The idealist doctrine then may be summed up by saying that each individual has two orderings, one which governs him in his everyday actions, and one … - Kenneth Arrow

Index numbers are, of course, desired for purposes other than to measure the cost of living. One obvious possibility is to consider some subset of cost-of- living items, such as food. The logic of the preceding argument goes through precisely provided we assume that the distribution of food expenditures in any period among different foods depends only on the total volume of food expenditures and is independent of the prices of other goods, for any given total volume of food expenditures. This does not deny substitution between foods and other commodities, but we assume that the total effect of this substitution is already reflected in the choice of a volume of food expenditures. In a broad way, similar considerations apply to the pricing of producers’ goods, which should be interpreted as reflecting indirectly consumers’ preferences. However, there is undoubtedly a good deal more in the detailed working out of the theory that has never been developed.

Dynamic analysis may have deeper implications if we depart from the analysis of stationary states. The frim must now serve some additional roles. In the absence of futures markets, the firm must serve as a forecaster and as a bearer of uncertainty. Further, from a general equilibrium point of view, the forecasts of others become relevant to the evaluation of the firm's shares and therefore possibly of the firm's behavior.

If the total number of alternatives is two, the method of majority decision is a social welfare function which satisfies Conditions 2–5 and yields a social ordering of the two alternatives for every set of individual orderings.