In this paper authors study the effect of recommender systems (CF) on sale diversity. Motivated by "Lorenz curve", They use Gini coefficient (G) for measuring the bias of a recommender system. First, they used the so-called "urn-model" to explore the biases analytically. In this setting a stochastic function ( e.g., sigmoid function) gives the probability that an item being recommended by the system at each point of time, based on the current marker share. THE MODEL SUGGESTS the average increase of concentration bias for different settings of the model.
C. Draude, G. Klumbyte, and P. Treusch. Proceedings of International Workshop on Bias in Information, Algorithms, and Systems co-located with 13th International Conference on Transforming Digital Worlds (iConference 2018), CEUR Workshop Proceedings, (2018)