Fair division under interval uncertainty

It is often necessary to divide a certain amount of money between n partici pants, i.e., to assign, to each participant, a certain portion w(i) greater than or equal to 0 of the whole sum (so that w(1) +...+ w(n) = 1). In some situations, from the fairness requirements, we can uniquely determine thes e "weights" w(i). However, in some other situations, general considerations do not allow us to uniquely determine these weights, we only know the inte rvals [w(i)(-),w(i)(+)] of possible fair weights. We show that natural fair ness requirements enable us to choose unique weights from these intervals; as a result, we present an algorithm for fair division under interval uncer tainty.