham , area_total_km2 = 135,765 , area_total_sq_mi = 52,419 , area_land_km2 = 131,426 , area_land_sq_mi = 50,744 , area_water_km2 = 4,338 , area_water_sq_mi = 1,675 , area_water_percent = 3.2 , area_rank = 30th , length_km = 531 , length_mi = 330 , width_km = 305 , width_mi = 190 , Latitude = 30°11' N to 35° N , Longitude = 84°53' W to 88°28' W , elevation_m = 150 , elevation_ft = 500 , elevation_max_m = 735.5 , elevation_max_ft = 2,413 , elevation_max_point = Mount Cheaha , elevation_min_m = 0 , elevation_min_ft = 0 , elevation_min_point = Gulf of Mexico , OfficialLang = English language, English , Languages = * English ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
