Comparing alternatives in pairs is a well-known method of ranking creation.Experts are asked to perform a series of binary comparisons and then, usingmathematical methods, the final ranking is prepared. As experts conduct theindividual assessments, they may not always be consistent. The level ofinconsistency among individual assessments is widely accepted as a measure ofthe ranking quality. The higher the ranking quality, the greater itscredibility. One way to determine the level of inconsistency among the pairedcomparisons is to calculate the value of the inconsistency index. One of theearliest and most widespread inconsistency indexes is the consistencycoefficient defined by Kendall and Babington Smith. In their work, the authorsconsider binary pairwise comparisons, i.e., those where the result of anindividual comparison can only be: better or worse. The presented work extendsthe Kendall and Babington Smith index to sets of paired comparisons with ties.Hence, this extension allows the decision makers to determine the inconsistencyfor sets of paired comparisons, where the result may also be "equal." Thearticle contains a definition and analysis of the most inconsistent set ofpairwise comparisons with and without ties. It is also shown that the mostinconsistent set of pairwise comparisons with ties represents a special case ofthe more general set cover problem.
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