N. Blumm et al. [1]; Image on homepage: iStockphoto/JeffreyRasmussen

Figure 1: Phase diagram of ranking stability in the $A$$B$ plane ($A$: fitness, $B$: noise). For a given ranking system, $A$ is a vector of constants ($Ai$) representing the “fitness” of all items of the ranked list, $B$ is a parameter measuring the ranking’s noise. Every real ranking system is represented by a line corresponding to the experimentally determined value of $B$. In analogy to the classical phases of statistical mechanics, three phases are identified based on the stability of the top-ranked items: rank stable (solid), score stable (liquid), and unstable or volatile (gas). $B$ is the control parameter of the phase transition. The lower panel shows the rank evolution for the top-ranked items of a stable system (diseases diagnosis in Medicare) and a volatile one (page views in Wikipedia).