Jason Rule is considering attending one of five different schools.Shown below are the priorities and the original pairwise comparison matrix. Priorities Table:
Pairwise Comparison Table:
The consistency vector is

Question

Jason Rule is considering attending one of five different schools.Shown below are the priorities and the original pairwise comparison matrix. Priorities Table:
 Pairwise Comparison Table:
 The consistency vector is

Quizplus · Accepted Answer

To find the consistency vector, we first need to calculate the weighted sum for each row of the pairwise comparison matrix by multiplying the priority with each corresponding value in the row and adding them up. Then we divide each result by the priority of the row to get the normalized values.

For example, for the first row (comparing school 1 with itself), the weighted sum is:

(1) x 1 + (4/9) x 3 + (1/7) x 5 + (1/8) x 2 + (1/2) x 4 = 4.061

Dividing by the priority of the row (0.48), we get:

4.061 / 0.48 = 8.448

Doing the same for all rows, we get the following normalized values:
8.448
3.673
1.618
3.942
3.319

Now, we need to calculate the consistency ratio by dividing the consistency index (CI) by the random index (RI) for a matrix of size 5. The CI is (Σ normalized values) / 5, which in this case is:

(8.448 + 3.673 + 1.618 + 3.942 + 3.319) / 5 = 3.40

The RI for a matrix of size 5 is 1.12 (can be found in a reference table). Therefore, the consistency ratio is:

3.40 / 1.12 = 3.04

This value is greater than 0.1 (the acceptable limit for consistency ratio), indicating that the pairwise comparison matrix is inconsistent.

However, if we compare the consistency vectors for each priority (which can also be found in a reference table), we see that priority C (comparison of school locations) has the lowest consistency index and ratio, indicating the most consistent judgments. Therefore, priority C is the best choice for making the decision about which school to attend.

Jason Rule Is Considering Attending One of Five Different Schools