Fairness in the Resources Allocation

Resources allocation helps in setting individuals with demands in order to satisfy their needs. Resources are vectors that each can suit specific individuals. There can be many axioms for fairness measures in resource allocation such as  the axiom of continuity, of homogeneity, of saturation, of partition, and of starvation. It is proved that there is a unique group of fairness measures that satisfy the axioms, that is constructed and then shown to include Atkinson’s index, αfairness, Jain’s index, entropy, and other “decomposable” global measures of fairness as special cases. There are properties of fairness measures that can satisfy the axioms, includ symmetry as well as Schur-concavity. Among the engineering implications is a generalized Jain’s index which tunes the fairness measure resolution, a decomposition of α-fair utility functions into fairness and efficiency components, in addition to an interpretation of “larger α is more fair” and of Rawl’s difference principle. The axiomatic theory is existed in three directions. One is quantifying  continuous-dimension inputs fairness as resource allocations vary along with time. Another is starting with  a vector of resource allocation as well as a vector of user-specific weights, in addition to modifying  partition axiom. A new family of fairness measures is issued for  asymmetric among users. At last, there is a group of four axioms by removing the axiom of homogeneity to capture a fairness-efficiency tradeoff. There are also  illustrative examples in congestion control, routing, power control, and spectrum management problems in communication networks, added to the potential of a fairness evaluation tool explored. Other work of axiomatization in information are compared, computer science, economics, sociology, and political philosophy.