 Social procedures are as old as the world. Divide and choose (also known as “I cut, you choose”) is a procedure for two-person fair division of some desirable or undesirable heterogeneous good. One person divides the good into what she believes to be equal shares, and the other person chooses. If the two participants have different value judgements on parts of the goods, it is possible that both participants feel that they received more than 50 percent of the goods. Indeed, let \(X\) be a set representing the good to be divided. A valuation function \(V\) for \(X\) is a function from \({{\cal P}}(X)\) to \([0,1]\) with the properties that \(V(\emptyset) = 0\), \(V(X) = 1\), and for all subsets \(A\), \(B\), it holds that \(A \subseteq B \subseteq X\) implies \(V(A) \leq V(B)\) (for explanation of notation, see supplement on  basic set theory).  Suppose \(V_m\) and \(V_y\) are functions for my and your valuation of the contents of \(X\). If \(V_m\) and \(V_y\) are different, this means that you and I value some items in \(X\) differently. It follows, as was already observed by Steinhaus in 1948, that there exists a division that gives both parties more than their due part; “this fact disproves the common opinion that differences in estimation make fair division difficult” (Steinhaus 1948).