Measuring Influence in Science: Standing on the Shoulders of Which Giants?

I study the measurement of the influence of scientists based on bibliographic data. I propose a new measure that accounts for indirect influence and allows to compare scientists across different fields of science. By contrast, common measures of influence that"count citations", such as the h-index, are unable to satisfy either of these two properties. I use the axiomatic method in two opposite ways: to highlight the two limitations of citation-counting schemes and their independence, and to carefully justify the assumptions made in the construction of the proposed measure.