On the influence of a ranking system

Ranking systems are becoming increasingly important in many areas, in the Web environment and academic life for instance. In a world with a tremendous amount of choices, rankings play the crucial role of influencing which objects are tasted or selected. This selection generates a feedback when the ranking is based on citations, as is the case for the widely used invariant method. The selection affects new stated opinions (citations), which will, in turn, affect the next ranking. The purpose of this paper is to investigate this feedback in the context of journals by studying some simple but reasonable dynamics. Our main interest is in the long run behavior of the process and how it depends on the preferences, in particular on their diversity. We show that multiple long run behaviors may arise due to strong self-reinforcing mechanisms at work with the invariant method. These effects are not present in a simple search model in which individuals are influenced by the cites of the papers they first read.