In AHP, the geometric mean on each comparison level is used. If you havr a group with 3 members and each of them had to to all pairwise comparisons in the model - then for each pairwise comparison you have to calculate group comparison.
Lets say that you compare X and Y with respect to Z.
One person gives Saaty comparison 1 (X is equally important as Y). The other says that X is 2 times more important as Y, and the third person says that X is 4 times more important as Y. Then, a group comparison is a third root of 1*2*4=2. This has to be done for each comparison.
Mr. Nikola Kadoc! What should be the method when number of respondents are more than 1. Should we multiply the number of respondents to the choice they select (say X is 2 times important than Y) and then take Geometric Mean? Please clarify
I think I answered this - group means "2 or more participants".
Let's say there are 3 people in the group.
Let's say we have 3 elements to compare (ex. three criteria).
THEN
Each person from group makes its own comparison table. It gives judgments independently of other 2 persons.
Then we aggregate all three comparison tables into one GROUP table by calculating the geometric means of all cells on the same positions.
After, the GROUP table is being used to calculate group priorities.
Ex. The first person make comparison table like:
1 2 2
1/2 1 1
1/2 1 1
The second person make comparison table like:
1 2 3
1/2 1 2
1/3 1/2 1
The third person make comparison table like:
1 3 5
1/3 1 2
1/5 1/2 1
THEN the GROUP table is
1 a b
1/a 1 c
1/b 1/c 1
"a" is calculated as follows:
- the position of a is (1, 2 ... first row, second column)
- calculating the geometric mean of three values on positions (1,2) in three respondents comparison matrices. Geometric meand of n elements is n'th square of elements product)
a=third square of (2*2*3)
Similarly,
b=third square of (2*3*5)
c=third square of (1*2*2)
After the GROUP matrix is determined, usual procedure for calculating the priorities can be applied.
If we want to see what are individual priorities, we can apply usual procedure for calculating the priorities on each participant pairwise comparison table.
The thing we should NOT do is to calculate the individual priorities and make geometric (or arithmetic) mean of priorities.
When I say usual procedure - I mean on several available procedures available to us when calculating the priorities from comparison table...
1) normalizing the comparison table (dividing each column with column sum) and multiplying the normalized matrix with itself until converge
2) normalization of comparison table, calculating the row averages of the normalized table...
...
Dear Nikola
Thank you,
Actually, I want to aggregate the results between the public and decision makers groups, I want to get the final result among them.
In other cases, the geometric mean is effective. However, when we want aggregate different groups' answers, it does not make sense.
Regards,
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