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An equitable division (EQ) is a division of a heterogeneous object (e.g. a cake), in which the subjective value of all partners is the same, i.e, each partner is equally happy with his/her share. Mathematically, that means that for all partners and : : Where: * is the piece of cake allocated to partner ; * is the value function of partner . It is a real-valued function that, for every piece of cake, returns a number that represents the utility of partner from that piece. Usually these functions are normalized such that and for every . == Comparison to other criteria == * Equitability (EQ) compares values of ''different'' people to ''different'' pieces; * envy-freeness (EF) compares values of ''the same'' person to ''different'' pieces; * Exact division (EX) compares values of ''different'' people to ''the same'' pieces. The following table illustrates the difference. In all examples there are two partners, Alice and Bob. Alice receives the left part and Bob receives the right part. || || || || (Alice and Bob don't agree on the values of the pieces). |- | || || || (Alice and Bob envy each other's share). || |- | || || (Alice enjoys her share more than Bob enjoys his share). || || |- | || || || (Bob envies Alice). || |- | || || || || |} Note that the table has only 6 rows, because 2 combinations are impossible: an EX+EF division must be EQ, and an EX+EQ division must be EF. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「equitable division」の詳細全文を読む スポンサード リンク
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