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Degrees of Cardinality and Aggregate Partial Orderings

C. Blackorby

Abstract

The problems associated with interpersonal comparisons are particularly intractable. This paper presents a procedure whereby the relative importance of any particular individual varies over the set of social states. In one sense, the stronger (relative to some norm) a person feels about any particular pairwise decision, the larger his say in that outcome. This procedure leads to a nested sequence of aggregate partial orderings which reflects this strength of preference. Under the assumptions presented it is also possible, given any two social states, to characterize the minimal amount of interpersonal comparison which is necessary in order to arrive at an aggregate ordering.