Distributional Equality and Aggregate Utility: Reply
The formulation of the argument for distributional equality by William Breit and William Culbertson is an improvement on that of The Economics of Control and is more effective in class. Their generalization of the to the case of increasing marginal utility (of income) offset by a greater degree of diminishing marginal utility elsewhere, is also an improvement. Their point that Paul Samuelson did not escape the ''equal ignorance assumption is well taken. Ambiguity, being a case of lack of clarity is a charge that can never successfully be refuted. However, I would like to deny a switching of conclusions. Perhaps the ambiguity would have been avoided if I had added the following words in Roman type to the italicized sentence quoted: . . if it is desired to maximize the total satisfaction in a society, the rational procedure, in the absence of the knowledge that would enable us to equalize the marginal utilities, is to maximize the probable total satisfaction-i.e., to divide income on an equlitarian basis. The theorem on page 32 is not than the and mild one of page 29. It is the same proposition. The ingenous device of the 100 million coconut islands in one way does more than is claimed for it and in another way, does less. If it were possible to divide the total population into pairs which had the same utility functions, the equalization of income within each pair would never involve a wrong movement to be offset by a right oine. That is why there is certainty of improvement from equalization on every island. Furthermore, there would be an absolute maximization, with certainty, of the total satisfaction of the pair on each island from their joint income. On the other hand, the parable assumes that the combined incomes of the pairs have somehow already been equalized; that for every individual in the half of the total population with incomes less than the mean, his partner in the other half of the population (with an identical utility function) has an income greater than the mean by the exact amount that his is less than the mean. (This implies incidentally that no individual has an income as as twice the mean unless his partner has a zero income.) If this is not the case, some islands will be richer than others. We will then have to equalize the incomes of the islands before we could conduct Breit and Culbertson's experiment. The parable, therefore, while not necessary for the meek that income equalization maximizes the probable total satisfaction, is not sufficient for the bold proposition (to which I have never subscribed) that income equalization increases total satisfaction with absolute certainty. Breit and Culbertson's development of their parable reflects the same discomfort they have seen in others. The pair on the island are not satisfied with the proof that the equalization of the incomes has maximized their probable satisfaction. Sharing a widespread human craving for certainty, they want to be quite sure that they have at least increased their actual total satisfactions. This assurance is unfortunately not available as long as the utility functions are unknown. Breit and Culbertson also are seeking for a certainty of gain in a much bolder and more interesting regarding realized satisfactions instead of the maximization of a mere probability, and are accurately represented by the island pair they have invented. They have imagined a certainty of gain only by imagining the discovery of identicalutility twins. But the whole point of the * University of California, Berkeley.