|
New States Paradox
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 fe ... [...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 (fair division), entitlement to them so that each person receives their due share. The central tenet of fair division is that such a division should be performed by the players themselves, without the need for external arbitration, as only the players themselves really know how they value the goods. There are many different kinds of fair division problems, depending on the nature of goods to divide, the criteria for fairness, the nature of the players and their preferences, and other criteria for evaluating the quality of the division. The archetypal fair division algorithm is divide and choose. The research in fair division can be seen as an extension of this procedure to various more complex settings. Description In game theory, fair division is the problem of dividing a set of resources among several people who have an Entitlement (fair division), entitlem ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Anonymity (social Choice)
In economics and social choice, a function satisfies anonymity, neutrality, or symmetry if the rule does not discriminate between different participants ahead of time. For example, in an election, a voter-anonymous function is one where it does not matter who casts which vote, i.e. all voters' ballots are equal ahead of time. Formally, this is defined by saying the rule returns the same outcome (whatever this may be) if the votes are "relabeled" arbitrarily, e.g. by swapping votes #1 and #2. Similarly, outcome-neutrality says the rule does not discriminate between different outcomes (e.g. candidates) ahead of time. Formally, if the labels assigned to each outcome are permuted arbitrarily, the returned result is permuted in the same way. Some authors reserve the term anonymity for agent symmetry and neutrality for outcome-symmetry, but this pattern is not perfectly consistent.{{Rp, 75 Examples Most voting rules are anonymous and neutral by design. For example, plurality voting i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Apportionment Paradox
An apportionment paradox is a situation where an apportionment—a rule for dividing discrete objects according to some proportional relationship—produces results that violate notions of common sense or fairness. 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. Several paradoxes related to apportionment and fair division have been identified. In some cases, simple adjustments to an apportionment methodology can resolve observed paradoxes. However, as shown by the Balinski–Young theorem, it is not always possible to provide a perfectly fair resolution that satisfies all competing fairness criteria. History An example of the apportionment paradox known as "the Alabama paradox" was discovered in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
United Network For Organ Sharing
The United Network for Organ Sharing (UNOS) is a Nonprofit organization, 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 in Virginia, Interstate 95 and Interstate 64 in Virginia, 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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Organ Transplantation
Organ transplantation is a medical procedure in which an 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 donor site to another location. Organs and/or 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, kidneys, liver, lungs, pancreas, intestine, thymus and uterus. Tissues include bones, tendons (both referred to as musculoskeletal grafts), corneae, skin, heart valves, nerves and veins. Worldwide, the kidneys are the most commonly transplanted organs, followed by the liver and then the heart. J. Hartwell Harrison performed the first organ removal for transplant ... [...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, Kansas * 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 * Webs ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vote-ratio Monotonicity
Vote-ratio, weight-ratio, or population-ratio monotonicity is a property of some apportionment methods. It says that if the entitlement for A grows at a faster rate than B (i.e. A grows proportionally more than B), A should not lose a seat to B. More formally, if the ratio of votes or populations A / B increases, then A should not lose a seat while B gains a seat. An apportionment method violating this rule may encounter population paradoxes. A particularly severe variant, where voting ''for'' a party causes it to ''lose'' seats, is called a no-show paradox. The largest remainders method exhibits both population and no-show paradoxes. Population-pair monotonicity Pairwise monotonicity says that if the ''ratio'' between the entitlements of two states i, j increases, then state j should not gain seats at the expense of state i. In other words, a shrinking state should not "steal" a seat from a growing state. Some earlier apportionment rules, such as Hamilton's method, do not s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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] |
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] |
Concordance (apportionment)
Static population-monotonicity, also called concordance, says that a party with more votes should not receive a smaller apportionment The legal term apportionment (; Mediaeval Latin: , derived from , 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 ... of seats. Failures of concordance are often called electoral inversions or majority reversals. References {{Economics-stub Apportionment (politics) ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
