TY - JOUR
T1 - On the possible merging functions
AU - Aczél, János
AU - Roberts, Fred S.
N1 - Funding Information:
Janos AczCl acknowledges the support of the Natural Sciences and Engineering Research Council of Canada under grant numbers A2972 and T6880 and the hospitality of the Universities of Central Florida and of Karlsruhe. Fred S. Roberts acknowledges the support of the U.S. National Science Foundation under grants IST-83-01496 and IST-86-04530 to Rutgers University. The authors thank Suh-ryung Kim, Sam Rosenbaum, and Barry Tesman for their helpful comments.
PY - 1989/6
Y1 - 1989/6
N2 - 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.
AB - 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.
KW - Merging functions, symmetry
KW - linear homogeneity
KW - price level
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U2 - 10.1016/0165-4896(89)90054-1
DO - 10.1016/0165-4896(89)90054-1
M3 - Article
AN - SCOPUS:38249021850
SN - 0165-4896
VL - 17
SP - 205
EP - 243
JO - Mathematical Social Sciences
JF - Mathematical Social Sciences
IS - 3
ER -