Reputation Systems and Nonnegativity

We present a voting system that is based on an iterative method that assigns a reputation to n + m items, n objects and in raters, applying some filter to the votes. Each rater evaluates a subset of objects leading to an n x m rating matrix with a given sparsity pattern. From this rating matrix a formula is defined for the reputation of raters and objects. We propose a natural and intuitive nonlinear formula and also provide an iterative algorithm that linearly converges to the unique vector of reputations and this for any rating matrix. In contrast to classical outliers detection, no evaluation is discarded in this method but each one is taken into account with different weights for the reputations of the objects. The complexity of one iteration step is linear in the number of evaluations, making our algorithm efficient for large data set.