Impact measures: What are they?

Abstract

A mathematical, axiomatic definition for the hitherto vague notion of "impact measure" is proposed. For this four conditions are defined on a given set of (rank-frequency) functions (of which the aim is to measure impact). The most typical condition explains how an impact measure should behave on the most productive sources appearing in this function (i.e. in the left side of this rank-frequency function). An overview of "classical" impact measures is provided and it is proved (in most but not in all cases) that they satisfy these conditions for impact measures. This approach can be compared with (but is different from) the approach in econometrics where one defines what concentration is for a (rank-frequency) function. In this way I embed the important notion of impact into the important Lorenz theory.