|
Brams–Taylor Procedure
The Brams–Taylor procedure (BTP) is a procedure for envy-free cake-cutting. It explicated the first finite procedure to produce an envy-free division of a cake among any positive integer number of players. History In 1988, prior to the discovery of the BTP, Sol Garfunkel contended that the problem solved by the theorem, namely n-person envy-free cake-cutting, was among the most important problems in 20th century mathematics. The BTP was discovered by Steven Brams and Alan D. Taylor. It was first published in the January 1995 issue of American Mathematical Monthly, and later in 1996 in the authors' book. Brams and Taylor hold a joint US patent from 1999 related to the BTP. Description The BTP divides the cake part-by-part. A typical intermediate state of the BTP is as follows: * A part of the cake, say X, is divided in an envy-free way among all partners. * The rest of the cake, say Y, remains undivided, but - * One partner, say Alice, has an Irrevocable Advantage (IA) ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Envy-free Cake-cutting
An envy-free cake-cutting is a kind of fair cake-cutting. It is a division of a heterogeneous resource ("cake") that satisfies the envy-free criterion, namely, that every partner feels that their allocated share is at least as good as any other share, according to their own subjective valuation. When there are only two partners, the problem is easy and was solved in antiquity by the divide and choose protocol. When there are three or more partners, the problem becomes much more challenging. Two major variants of the problem have been studied: * Connected pieces, e.g. if the cake is a 1-dimensional interval then each partner must receive a single sub-interval. If there are n partners, only n-1 cuts are needed. * General pieces, e.g. if the cake is a 1-dimensional interval then each partner can receive a union of disjoint sub-intervals. Short history Modern research into the fair cake-cutting problem started in the 1940s. The first fairness criterion studied was proportional divi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sol Garfunkel
Solomon "Sol" Garfunkel born 1943, in Brooklyn, New York, is an American mathematician who has dedicated his career to mathematics education. Since 1980, he has served as the executive director of the award-winning non-profit organization " Consortium for Mathematics and Its Applications", working with teachers, students, and business people to create learning environments where mathematics is used to investigate and model real issues in our world. Garfunkel is best known for hosting the 1987 PBS series titled "For All Practical Purposes: An Introduction to Contemporary Mathematics", followed by the 1991 series, "Algebra: In Simplest Terms", both often used in classrooms. Early life At the age of 24, Garfunkel received his PhD in Mathematical Logic from the University of Wisconsin–Madison. While in attendance he worked with Howard Jerome Keisler, Michael D. Morley, and Stephen Kleene. Garfunkel then worked at Cornell University and the University of Connecticut at Storrs. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Steven Brams
Steven J. Brams (born November 28, 1940 in Concord, New Hampshire) is an American game theory, game theorist and political scientist at the New York University Department of Politics. Brams is best known for using the techniques of game theory, public choice theory, and social choice theory to analyze voting systems and fair division. He is one of the independent discoverers of approval voting, as well as extensions of approval voting to multiple-winner elections to give proportional representation of different interests. Brams was a co-discoverer, with Alan D. Taylor, Alan Taylor, of the first envy-free cake-cutting solution for ''n'' people. Previous to the Brams-Taylor procedure, the cake-cutting problem had been one of the most important open problems in contemporary mathematics. He is co-inventor with Taylor of the fair-division procedure, adjusted winner, which was patented by New York University in 1999 (# 5,983,205). Adjusted winner has been licensed to a Boston law firm, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Alan D
Alan may refer to: People *Alan (surname), an English and Turkish surname *Alan (given name), an English given name **List of people with given name Alan ''Following are people commonly referred to solely by "Alan" or by a homonymous name.'' *Alan (Chinese singer) (born 1987), female Chinese singer of Tibetan ethnicity, active in both China and Japan *Alan (Mexican singer) (born 1973), Mexican singer and actor * Alan (wrestler) (born 1975), a.k.a. Gato Eveready, who wrestles in Asistencia Asesoría y Administración *Alan (footballer, born 1979) (Alan Osório da Costa Silva), Brazilian footballer *Alan (footballer, born 1998) (Alan Cardoso de Andrade), Brazilian footballer *Alan I, King of Brittany (died 907), "the Great" *Alan II, Duke of Brittany (c. 900–952) *Alan III, Duke of Brittany(997–1040) *Alan IV, Duke of Brittany (c. 1063–1119), a.k.a. Alan Fergant ("the Younger" in Breton language) *Alan of Tewkesbury, 12th century abbott *Alan of Lynn (c. 1348–1423), 15th cen ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
American Mathematical Monthly
''The American Mathematical Monthly'' is a mathematical journal founded by Benjamin Finkel in 1894. It is published ten times each year by Taylor & Francis for the Mathematical Association of America. The ''American Mathematical Monthly'' is an expository journal intended for a wide audience of mathematicians, from undergraduate students to research professionals. Articles are chosen on the basis of their broad interest and reviewed and edited for quality of exposition as well as content. In this the ''American Mathematical Monthly'' fulfills a different role from that of typical mathematical research journals. The ''American Mathematical Monthly'' is the most widely read mathematics journal in the world according to records on JSTOR. Tables of contents with article abstracts from 1997–2010 are availablonline The MAA gives the Lester R. Ford Awards annually to "authors of articles of expository excellence" published in the ''American Mathematical Monthly''. Editors *2022– ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
US Patent
Under United States law, a patent is a right granted to the inventor of a (1) process, machine, article of manufacture, or composition of matter, (2) that is new, useful, and non-obvious. A patent is the right to exclude others, for a limited time (usually, 20 years) from profiting of a patented technology without the consent of the patent-holder. Specifically, it is the right to exclude others from: making, using, selling, offering for sale, importing, inducing others to infringe, applying for an FDA approval, and/or offering a product specially adapted for practice of the patent. United States patent law is codified in Title 35 of the United States Code, and authorized by the U.S. Constitution, in Article One, section 8, clause 8, which states: Patent law is designed to encourage inventors to disclose their new technology to the world by offering the incentive of a limited-time monopoly on the technology. For U.S. utility patents, this limited-time term of patent i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Brams–Taylor–Zwicker Procedure
The Brams–Taylor–Zwicker procedure is a protocol for envy-free cake-cutting An envy-free cake-cutting is a kind of fair cake-cutting. It is a division of a heterogeneous resource ("cake") that satisfies the envy-free criterion, namely, that every partner feels that their allocated share is at least as good as any other sha ... among 4 partners. The procedure uses a variation of Austin's procedure for two partners and general fractions. That procedure allows two partners to divide an entire cake to k pieces, each of which is worth exactly 1/k for both of them. The main procedure works as follows. A. Use Austin's procedure with k=4 and partners #1 and #2. So we have 4 pieces that the first two partners believe to be of exactly identical value of 1/4. B. Partner #3 trims one piece to create a two-way tie for the largest; the partners now choose pieces in reverse order (#4, #3, #2, #1). Either #4 or #3 must take the trimmed piece. This creates an envy-free division for the entir ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Envy-free Cake-cutting
An envy-free cake-cutting is a kind of fair cake-cutting. It is a division of a heterogeneous resource ("cake") that satisfies the envy-free criterion, namely, that every partner feels that their allocated share is at least as good as any other share, according to their own subjective valuation. When there are only two partners, the problem is easy and was solved in antiquity by the divide and choose protocol. When there are three or more partners, the problem becomes much more challenging. Two major variants of the problem have been studied: * Connected pieces, e.g. if the cake is a 1-dimensional interval then each partner must receive a single sub-interval. If there are n partners, only n-1 cuts are needed. * General pieces, e.g. if the cake is a 1-dimensional interval then each partner can receive a union of disjoint sub-intervals. Short history Modern research into the fair cake-cutting problem started in the 1940s. The first fairness criterion studied was proportional divi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Adjusted Winner Procedure
Adjusted Winner (AW) is a procedure for envy-free item allocation. Given two agents and some goods, it returns a partition of the goods between the two agents with the following properties: # Envy-freeness: Each agent believes that his share of the goods is at least as good as the other share; # Equitable division, Equitability: The "relative happiness levels" of both agents from their shares are equal; # Pareto-optimality: no other allocation is better for one agent and at least as good for the other agent; # At most one good has to be shared between the agents. For two agents, Adjusted Winner is the only Pareto optimal and equitable procedure that divides at most a single good. The procedure can be used in divorce settlements and partnership dissolutions, as well as international conflicts. The procedure was designed by Steven Brams and Alan D. Taylor. It was first published in their book on fair division and later in a stand-alone book. The algorithm has been commercialized t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fair Division Protocols
A fair (archaic: faire or fayre) is a gathering of people for a variety of entertainment or commercial activities. Fairs are typically temporary with scheduled times lasting from an afternoon to several weeks. Types Variations of fairs include: * Art fairs, including art exhibitions and arts festivals * County fair (USA) or county show (UK), a public agricultural show exhibiting the equipment, animals, sports and recreation associated with agriculture and animal husbandry. * Festival, an event ordinarily coordinated with a theme e.g. music, art, season, tradition, history, ethnicity, religion, or a national holiday. * Health fair, an event designed for outreach to provide basic preventive medicine and medical screening * Historical reenactments, including Renaissance fairs and Dickens fairs * Horse fair, an event where people buy and sell horses. * Job fair, event in which employers, recruiters, and schools give information to potential employees. * Regional or state fair, an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
