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The surplus procedure (SP) is a fair division protocol for dividing goods in a way that achieves proportional equitability. It can be generalized to more than 2=two people and is strategyproof. For three or more people it is not always possible to achieve a division that is both equitable and envy-free.
Criticisms of the paper
There have been a few criticisms of aspects of the paper. In effect the paper should cite a weaker form of Pareto optimality and suppose the measures are always strictly positive.
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