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 three axioms, consistency with worse scientists, consistency with better scientists, and full range. We also introduce a new index, the junior/senior-index, which combines the best features of the h-index with those of the i10-index.