This new mathematical method for equitable cake sharing actually leads to a version of Zeno’s paradox. The problem is that the cake remnant left after the referee gives the two eaters their respective, equally valued pieces is no more likely than is the cake as a whole to be homogeneously desirable, thus creating the same problem in equitably dividing it as was faced in dividing the whole cake—and so on for all the successive remnants. The problem of infinite regress can be solved, however, by a simple revision to the procedure: After the initial, equitable cut, the referee eats the remaining portion.

Naomi Scheman
Minneapolis, Minn.

From the Nature Index

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