A Unique Family of Functions for Fainess Measures

Fairness can have many different interpretations and criteria. Various fairness measures have been proposed across different scientific disciplines. 

Jain’s index [1] is very popular in network resource allocation.

It has been shown in [2] that many fairness measures can be explained via a single family function f_beta(.). For example, the Jain’s index corresponds to the special case of beta = -1.

References
[1] R. K. Jain, D.-M. W. Chiu, and W. R. Hawe, “A Quantitative Measure of Fairness and Discrimination for Resource Allocation in Shared Computer System,” Tech. Rep., 1984.
[2] T. Lan, D. Kao, M. Chiang, A. Sabharwal, and M. Hiang, “An Axiomatic Theory of Fairness in Network Resource Allocation,” in Proc. IEEE INFOCOM, Mar. 2010, pp. 1–9.