In a world with a tremendous amount of choices, ranking systems are becoming increasingly important in helping individuals to find information relevant to them. As such, rankings play a crucial role of influencing the attention that is devoted to the various alternatives. This role generates a feedback when the ranking is based on citations, as is the case for PageRank used by Google. The attention bias due to published rankings affects new stated opinions (citations), which will, in turn, affect the next ranking. The purpose of this paper is to investigate this feedback by studying some simple but reasonable dynamics. We show that the long run behavior of the process much depends on the preferences, in particular on their diversity, and on the used ranking method. Two main families of methods are investigated, one based on the notion of 'handicaps', the other one on the notion of peers' rankings.
