Procedural interpretation and associated consistency for the egalitarian Shapley values

An α-egalitarian Shapley value is the convex combination of the Shapley value and the equal division value in terms of a social selfish coefficient α∈[0,1] reconciling the two polar opinions of marginalism and egalitarianism. We present a procedural interpretation for every egalitarian Shapley value. We also characterize each α-egalitarian Shapley value by associated consistency, continuity and the α-dummy player property. The Jordan normal form approach is applied as the pivotal technique to accomplish the most important proof.