Socro-Econ. PIon. So, Vol.13. pp 175-176 @ Pcrgaman Press Ltd..1979 Pnnted inGreat Bntam NOTE zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONM SCALING AND THE LOGIC OF PREFERENCE: A POSER G. H. PIRIE Department of Geography and Environmental Studies, University of the Witwatersrand, I Jan Smuts Avenue, Johannesburg 2001, South Africa zyxwvutsrqponmlkjihgfedcbaZYXWVUT (deceives 1 November 1978) INTRODUCTION In the social sciences, research and thinking on individual and group preferences appears to be divided into two camps, the one empirical and the other theoretical. The empiricists form a truly catholic club, members having a wide variety of interests. Quan- titative techniques (principally scaling) are used to compact in- dividual preferences into a statement of group preference for alternatives among, for example, transport modes, residential environments and shopping centers. On the other hand there is the axiomatic, theoretical approach to social choice. The work of each school seemsto have gone largely unnoticed by the other. It is the modest aim of this brief note to bring the two into rightful juxtaposition and to raise a query about the consistency of their findings. EMPDUCAL RESEARCH Data on individual preferences are generally assembled under carefully controlled conditions in one of two ways: by direct enquiry using a pairwise comp~ison questionn~re design, or by inference from records of individual behavior. In either case square matrices are compiled in which entries indicate the num- ber of occasions one of a pair of alternatives was judged prefer- able to the other. It is not strictly necessary that every individual involved in the study should provide information on all possible pairs. Questionnaires which are pairwise incomplete are per- missable, and indeed, the revealed preference approach yields information on first choices only in the absence of dominance assumptions. The task is to combine individual preferences represented in the matrix into a single group preference function. In substantive terms the task is interpreted as one of ordering each of the alternatives under consideration on a scale of preference as judged by one and all. The translation of individual preferences into a group preference is accomplished either by the statistic- ally-founded unidimensionai scaling techniques pioneered by Thurstone, or by mathematic~ly-based multidimensional scaling. The techniques are pattern seeking only and do not allow for bargaining or other speculative adjustments of individual pref- erences. Scaling is obviously convenient for if there is any semblance of agreement on preferred alternatives among individuals then a collective preference always may be found. At least this is the inte~~tation of the scale if individual responses do have some- thing to do with real choice and preference. THRORRTICAL RISEARCH A massive amount of study has been completed concerning the logical properties of individual and collective preferences (see II-31 for in~oductory accounts). ~minating the entire field is the famous im~ssibility theorem of Arrow [4]. In Sen’s words, Arrow’s classic study involved itself with the “rules of collective choice which make the preference ordering of society a function of individual preference orderings, so that if the latter set is specified, the former must be fully determined” (151, p. 2). It was assumed by Arrow that individual preferences for alternatives would be expressed as orderings. This assump- tion involves nothing other than assumptions about the relations of preference and indifference, indeed, about rational behaviour. The connexity assumption is that for each pair of alternatives either one is preferred to the other or they are indifferent. The second assumption is the much used one of t~nsitivity. and the thiid assumption, “so mild that it is best looked at as a condition.. . of sanity rather than of rationality” ([5], p. 3) is that of reflexivity: every alternative is at least as good as itself. Arrow put forward four additional conditions which had to be met for social choice orderings to be derived from individual choice orderings. The first was that the aggregation procedure, or collective choice rule, should work for every logically possible ordering of individual preferences. This is the condition of un- restricted domain. Second, Arrow required that the collective choice rule should satisfy the Pareto principle: if every subject prefers x to y then the collective ordering should also show x preferred to y. Third, it was made a requirement that a social choice over a set of alternatives should depend only on the orderings of these same alternatives by each individual. This is the condition termed the independence of irrelevant alternatives. The final condition, non~ictatorship, was that no individuals preferences should automatically be those of society irrespective of the preferences of other individuals. From these intuitively acceptable conditions Arrow proved this remarkable, completely general impossibility theorem: “there can be no constitution simultaneously satisfying the con- ditions of collective rationality, the Pareto principfe, the in- de~ndence of irrelevant alternatives and nondic~torship” (141, p. 228). Alternatively, “the only methods of passing from in- dividual tastes to social preferences.. . are either imposed or dictatorial” ([6], p. 59). A POSER This brief exposition of empirical and theoretical orientations in preference research has uncovered an awkward contradiction in the findings of the two schools. Fmpiovina the mechanical device of scaling, preference orderings can be-distilled from data on individual preference such that the orderings for individuals are preserved and a mathematically satisfactory representation of patterned data is achieved. On a logical plane though it is axiomatic that a social preference ordering cannot be derived from individual preference orderings without violating some eminently reasonable conditions on social choice. Can one con- clude other than that empirically derived preference functions are a sham? Quite clearly it is important to understand how scaling functions as a collective choice rule-what logical pro- perties scaling is vested with and how appealing these are. A conscious effort must be made to ally the mechanics and logic of preference aggregation. This is perhaps the role of axiomatic measurement theory which according to Cliff provides the basis for a revolution in the definition of psychological variables. Axiomatic systems “free the investigator from having to assume that scme physical or objective index is, in its literal form, the psychological variable.. [and] .show how he can use the data relations themselves instead to define, or at least narrowly limit, the nature of his variables and the forms of his theories” ((71, p. 477). I75