We suggest a revision to the PageRank random surfer model that considers the
influence of a population of random surfers on the PageRank vector. In the
revised model, each member
of the population has its own teleportation parameter chosen from a
probability distribution, and consequently, the ranking vector is random.
We propose three algorithms for computing the statistics of the random ranking
vector based respectively on
(i) random sampling, (ii) paths along the links of the underlying graph, and (iii) quadrature formulas.
We find that the expectation of the random ranking vector produces similar
rankings to its deterministic analogue, but the standard deviation
gives uncorrelated information (under a Kendall-tau metric) with myriad
potential uses. We examine applications of this model to web spam.