Some Combinatorial Aspects of Paired Comparisons

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Abstract

In paired comparison experiments, two alternatives, of a set of alternatives exhibiting some common but quantitatively intractable quality, are compared at a time. We assume that judgments on each pair may end up in ties apart from one alternative being preferred to another. In such a situation, we define and find (a) a measure of consistency in preference of judges - distribution of the measure and related tests of hypotheses, (b) a measure of agreement among the judges - distribution and related tests of hypotheses. We also find distributions of scores obtained by the alternatives (objects) and of their related functions and answer the questions like (i) what score must a specified object get to be regarded as significantly better than average? (ii) what constitutes a significant difference in scores between two specified objects?

Original languageEnglish (US)
Pages (from-to)1-30
Number of pages30
JournalAmerican Journal of Mathematical and Management Sciences
Volume13
Issue number1-2
DOIs
StatePublished - Jan 1 1993

All Science Journal Classification (ASJC) codes

  • Business, Management and Accounting(all)
  • Applied Mathematics

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