Scholarly influence

We introduce a new class of measures of scholarly influence, which we term step-based indices. This class includes the prominent h-index, the publication count, and the i10-index. We show that the class of step-based indices is characterized by two axioms, consistency with worse scientists and consistency with better scientists. We also introduce a new index, the junior/senior-index, which is a step-based index that combines the best features of the h-index with those of the i10-index.