Fairness in selecting multiple objects under diversity requirements

Our concern is with the quantification of the concept of fairness when we are selecting a subset of n elements from a set of elements T. We are particularly interested in the situation in which the set of T elements is viewed as consisting of q distinct categories, and a prescribed number of the n chosen objects must be selected from each of the q categories. We suggest a measure of fairness and investigate its performance under a number of different diversity requirements on the selection from the different categories.