Scitovsky Reversals and the Double Criteria:

Not only  the strong Kaldor criteria  is unable  to compare various allocations consistently, but  also there are problems regarding  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. Scitovsky pointed out that if some situation position, say B,  is shown to be  an  improvement over position A on Kaldor-Hicks criterion, it may be possible that position A is also shown to  be  an  improvement over  B  on  the  basis  of same  criterion.  For  getting consistent  results when  position  B  has  been  revealed  to  be  preferred  to position A on  the basis of a welfare criterion, then position A must  not be preferred to position B on the same criterion.

Suppose  in  a production economy, the production  conditions change due  to change in  technology. This will lead to the shift of the position and as a result the move  from PPF_D  to PPF_F.  In  order to judge  whether  this technological change  improved  or  worsened  welfare, the corresponding Pareto-optimal  points D  and  F  represented by  the  tangencies of CIC_D with PPF_D  and CIC_F  with PPF_F  can be compared.

It  can  be  seen that CIC_D  and CIC_F intersect each other, which  implies that intersecting CIC_s  imply Pareto-improvements. This means that  F  is Pareto- superior to E. Moreover, E represents the same level of "aggregate"  utility as D as  they are on the same CIC_D.  Thus, from D, it is possible  to hypothetically redistribute goods and outputs so  that  we  obtain a Pareto-improvement.
According to the weak Kaldor criteria, situation F is superior to D. However, by  a reverse argument, it can be  seen that  as a  result of the movement from PPF_F to  PPF_D, D  is  Pareto-superior to G and G yields the same level of "aggregate"  utility as F as  it  lies on CIC_F. Thus, by  the weak Kaldor criteria again, situation D  is  ranked  higher than  that  of F.  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.

Therefore, Scitovsky suggested that resolution to this reversal paradox might be done by  combining both the Hicks and Kaldor criteria. This is explained in the figure above. As can be seen from the figure, the movement from D to F fulfills the Kaldor criteria but not the Hicksian one, asfiom D,  it is possible  to undertake hypothetical  lump-sum  redistribution within PPF_D  that achieves a Pareto-improvement over F (e.g.,  a point slightly above G in PPF_D  is a Pareto- improvement  over G and thus over F). The Scitovsky double criteria state 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.