Austin moving-knife procedure

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 ${\displaystyle 1/n}$ of the cake. This is in contrast to proportional division procedures, which give each partner at least ${\displaystyle 1/n}$ of the cake, but may give more to some of the partners.

When ${\displaystyle n=2}$, 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).

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