The Measurement of Social Welfare

By Jerome Rothenberg | Go to book overview

CHAPTER 8
Finite Rankings and Preference Intensity

8-1. A Model of Social Choice

It will be remembered from Chapter 6, concerning the modification of Arrow's condition on irrelevant alternatives, that there are two distinct avenues by which preference intensities may be introduced into the Social Welfare Function.1 An example of one of them, construction of cardinal individual utility indices, has been discussed in the last chapter. In this chapter I should like to illustrate briefly the second approach, that made through individual orderings alone. The particular model dealt with is that of Leo A. Goodman and Harry Markowitz, presented in "Social Welfare Functions Based on Individual Rankings."2

The point of departure for this model is the kind of circumstance envisaged in Chapter 6. In two different situations, a given individual prefers alternative x to y. But in the first situation he prefers y to every other possible alternative (excepting only x), while in the second situation he prefers every alternative to y. It is claimed to be intuitively obvious that the individual has a greater preference intensity for x over y in the second situation when y is his last choice than in the first when y is his second choice. In this example, the number of alternatives which are ordered intermediately between any two given alternatives, or more simply, the rank numbers of the given alternatives, presumably throw light on

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1
We shall see what is in effect a third avenue, group choice, in Chapter 13.
2
The American Journal of Sociology, Vol. LVII, No. 3 ( November, 1952), 257-262.

-180-

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