|
Coherence (fairness)
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] |
Fair Division
Fair division is the problem in game theory of dividing a set of resources among several people who have an entitlement to them so that each person receives their due share. That problem arises in various real-world settings such as division of inheritance, partnership dissolutions, divorce settlements, electronic frequency allocation, airport traffic management, and exploitation of Earth observation satellites. It is an active research area in mathematics, economics (especially social choice theory), dispute resolution, etc. The central tenet of fair division is that such a division should be performed by the players themselves, maybe using a mediator but certainly not an arbiter as only the players really know how they value the goods. The archetypal fair division algorithm is divide and choose. It demonstrates that two agents with different tastes can divide a cake such that each of them believes that he got the best piece. The research in fair division can be seen as an exten ... [...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] |
United Network For Organ Sharing
The United Network for Organ Sharing (UNOS) is a non-profit, scientific and educational organization that administers the only Organ Procurement and Transplantation Network (OPTN) in the United States, established () by the U.S. Congress in 1984 by Gene A. Pierce, founder of United Network for Organ Sharing. Located in Richmond, Virginia, the organization's headquarters are situated near the intersection of Interstate 95 and Interstate 64 in the Virginia BioTechnology Research Park. Activities United Network for Organ Sharing is involved in many aspects of the organ transplant and donation process: * Managing the national transplant waiting list, matching donors to recipients. * Maintaining the database that contains all organ transplant data for every transplant event that occurs in the U.S. * Bringing together members to develop policies that make the best use of the limited supply of organs and give all patients a fair chance at receiving the organ they need, regardless of age, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Organ Transplantation
Organ transplantation is a medical procedure in which an organ (anatomy), organ is removed from one body and placed in the body of a recipient, to replace a damaged or missing organ. The donor and recipient may be at the same location, or organs may be transported from a Organ donation, donor site to another location. Organ (anatomy), Organs and/or Tissue (biology), tissues that are transplanted within the same person's body are called autografts. Transplants that are recently performed between two subjects of the same species are called allografts. Allografts can either be from a living or cadaveric source. Organs that have been successfully transplanted include the Heart transplantation, heart, Kidney transplantation, kidneys, Liver transplantation, liver, Lung transplantation, lungs, Pancreas transplantation, pancreas, Intestinal transplant, intestine, Thymus transplantation, thymus and uterus transplantation, uterus. Tissues include Bone grafting, bones, tendons (both referr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Contested Garment Rule
The contested garment (CG) rule, also called concede-and-divide, is a division rule for solving problems of conflicting claims (also called "bankruptcy problems"). The idea is that, if one claimant's claim is less than 100% of the estate to divide, then he effectively ''concedes'' the unclaimed estate to the other claimant. Therefore, we first give to each claimant, the amount conceded to him/her by the other claimant. The remaining amount is then divided equally among the two claimants. The CG rule first appeared in the Mishnah, exemplified by a case of conflict over a garment, hence the name. In the Mishnah, it was described only for two-people problems. But in 1985, Robert Aumann and Michael Maschler have proved that, in every bankruptcy problem, there is a unique division that is consistent with the CG rule for each pair of claimants. They call the rule, that selects this unique division, the CG-consistent rule (it is also called the Talmud rule). Problem description There i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Proportional Rule (bankruptcy)
The proportional rule is a division rule for solving bankruptcy problems. According to this rule, each claimant should receive an amount proportional to their claim. In the context of taxation, it corresponds to a proportional tax. Formal definition There is a certain amount of money to divide, denoted by ''E'' (=Estate or Endowment). There are ''n'' ''claimants''. Each claimant ''i'' has a ''claim'' denoted by ''c_i''. Usually, \sum_^n c_i > E, that is, the estate is insufficient to satisfy all the claims. The proportional rule says that each claimant ''i'' should receive r \cdot c_i, where ''r'' is a constant chosen such that \sum_^n r\cdot c_i = E. In other words, each agent gets \frac\cdot E. Examples Examples with two claimants: * PROP(60,90; 100) = (40,60). That is: if the estate is worth 100 and the claims are 60 and 90, then r = 2/3, so the first claimant gets 40 and the second claimant gets 60. * PROP(50,100; 100) = (33.333,66.667), and similarly PROP(40,80; 100) = ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Webster Method
Webster may refer to: People *Webster (surname), including a list of people with the surname *Webster (given name), including a list of people with the given name Places Canada *Webster, Alberta *Webster's Falls, Hamilton, Ontario United States *Webster, California, in Yolo County *Webster, San Diego, California, a neighborhood *Webster, Florida *Webster, Illinois *Webster, Indiana *Webster, Iowa, in Keokuk County *Webster, Madison County, Iowa *Webster City, Iowa, in Hamilton County *Webster, Kentucky *Webster Parish, Louisiana *Sabattus, Maine, formally Webster, Maine *Webster Plantation, Maine *Webster, Massachusetts, a New England town **Webster (CDP), Massachusetts, the main village in the town * Webster, Michigan, an unincorporated community *Webster, Minnesota *Webster, Nebraska *Webster, New Hampshire *Webster, New York, a town **Webster (village), New York, in the town of Webster *Webster, North Carolina *Webster, North Dakota *Webster, Ohio, in Darke County *Webster, P ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vote-ratio Monotonicity
Vote-ratio monotonicity (VRM) is a property of apportionment methods, which are methods of allocating seats in a parliament among political parties. The property says that, if the ratio between the number of votes won by party A to the number of votes won by party B increases, then it should NOT happen that party A loses a seat while party B gains a seat. The property was first presented in the context of apportionment of seats in a parliament among federal states. In this context, it is called population monotonicity or population-pair monotonicity. The property says that, if the population of state A increases faster than that of state B, then state A should not lose a seat while state B gains a seat. An apportionment method that fails to satisfy this property is said to have a population paradox. Note the term "population monotonicity" is more commonly used to denote a very different property of resource-allocation rules; see population monotonicity. Therefore, we prefer to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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] |
Anonymity (social Choice)
In social choice theory, Anonymity is a basic requirement of a social choice rule. It says that the rule does not discriminate apriori between different voters. In other words, the rule returns the same outcome (whatever this outcome may be) if the vector of votes is permuted arbitrarily.{{Cite book, last=Felix Brandt, chapter-url=https://books.google.com/books?id=0qY8DwAAQBAJ&dq=multiwinner++voting+a+new+challenge&pg=PA27, title=Trends in Computational Social Choice, date=2017-10-26, publisher=Lulu.com, isbn=978-1-326-91209-3, editor-last=Endriss, editor-first=Ulle, language=en, chapter=Roling the Dice: Recent Results in Probabilistic Social Choice Anonymous rules Most voting rules are anonymous by design. For example, plurality voting is anonymous, since only counts the number of votes received by each candidates, regardless of who cast these votes. Similarly, the utilitarian rule and egalitarian rule are both anonymous, since the only consider the set of utilities, regardless ... [...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] |
