Scitovsky Reversals and the Double Criteria
Granted that the strong Kaldor criteria is lacking in its ability to compare allocations, problems also arise with the weak Kaldor criteria for comparisons of welfare under different types of change. The famous Scitovsky reversal paradox, first identified by Tibor Scitovsky, uncovered an important drawback of the weak Kaldor criterion. Suppose we are in a production economy and suddenly the production conditions change so that, as in Figure below, we move from PPFD to PPFF. In order to judge whether this technological change improved or worsened welfare, we should attempt to compare the corresponding Pareto-optimal points D and F represented by the tangencies of CICD with PPFD and CICF with PPFF.
However, notice that CICD and CICF intersect each other. Specifically, recall that intersecting CICs imply Pareto-improvements: note that F is Pareto-superior to E and E, of course, represents the same level of “aggregate” utility as D as it lies on CICD. Thus, from D, it is possible to hypothetically redistribute goods and outputs so that we obtain a Pareto-improvement. Thus, according to the weak Kaldor criteria, situation F is superior to D. However, by a reverse argument, we can note that moving from PPFF to PPFD, we can see that D is Pareto-superior to G and G yields the same level of “aggregate” utility as F as it lies on CICF. Thus, by the weak Kaldor criteria again, situation D is ranked higher than situation F. Thus, there is a “reversal” of rankings between D and F by the weak Kaldor criteria as F is better than D and D is better than F.
Scitovsky (1941) suggested that the resolution to this reversal paradox might be combining both the Hicks and Kaldor criteria. Notice that the movement from D to F fulfills the Kaldor criteria but not the Hicksian one as, from D, it is possible to undertake a hypothetical lump-sum redistribution within PPFD that achieves a Pareto-improvement over F (e.g. a point slightly above G in PPFD is a Pareto-improvement over G and thus over F). Thus, the Scitovky double criteria states that an allocation is preferred to another if it fulfills both the Kaldor and Hicks criteria. This would, it seems, eliminate Scitovsky reversals as that depicted in Figure above. Thus when the two utility possibility curves are non-intersecting and change involves movement from a position on a lower utility possibility curve to a position on a higher utility possibility curve, the change raises social welfare on the basis of the Kaldor-Hicks-Scitovsky criterion. This occurs only when a change brings about increase in aggregate output or real income.