We generalize the refinement ordering for well calibrated probability forecasters to the case were the debtors under consideration are not necessarily identical. This ordering is consistent with many well known skill scores used in practice. We also add an illustration using default predictions...

The paper explores the relationship between various orderings among probability forecasts that have been suggested in the literature. It is shown that well calibrated forecasters are in general not comparable according to the domination ordering suggested by Vardeman and Meeden (1983), that the...