Efficiency First or Equity First?: Two Principles and Rationality of Social Choice

The Pareto efficiency criterion is often in conflict with the equity criteria as no-envy or as egalitarian-equivalence: An allocation x that is Pareto superior to another allocation y can be inferior to y in consideration of equity. This paper formalizes two differnet principles of social choice under possible conflict of efficiency and equity. The efficiency-first principle requires that we should always select from efficient allocations, and when the efficiency criterion is not at all effective as a guide for selection, i.e., when all the available allocations are efficient or there is no efficient allocation, we should apply an equity criterion to choose desirable allocations. The equity-first principle reverses the lexicographic order of application of the two criteria. We examine rationality of the social choice rules satisfying these two principles. It is shown that the degree of rationality varies widely depending on which principle the social choice rules represent. Several impossibility and possibility results as well as a characterization theorem are obtained.