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Weighted decision matrix

List the options, list what matters with a weight for each, then score every option. The ranking updates as you type, and the table below it shows how robust the winner is.

Scores

Option Cost (×5)Travel time (×3)Meeting space (×2)
Lakeside lodge
City hotel
Farm barn

Winner

Lakeside lodge

Weighted score 3.80 out of 5, ahead of City hotel on 3.70.

Rank Option Weighted Unweighted
1 Lakeside lodge 3.80 4.00
2 City hotel 3.70 3.33
3 Farm barn 3.60 3.33

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How robust is the winner?

Each row moves one weight and holds the others still. It shows the nearest weight at which another option would draw level with the current winner.

Criterion Weight now What would change the winner
Cost 5 City hotel draws level with the leader if this weight goes up from 5 to 5.5.
Travel time 3 City hotel draws level with the leader if this weight goes down from 3 to 2.7.
Meeting space 2 City hotel draws level with the leader if this weight goes down from 2 to 1.0.

The method: a weighted sum

This is the weighted sum model, the simplest and most widely used way of scoring options against several criteria. For each option, every score is multiplied by its criterion’s weight and the products are added:

Dividing by the sum of the weights does not change the ranking; it only makes the number readable. A weighted score of 3.8 on a 1–5 scale means “on balance, a bit under a 4”. The unweighted column is the plain average of the scores, shown so you can see how much the weights themselves are doing.

A worked example

A team is choosing a venue for an offsite. Cost matters most (weight 5), then travel time (3), then the quality of the meeting room (2). Each venue is scored 1 to 5, where 5 is best, so the cheapest venue gets the highest cost score.

The lodge wins, but narrowly, and the robustness table explains why that matters. The city hotel is cheapest, so if the team cared a little more about cost (a weight of 5.5 instead of 5) the hotel would draw level. The lodge’s lead rests on its short travel time. That is the kind of thing worth saying out loud before booking: “we are choosing the lodge because we are treating travel time as more than half as important as cost. Is that right?”

How the robustness check works

Hold all weights but one fixed. Every option’s total is then a straight line in that one weight, so the point where a rival’s line crosses the winner’s can be solved exactly: w* = (restwinner − restrival) ÷ (scorerival − scorewinner), where “rest” is the total from all the other criteria. The table reports the crossing closest to the current weight. If a criterion’s weight would need to double or fall to zero before anything changes, the choice does not hinge on it and there is little point arguing about it.

Where a weighted matrix goes wrong

More formal methods exist, such as the analytic hierarchy process (AHP), which derives weights from pairwise comparisons, and outranking methods that avoid full compensation. They answer the same question with more effort. For most group decisions a transparent weighted sum, plus an honest look at its sensitivity, is enough.

Common questions

What is a weighted decision matrix?

A table with the options as rows and the things you care about as columns. Each criterion gets a weight for how much it matters, each option gets a score on each criterion, and an option’s total is the sum of score × weight. It is also called a weighted scoring model or, in decision science, the weighted sum model.

Do the weights need to add up to 100?

No. Only the ratios between weights matter. Weights of 5, 3 and 2 give exactly the same ranking as 50%, 30% and 20%. The results are shown as a weighted average on your scoring scale, so a result of 3.8 on a 1–5 scale reads naturally whatever numbers you used for weights.

What scale should the scores use?

Any scale, as long as it is the same for every criterion and higher always means better. 1 to 5 is quick and good enough for most decisions; 1 to 10 gives more room when options are close. For a cost criterion, score the cheapest option highest.

How is this different from a Pugh matrix?

A Pugh matrix picks one option as the baseline and scores every other option as better (+), the same (0) or worse (−) on each criterion. It is quicker and good for early screening. A weighted matrix scores every option on a common scale and is better once you are choosing between a few serious candidates.

How can a group use this together?

Agree the criteria and weights first, as a group, before anyone scores. Then either score together or have each person fill in the matrix and share their link, and compare. Disagreement about weights is usually the real disagreement, and the sensitivity table shows whether it actually changes the answer.

The matrix picked an option nobody likes. Now what?

That is useful information. Usually a criterion is missing, or a weight does not reflect what people actually care about. Add the missing criterion and see whether the ranking moves. A matrix structures a discussion; it does not replace it.

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