A graph-based approach to inequality assessment

• We study inequality measurement on graph theory framework.
• Graph represents the set of connections between income sources for the population.
• Different policies can be implemented to reduce inequality based on the graph structure.
• A multifactorial inequality index is introduced to outline an example.

In a population consisting of heterogeneous types, whose income factors are indicated by nonnegative vectors, policies aggregating different factors can be represented by coalitions in a cooperative game, whose characteristic function is a multi-factor inequality index. When it is not possible to form all coalitions, the feasible ones can be indicated by a graph. We redefine Shapley and Banzhaf values on graph games to deduce some properties involving the degrees of the graph vertices and marginal contributions to overall inequality. An example is finally provided based on a modified multi-factor Atkinson index.