Does the answer survive scrutiny?
Any matrix produces a winner. This one tells you how far a weight would have to move before the winner changes — which is the only thing that makes the exercise worth doing.
Scoring, and whether the answer survives being questioned
The ranking takes a minute. The useful part is how far a weight would have to move before the winner changes.
Criteria and weights
Options and scores
Ranking
Would a different weight change the answer?
This is the question that decides whether the matrix is analysis or decoration.
How scores are combined
Weights are normalised to sum to 1, so you can type 3, 5, 2 without making them add to 100 — and totals stay comparable when a criterion is added or removed.
Scores are normalised by ratio within each criterion: value ÷ best, or best ÷ value where lower is better. Not min-max.
Min-max is the obvious choice and it is wrong here. It stretches every criterion to span the full 0-to-1 range, so the best option always scores 1 and the worst always 0 however close they really are. With two options it is completely degenerate. Ratio normalisation keeps a 4% difference looking like 4%.
Sensitivity varies one criterion's weight from 0 to 100% while re-normalising the others proportionally, and reports the point at which the winner changes.
The ranking is not the output
Any weighted matrix produces a winner. The question worth asking is whether that winner survives a reasonable disagreement about the weights — because the weights are the part somebody made up.
If the answer flips when a criterion moves from 20% to 25%, you have not made a decision, you have recorded a preference and dressed it in arithmetic. If the answer holds across every plausible weighting, the matrix has genuinely told you something and the meeting can be short.
Weights get chosen to produce the answer
It is worth naming the failure mode. People frequently arrive with a preferred option and adjust the weights until the matrix agrees, usually without noticing they are doing it.
The defence is to set the weights before scoring anything, ideally with people who have not yet seen the options, and to write down why each weight is what it is. Sensitivity analysis then does the rest: if the conclusion only holds at one precise weighting, that is visible rather than hidden.
Beware criteria that measure the same thing
"Cost", "licence fee" and "total cost of ownership" as three separate criteria give cost three votes. The matrix cannot detect this, and the result is a decision dominated by whichever consideration happened to get described in the most ways.
Before scoring, check that each criterion could move independently of the others. If two always rise and fall together, they are one criterion.