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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Austin moving-knife procedures ： ウィキペディア英語版 Austin moving-knife procedures 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 involve $n=2$ 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 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.