The Measurement of Intellectual Influence

We examine the problem of measuring influence based on the information contained in the data on the communications between scholarly publications, judicial decisions, patents, web pages, and other entities. The measurement of influence is useful to address several empirical questions such as reputation, prestige, aspects of the diffusion of knowledge, the markets for scientists and scientific publications, the dynamics of innovation, ranking algorithms of search engines in the World Wide Web, and others. In this paper we ask why any given methodology is reasonable and informative applying the axiomatic method. We find that a unique ranking method can be characterized by means of five axioms: anonymity, invariance to citation intensity, weak homogeneity, weak consistency, and invariance to splitting of journals. This method is easily implementable and turns out to be different from those regularly used in social and natural sciences, arts and humanities, and computer science.Intellectual Influence, Citations, Ranking Methods, Consistency.