Non-welfaristic theories of justice: Is "the intersection approach" a solution to the indexing impasse?

Rawls (1971, 1993) suggests that a primary goods index should be the basis for interpersonal comparisons in a theory of justice, but it is well known that in general this approach is not compatible with the Pareto principle. This is the indexing impasse. Sen (1985, 1991) argues that this is partly due to the fact that the approach does not take note of the citizen's orderings of these bundles of valuable objects. He suggests an "intersection approach", which is an incomplete approach to interpersonal comparisons based on judgements that are shared implications of the relevant set of weighting schemes. In this paper, we show that "the intersection approach" does not provide any solution to the indexing impasse. Unless the individuals have identical preferences, "the intersection approach" is incompatible with the Pareto principle.