Brams–Taylor–Zwicker Procedure

	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]
	Austin Moving-knife Procedure The Austin moving-knife procedures are procedures for equitable division of a cake. They allocate each of ''n'' partners, a piece of the cake which this partner values as ''exactly'' 1/n of the cake. This is in contrast to proportional division procedures, which give each partner ''at least'' 1/n of the cake, but may give more to some of the partners. When n=2, the division generated by Austin's procedure is an exact division and it is also envy-free. Moreover, it is possible to divide the cake to any number ''k'' of pieces which both partners value as exactly 1/''k''. Hence, it is possible to divide the cake between the partners in any fraction (e.g. give 1/3 to Alice and 2/3 to George). When n>2, the division is neither exact nor envy-free, since each partner only values his own piece as 1/n, but may value other pieces differently. The main mathematical tool used by Austin's procedure is the intermediate value theorem (IVT). Two partners and half-cakes The basic procedures ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
picture info	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]