Klein, Wright, and Wieczorek (2020), hereafter KWW, presents a simple novel measure of uncertainty for an estimated ranking by constructing a joint confidence region (INDI) using overlapping intervals of ”individual” population parameters θ_k for the (unknown) true ranking of K populations, k = 1, 2, ..., K. In this paper, we consider the same topic but construct a new joint confidence region (DIFF) using intervals for “differences” of population parameters of the type θ_k − θ_k'  where k ≠ k' . With this new approach and for each k and k', we ask which such intervals overlap the number 0. We derive properties of both approaches and prove a condition under which the new joint confidence region (DIFF) shows no greater uncertainty than the uncertainty of the INDI joint confidence region.