Consider the thought process behind the purchase of a product, where a potential buyer leverages several inputs (location, social milieu, advertising in media, product literature, social trends as marked by Twitter etc.) and converts this high-dimensional space into a single input: priority. Yet priority is nothing but ranking of an object and therefore serves as a coarse-grained (low-dimensional) metric of myriad processes occurring in socio-economic systems. Indeed, one might say the world is addicted to ranking: everything from the sales of products to the careers of scientists to the performance of countries in international trade, are driven by measured or perceived differences between them. Yet, little scientific attention is devoted to the dynamical and generative processes that underlie the ranking process. This is understandable as ostensibly the sheer diversity of the systems under consideration make it a rather daunting task to seek any systemic or universal properties.

Having said that, in this talk I’ll attempt to do just that. I’ll begin by introducing the concept of ‘’ranking stability” as it relates to eigenvalue algorithms—such as Google’s PageRank—and then move on to the empirical examination of a plethora of temporal datasets that enables us to develop a “phenomenological theory” capturing the dynamics of ranking. Implications and future directions will also be explored.