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This paper relates the notion of fairness in online routing and load balancing to vector majorization as developed by Hardy, Littlewood, and Polya [11]. We define &agr;-supermajorization as an approximate form of vector majorization, and show that this definition generalizes and strengthens the prefix measure proposed by Kleinberg, Rabani and Tardos [14] as well as the popular notion of max-min fairness.The paper revisits the problem of online load-balancing for unrelated 1-∞ machines from the viewpoint of fairness. We prove that a greedy approach is &Ogr;(log n)-supermajorized by all other allocations, where n is the number of jobs. This means the greedy approach is globally &Ogr;(log n)-fair. This may be constrasted with polynomial lower bounds presented in [9] for fair online routing.We also define a machine-centric view of fairness using the related concept of submajorization. We prove that the greedy online algorithm is globally &Ogr;(log m)-balanced, where m is the number of machines.