Abstract
Abstract In this paper, we study merging functions, functions which combine individual judgements into a merged or aggregate or consensus judgement. In particular, we study such functions under several simple axioms, symmetry, linear homogeneity, and agreement (which says that if all individuals agree, the merged judgement agrees with those of all of the individuals). We show that under one or more of these assumptions, the possible merging procedures are very few if we want certain statements involving the merged functions to be meaningful in the precise sense used in the theory of measurement, and that in many cases the arithmetic mean or the geometric mean are the only possible merging functions. The results are applied to group consensus problems, to performance analysis of alternative new technologies or of students or job applicants, and to the development of measures of price level.
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