You have N people and wish to divide a resource between them so that everyone is content that no-one has more than they. How do you do that?

With two people, you can try "you cut, I'll choose". That works if the person who cut believes they did so exactly, otherwise they will envy the other person for taking the larger piece. In this case, we have to assume that the cutter can cut as perfectly as they need.

	1 What algorithm can we use for N people?
	1 What assumptions underlie the algorithm?

See also http://mathworld.wolfram.com/CakeCutting.html

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A good reference is ''Fair Division'' by Steven J. Brams and Alan D. Taylor (ISBN 0-521-55390-3 [hb] or ISBN 0-521-55644-9 [pb]). The authors also have a patent (#5983205) on the "Adjusted Winner" and "Proportional Allocation" schemes. -- ErykVershen
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CategoryAlgorithm