Preference Strength and Two Kinds of Ordinalism*

In his paper "Extended Sympathy and the Possibility of Social Choice", Professor Arrow first considers an approach to individual utilities which is "strictly ordinal" and rules out interpersonal comparisons. This is the approach he took when he formulated his original impossibility theorem [1]. He then takes up an approach which allows interperso~al comparisons, but only of an ordinal kind. The strictly ordinal approach without interpersonal comparisons turns out to lead to a dead end, and the second approach the one that allows interpersonal comparisons of an ordinal kind alone leads either to lexical mz'ximax or to lexical maximin. What are we to make of ~11 this? The approach without interpersonal comparisons leads to a dead end in the sense that it is inconsistent with certain other conditions: in the version of the Arrow theorem in the paper I am discussing, with the conditions of Binary Relevancy, Anonymity, and the Weak Pareto Principle. A further condition is built into the formalism Arrow uses: that the just or optimal alternatives from among the feasible alternatives are determined by a weak ordering which is independent of the feasibility of alternatives. The ordinal approach without interpersonal comparisons, then, is discredited by the Arrow theorem only in so far as these other conditions are plausible. Just what, more precisely, is the approach that is supposed to lead to trouble? I can think of two positions the term 'a strictly ordinal approach' might designate; I shall call them 'Basic Ordinalism' and 'Pairwise Ordinalism'. One is this.