Equity Criteria Based on the Dominance Principle and Individual Preferences: Refinements of the Consensus Approach

This paper examines the problem of the indexing dilemma in the context of an ordinal interpersonal comparison of individual situations and proposes a new class of equity criteria based on the dominance principle and individual preferences. First, we show that an interpersonal comparison ordering that satisfies the dominance principle and the monotonicity condition must be a consensus ranking, which requires that individual i's situation with consumption bundle x should be better than j's situation with y whenever all individuals strictly prefer x to y. Second, we propose a new class of equity criteria based on the worst evaluation of each person's situation, which is a class of ordering extensions of interpersonal rankings that respect the consensus condition. In addition, we show its representation theorem and characterize maximin orderings based on our criteria. Third, possibility and impossibility results between the Pareto principle and dominance methods are obtained. Then, we propose a class of median rules as another equity criterion that satisfies the weak Pareto and dominance principles.