A model of the relationship between the variations of effectiveness and fairness in information retrieval

The requirement that, for fair document retrieval, the documents should be ranked in the order to equally expose authors and organizations has been studied for some years. The fair exposure of a ranking, however, undermines the optimality of the Probability Ranking Principle and as a consequence retrieval effectiveness. It is shown how the variations of fairness and effectiveness can be related by a model. To this end, the paper introduces a fairness measure inspired in Gini’s index of mutability for non-ordinal variables and relates it to a general enough measure of effectiveness, thus modeling the connection between these two dimensions of Information Retrieval. The paper also introduces the measurement of the statistical significance of the fairness measure. An empirical study completes the paper.