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- Dividing candy among children
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- Settling an estate among heirs
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- Dividing common property in a divorce settlement
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- Apportioning seats in the House of Representatives Terminology
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- fair division problem - consists of N players (P1, P2, ¼, PN) and a set of goods (which is called S).
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- fair share - any share that in the opinion of the player receiving it has a value of at least 1/N of the total value of the set of goods S.
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- fair division scheme - any systematic procedure for solving a fair division problem Conditions for Fair Division Schemes to Satisfy
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- The procedure is decisive. (Fair division is guaranteed if the procedure's rules are followed correctly.)
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- The procedure is internal. (No outside arbitration!!)
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- The procedure assumes that the players have no knowledge of one another's value system. (No inside information!!)
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- The procedure assumes the players are rational. Important Note It is possible for a player to misplay the game (e.g., because of greed) and end up with an unfair share. A fair division scheme can only guarantee that it is impossible for the remaining players or bad luck (if you believe in such a thing) to conspire to deny any player his or her fair share. Types of Fair Division Problems
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- Continuous - Dividing a piece of land, a pizza, ice cream, a soda, a LARGE sum of money (in most instances)
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- Discrete - Set S is made up of indivisible objects such as houses, cars, jewelry, hard candy (in most instances)
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- Mixed - The set of goods S contains some continuous and some discrete items. The Methods
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- The Divider Chooser Method
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- The Lone Divider Method
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- The Lone Chooser Method
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- The Last Diminisher Method
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- The Method of Sealed Bids
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- The Method of Markers
Methods for Continuous Problems
Methods for Discrete Problems
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