cross within this space, but cross elsewhere - outside the points being compared. In Figure 3.2A this is the case.

Situation b is clearly superior to a by a Kaldor compensation test. There is no Scitovsky reversal. From b, a redistribution may be made to b', and b' is clearly Pareto superior to a. And a move from b to a finds no redistribution along UA that is superior to b. Samuelson pointed out, however, that there is a point a" that is superior to b", and that b' is a redistribution of the goods available at b. Samuelson suggests that position b be regarded as superior to position a only if the utility frontier curves do not cross. To say this another way, Samuelson suggests that the state of the world 2 would be called superior to state 1 only if for any distributional arrangement of the state 1 goods there is a Pareto superior arrangement in state 2. This is often called the Samuelson test or condition (Mishan 1981, pp. 313-314). Scitovsky actually noted the possibility discussed by Samuelson, but believed that comparisons should involve the positions being actually considered. The Samuelson criterion in some cases is more restrictive than KH, and its use would entail a greater status quo bias. In fact, Samuelson is even more restrictive than Pareto. Not only does Samuelson object to moving from a to b and then to b', but he would apparently object to moving directly from a to b', even though a direct move to b' is Pareto efficient, since a" is Pareto superior to b". Thus all projects that fail the Scitovsky test would also fail the Samuelson test, but in addition, there would be others that would fail only the Samuelson test.

For an example that would pass Samuelson, imagine two utility frontier curves that do not cross. One might compare two positions on these different curves, neither of which is Pareto superior to the other. However, Samuelson's criterion would allow the selection of the position on the higher of the two utility frontier curves, even though in moving from one position to another some are worse off. Thus Samuelson does not allow some moves, even though they are Pareto efficient, but his test does allow some moves that are not Pareto efficient.

Under KHZ, we assume that all efficient changes which are possible under a legal regime have already been made; therefore, we should only compare points which are first-best positions.

The example provided by Table 3.4A at hand is additionally instructive. Note that even though the Kaldor (strong) test is passed, the EV and the CV tests and the KHZ net benefits test are all failed. (Possibility 1 has KHZ net benefits of zero; the status quo always has an efficiency of zero, and is the best state only if every other regime would result in a net loss.) Possibility 2 has KHZ net benefits of -5, since A would have a cost of 10 if he lost one of his acres of wheat, while B would only gain 5 if she acquired a second acre of cotton.

Possibility 3 shows us that the net benefit test and the CV and the EV tests can be passed even though the Hicks (strong) test failed. Possibility 3 has an EV and a CV and KHZ net benefits of +20. B undergoes no change, and A has a benefit of 20 when he acquires a new acre of cotton.

Possibility 4 has an EV and a CV of -1, since A has a cost of 10 when he loses his second acre of wheat and B only has a benefit of 9 when she acquires an acre of wheat. Note that possibility 4 is better than possibility 2, because it results in a lower net loss than possibility 2 does, but that the status quo is actually better than possibility 4.

However, possibility 4 can also be the best state, if we plug in different numbers, which are also consistent with Coleman's example. See Table 3.5A.

Table 3.5A

Retain 2nd acre of wheat $5

Acquire 1st acre of cotton $9

Acquire 1st acre of wheat $20

Acquire 2nd acre of cotton $10

Possibility 2 has an efficiency of +5, since B has a benefit of 10 and A has a cost of 5. Possibility 3 has an efficiency of +4, since A has a benefit of 4 (or, if you prefer, A has both a benefit of 9 and a cost of 5), and B has no change in wealth. Possibility 4 has an efficiency of +15, since B has a benefit of 20 and A has a cost of 5. Again, we see that possibility 3 is better than possibility 1, and possibility 4 is better than possibility 2.19 Among other things, this discussion shows that saying that a pair of states are the first-best states does not necessarily mean that both of them are better than any one of the other states; it simply means that one of the pair will always be the best state possible.

This sort of result helps explain why KHZ does not embrace the Kaldor and Hicks tests, although the examples refer only to the strong test. The logic of the Kaldor (strong) test is that a proposed rule is better than the status quo if possibility 3 is better than the status quo. However, in Table 3.4A I have shown that it is possible for the proposed rule change (possibility 2) to be worse than the status quo (possibility 1) even if possibility 3 is better than the status quo. This means that even if a rule would be Pareto superior to the status quo after compensation, it might be less efficient than the status quo before compensation. Of course, since possibility 3 is the best choice of all, in a sense it does not matter whether possibility 1 is better than possibility 2. However, it is noteworthy that the prediction of the Kaldor (strong) test is incorrect.

The logic of the Hicks (strong) test is that a proposed rule is not better than the status quo if possibility 4 is better than proposed rule change. However, in Table 3.5A I have shown that possibility 4 is better than the status quo and the proposed rule change, but the proposed rule change (possibility 2) is more efficient than the status quo (possibility 1). Therefore, the Hicks (strong) test makes a prediction which is incorrect.

This appendix has shown that the possibility of preference reversal is only possible when comparing second-best states and is also only possible when using the KH potential compensation tests. It is not, however, possible when using the KHZ net benefits test. Even if a project is subject to Scitovsky reversal, this does not present a dilemma or paradox for KHZ, since WTP and WTA evaluation will unambiguously rank one regime over all of the others.

This issue is also related to the one of choosing among first-best positions and of choosing between a first-best and a second-best position. As Mishan (1981, pp. 359-376) has shown, however, the choice between these sorts of positions (or indeed between second-best positions) can be reduced to a choice of income distribution. This income distribution is a good in KHZ analysis. In so far, then, as KHZ provides a method of choosing between different distributions, it offers a method of choice without contradiction.

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