Journal
INTERNATIONAL JOURNAL OF INFORMATION TECHNOLOGY & DECISION MAKING
Volume 4, Issue 2, Pages 167-176Publisher
WORLD SCIENTIFIC PUBL CO PTE LTD
DOI: 10.1142/S0219622005001453
Keywords
social welfare function; analytic hierarchy process; synthesis; geometric mean; possibility
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This paper gives a brief overview of the well-known impossibility-possibility theorem in constructing a social welfare function from individual functions. The Analytic Hierarchy Process uses a fundamental scale of absolute numbers to represent judgments about dominance in paired comparisons. It is shown that it is possible to derive such a function in two ways. One is from the synthesized functions of the judgments of each of the individuals. The other is obtained by first combining corresponding pairwise comparison judgments made by all the individuals, thus obtaining a matrix of combined judgments for the group and then deriving a welfare function for the group. With consistency the four conditions imposed by Arrow are satisfied. With inconsistency, an additional condition is needed.
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