Fair Division Under Interval Uncertainty

It is often necessary to divide a certain amount of money between n participants, i.e., to assign, to each participant, a certain portion w i 0 of the whole sum (so that w1 + : : : + wn = 1). In some situations, from the fairness requirements, we can uniquely determine these "weights" w i . However, in some other situations, general considerations do not allow us to uniquely determine these weights, we only know the intervals [w \Gamma i ; w + i ] of possible fair weights. We show that natural fairness requirements enable us to choose unique weights from these intervals; as a result, we present an algorithm for fair division under interval uncertainty. 1 Introduction to the Problem The general problem of fair division. It is often necessary to divide a certain amount of money between n participants, i.e., to assign, to each participant, a certain portion w i 0 of the whole sum (so that w 1 + : : : + wn = 1). In some situations, we do not know the exact weights. In some situatio..