On evaluating income distributions: Rank dominance, the Suppes-Sen grading principle of justice, and Pareto optimality

3. Summary and conclusions

Rawls's study (1970) suggests the rank-dominance condition for evaluating income distributions. Rank-optimal (non-rank-dominated) income distributions are always Pareto optimal; however, Pareto optimality implies rank optimality if and only if a symmetry condition on the set of attainable income distributions — dubbed equal opportunity — holds. Rank dominance is equivalent to the Suppes-Sen (1970) justice grading principle as applied to attainable income distributions. The set of attainable income distributions is defined so as to recognize possible interdependence between total income and the distribution of income.

We also note that if total income is independent of the distribution of income — as is the case in many equality-of-income studies — then the equal opportunity condition is automatically satisfied; hence the Pareto and rank-dominance criteria are equivalent.