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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'' of the cake. This is in contrast to proportional division procedures, which give each partner ''at least'' of the cake, but may give more to some of the partners. When , 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 , the division is neither exact nor envy-free, since each partner only values his own piece as , 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 involve partners who want to divide a cake such that each of them gets exactly one half. 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「Austin moving-knife procedures」の詳細全文を読む スポンサード リンク
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