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For two people there is a simple solution: the so-called Divide And Choose method. One person divides the resource into what they believe are equal halves, and the other person chooses the "half" they prefer. Thus, the person making the division has an incentive to divide as fairly as possible: for if they do not, they will likely receive an undesirable portion. Fair division is usually taught in lower level college math courses and, surprisingly, can elude math majors. MANY PLAYERS The problem can be extended to three or more people, but the method for finding an optimum solution becomes complicated. One method continues the division to successively smaller "equal" portions. The first person divides the resource into what they believe are equal halves. The second then chooses a half, and each of these two people then divide their portion into thirds. The third person picks two of the resulting portions: one from the first person and one from the second person. If there are four people, each of the first three people divides their portions into fourths, and the process continues. A problem with this approach is that the portions may become reduced to absurdly small sizes. Another method begins with the first person portioning off of the resource (for people). Each following person then examines the portion in turn, removing a part for themselves if they believe the portion to be larger than . The last person to remove part receives the portion. The process continues until the entire resource has been fairly divided. The problem may be modified by requiring the division to be . VARIANTS Some cake-cutting procedures are ''discrete'', whereby players make cuts with a Knife (usually in a sequence of steps). Moving-knife Procedure s, on the other hand, allow continuous movement and can let players call "stop" at any point. A variant of the fair division problem is Chore Division : this is the "dual" to the cake cutting problem in which an undesirable object is to be distributed amongst the players. The canonical example is a set of chores that the players between them must do. Note that "I cut, you choose" works for chore division. Other variants include cakes which contain indivisible items (i.e. nuts or berries on the cake) which must be fairly distributed between players (such pieces are referred to as ''atoms''), or the requirement of having Connected pieces (i.e. only whole pieces and not fragments are allowed). LIMITATIONS The nature of the resource to be divided may affect fair division. The classic example is the tale of proposes to settle a dispute between two women who each claim a child by dividing the child in half. SEE ALSO
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