Non-Binary Social Choice: Revealed Preferential Interpretation

Abstract

In this paper, the framework of social choice theory is transformed in terms of the revealed preference relation. The reader may realize that this transformation relaxes the traditional framework without essentially changing Arrow's (1963) original requirements and that his General Possibility Theorem (GPT) and the related results so far achieved still hold. The introduction of the revealed preference is motivated by a traditional narrow interpretation of Arrow into a choice functional framework in which the base relation is used. The base relation pays attention to choices over pairs only, and all the choices from the set of larger-than-pairs are actually given no role in the analysis. However, because of its binary relational structure (see Sen, 1977), Arrow's original framework is appropriate for any size of subsets of alternatives, not only for pairs, and it does not necessarily require the choice based on all non-empty subsets of the set of all alternatives. If we are seriously to consider the generality of his General Possibility Theorem, Arrow's framework has to be transformed so as to satisfy the above points. This can be done by introducing the revealed preference relation. The motivation of the revealed preference originally comes from the realization that it is almost impossible to get complete information in an actual case and that only some preferences are revealed (Samuelson, 1938). Thus, it is obvious that the revealed preference is based on the imperfection of information for preferences and need not be induced from pairwise comparisons only.