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The Price of Unfairness

Here, measures for unfairness in resource allocation problems are studied. The extremity of such measures should match with an intuitive concept of an unfair allocation. To achieve a computational model for unfairness, various fairness models are extended to cover a related meaning of unfairness as well. In addition to the lexicographic maxmax relation, a model based on exponential utilities is introduced. Furthermore, a new mean, the symmetric Lehmer mean is identified as being able to favour allocations restricted to a subset of users only. Case examples of network flow control problems show feasibility of the proposed unfairness measures, as well as specific differences. Especially the symmetric Lehmer mean appears capable to handle unfairness in a much more nuanced way, while lexicographic maxmax appears as the computationally most convenient and also most intuitive measure. In all cases it can be shown that unfair allocations are not always efficient and that there is a price of unfairness as well.