Shown below is an incomplete pairwise comparison matrix for three alternatives.What comparison factor should A3 receive when compared to A2?
A)3
B)1/3
C)7
D)1/7
E)None of the above

Question

Shown below is an incomplete pairwise comparison matrix for three alternatives.What comparison factor should A3 receive when compared to A2? 
A)3 
B)1/3 
C)7 
D)1/7 
E)None of the above

Quizplus · Accepted Answer

Since the pairwise comparison matrix is incomplete, we cannot say for certain what the exact comparison factor between A3 and A2 should be. However, we can use the transitivity property of pairwise comparisons to determine an estimate.

For example, if A1 is preferred over A2 with a factor of 2, and A2 is preferred over A3 with a factor of 3, then we can estimate that A1 is preferred over A3 with a factor of 6 (2 x 3). Therefore, to maintain consistency in the pairwise comparison matrix, A3 should be compared to A2 with a factor of 1/6 (the reciprocal of 6).

The only answer choice that represents 1/7, which is the reciprocal of 7, is D. Therefore, D is the best choice.

Shown Below Is an Incomplete Pairwise Comparison Matrix for Three