Fair Division

Fair division analyzes how to divide divisible or indivisible goods among two or more players in order to satisfy certain criteria of fairness. The problem of fair division goes back at least to the Bible. Abraham and Lot had to decide who would get Canaan and who Jordan; Solomon had to decide which of two women was the mother of a disputed baby. What was a fair solution in each case? This entry first discusses the criteria of fair division, followed by specific procedures and some applications in political science and everyday life.

The oldest known procedure for dividing a single divisible good, such as a cake or land, between two players is “I cut, you choose,” or divide-and-choose. The same procedure can be used if there are multiple indivisible goods: The divider partitions the items into two piles, and the chooser selects one pile. If the divider has no knowledge of the chooser's preferences, the divider should divide the items 50/50. That way, whichever pile the chooser selects, the divider is assured of getting 50%. The chooser, by contrast, will get more than 50% if she thinks that the two piles are unequal and selects the one that she thinks is more valuable. If, however, the divider knows the chooser's preferences, he can exploit this information to make one pile slightly more valuable than 50% for the chooser, so the chooser will select that, keeping for the divider the pile he values more (assuming that he values items different from what the chooser values). It is important to note here that fairness does not refer to an “objective” criterion of equality but agreement according to one's subjective preferences.