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> 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.
This is not possible. The sum of n times 1/n is already 1, you can't create more cake. So if some get more than 1/n, some will get less than 1/n. Also, shouldn't it be "which gives" instead of "which give"?
I think the sentence should be changed to: This is in contrast to proportional division procedures, which gives each partner at least 1/n of the cake by his/her own subjective valuation, but may give more to some of the partners.