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)\u3e=0 of the whole sum (so that w(1)+...+w(n)=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-(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