The Shapley distance is introduced as a measure of the extent to which output sharing among the stakeholders of an organization can be considered unfair. In fact, 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. Therefore, this chapter contributes to the literature that studies economic inequality using game theory. In particular, we provide an axiomatic characterization to a notion of unfairness, namely 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 and how unfairness can be further unbundled to determine its origins. The analysis has implications that can be tested using real-world data sets.
Aguiar, Victor and Pongou, Roland and Serrano, Roberto and Tondji, Jean-Baptiste, An Index of Unfairness (March 9, 2019). Aguiar, V. H., Pongou, R., Serrano, R., & Tondji, J. B. (2019). An Index of Unfairness. In Handbook of the Shapley Value (pp. 31-48). CRC Press Taylor and Francis., Available at SSRN: https://ssrn.com/abstract=3350034 or http://dx.doi.org/10.2139/ssrn.3350034
Handbook of the Shapley Value