An index of unfairness

Aguiar et al. (2018) propose the Shapley distance as a measure of the extent to which output sharing among the stakeholders of an organization can be considered unfair. It measures the distance between an arbitrary pay profile and the Shapley pay profile under a given technology, the latter profile defining the fair distribution. We provide an axiomatic characterization of the Shapley distance, and show that it can be used to determine the outcome of an underlying bargaining process. We also present applications highlighting how favoritism in income distribution, egalitarianism, and taxation violate the different ideals of justice that define the Shapley value. The analysis has implications that can be tested using real-world data sets.