Some modern information access tasks such as natural language dialogue tasks are difficult to evaluate, for often there is no such thing as the ground truth: different users may have different opinions about the system's output. A few task designs for dialogue evaluation have been implemented and/or proposed recently, where both the ground truth data and the system's output are represented as a distribution of users' votes over bins on a non-nominal scale. The present study first points out that popular bin-by-bin measures such as Jensen-Shannon divergence and Sum of Squared Errors are clearly not adequate for such tasks, and that cross-bin measures should be used. Through experiments using artificial distributions as well as real ones from a dialogue evaluation task, we demonstrate that two cross-bin measures, namely, the Normalised Match Distance (NMD; a special case of the Earth Mover's Distance) and the Root Symmetric Normalised Order-aware Divergence (RSNOD), are indeed substantially different from the bin-by-bin measures.Furthermore, RSNOD lies between the popular bin-by-bin measures and NMD in terms of how it behaves. We recommend using both of these measures in the aforementioned type of evaluation tasks.