Sometimes making decisions becomes difficult due to information overload. We have so many criteria to ponder that it’s hard to decide which option is best, and we end up making suboptimal decisions, or worse, no decision at all.
One way to address this problem is through the use of a Decision Matrix (a.k.a. Selection Matrix). A Decision Matrix is a very powerful yet underused tool that allows us to organise our data to easily make decisions.
A Decision Matrix can be used whenever we have at least two options to choose from, and more than one decision criteria. For example, pretend we’re comparing three houses to buy based on their price, floor area and garage spaces:
| House | Price | Floor Area | Garage Spaces |
|---|---|---|---|
| House 1 | $720,000 | 210 m² | 1 |
| House 2 | $740,000 | 190 m² | 2 |
| House 3 | $770,000 | 160 m² | 3 |
We’ll use the data in Table 1 to demonstrate how to use a decision matrix. We’ll start with a scored matrix approach.
Scored Decision Matrix
To use a scored selection matrix, we need to define some scores for each criteria. For example:
| Criteria | Value Range | Points |
|---|---|---|
| Price | < $700,000 | 10 |
| < $800,000 | 5 | |
| > $800,000 | 0 | |
| Floor Area | > 200 m² | 10 |
| > 150 m² | 5 | |
| < 150 m² | 0 | |
| Garage Spaces | 3 or more | 10 |
| 2 | 5 | |
| 1 or less | 0 |
These scores show how much we care about each criteria. We can use them to make a matrix and see which house is the best choice. In this case, and based on the criteria we chose and the scores we gave, House 3 would be the best option, as shown in Table 3:
| House | Price | Floor Area | Garages | Total |
|---|---|---|---|---|
| House 1 | 5 | 10 | 0 | 15 |
| House 2 | 5 | 5 | 5 | 15 |
| House 3 | 10 | 5 | 10 | 25 |
Scored matrices are useful when we want a fast and simple way to compare things. They are good for everyday choices, especially when we use our feelings or personal preferences more than exact data.
Normalised Decision Matrix
If we want to be more precise and compare options based on real numbers, we can use a Normalised Decision Matrix instead. In this approach, we normalise the values for each criteria so they are on the same scale. This gives each option a fair score based on data.
For our example, the normalisation functions and evaluation for each house are shown next:
Normalise Price
house_price - min_price
score(house_price) = 1 - -------------------------
max_price - min_price| House | Price | Score |
|---|---|---|
| House 1 | $720,000 | 1 – (720-720)/50 = 1.00 |
| House 2 | $740,000 | 1 – (740-720)/50 = 0.60 |
| House 3 | $770,000 | 1 – (770-720)/50 = 0.00 |
Normalise Area
house_area - min_area
score(house_area) = -------------------------
max_area - min_area| House | Area | Score |
|---|---|---|
| House 1 | 210 m² | (210-160)/50 = 1.00 |
| House 2 | 190 m² | (190-160)/50 = 0.60 |
| House 3 | 160 m² | (160-160)/50 = 0.00 |
Normalised Garage Spaces
house_garages - min_garages
score(house_garage) = -------------------------
max_garages - min_garages| House | Garages | Score |
|---|---|---|
| House 1 | 1 | (1-1)/2 = 0.00 |
| House 2 | 2 | (2-1)/2 = 0.50 |
| House 3 | 3 | (3-1)/2 = 1.00 |
After we evaluate each function, we can update our decision matrix as follows:
| House | Price | Floor Area | Garages | Total |
|---|---|---|---|---|
| House 1 | 1.00 | 1.00 | 0.00 | 2.00 |
| House 2 | 0.60 | 0.60 | 0.50 | 1.70 |
| House 3 | 0.00 | 0.00 | 1.00 | 1.00 |
Once we calculate the scores, we can compare the totals to find the best option based on the data.
House 1 is or best choice when using the Normalised Decision Matrix, rather than House 3 when using a Scored Decision Matrix. This doesn’t mean one method is better. Each highlights different priorities. The Scored Matrix reflects our personal preferences, so House 3 wins based on the rules we set, while the Normalised Matrix removes that bias.
Normalised Decision Matrices are especially useful when comparing things with different units like price, floor area, and garage spaces. While it involves some maths, it’s a great tool for bigger or more complex decisions where precision is important.
Weighted Decision Matrix
Sometimes we want to use a normalised matrix, but not all criteria are equally important. In these cases, we can assign weights to reflect the relative importance of each criteria.
Coming back to our example, if the number of garage spaces is more important than the floor area and the price, we could define some weights that acknowledge this:
| Price | Floor Area | Garages |
|---|---|---|
| 1.00 | 2.50 | 3.00 |
If we apply these weights to the results from table 7, we get the following weighted decision matrix:
| House | Price | Floor Area | Garages | Total |
|---|---|---|---|---|
| House 1 | 1.00 | 1.0×2.5 = 2.5 | 0.00 | 3.50 |
| House 2 | 0.60 | 0.6×2.5 = 1.5 | 0.5×3 = 1.5 | 3.60 |
| House 3 | 0.00 | 0.00 | 1.0×3 = 3.0 | 3.00 |
By using these weights, this time we find that our best option is House 2. This shows how assigning different importance to each criteria can change the outcome to reflect our priorities.
Pros/Cons Matrix
A the main issue with decision matrices is that we need to define a score for each criteria, which can be time-consuming and require some mental effort. When we want a quick, intuitive method, a pros/cons matrix may be a better fit.
Pros and cons matrices are similar to the matrices we’ve seen already, but instead of giving each criterion a numerical score, we simply mark whether a criteria is met or not:
| House | Price | Floor Area | Garage spaces |
| House 1 | ✅ | ✅ | ❌ |
| House 2 | ✅ | ❌ | ✅ |
| House 3 | ❌ | ❌ | ✅ |
A common approach is to use a tick or a cross, like in Table 10. This matrix provides qualitative data that we can use to visually compare our options. Although they don’t offer strong numeric values, they are great to spark conversations on important topics and get teams aligned when making decisions.
Tools
No matter which type of decision matrix we choose, we can create one on a piece of paper, a Word doc, or even a Confluence page, especially if they are simple. However, when the number of options or criteria start to grow, or the formula to calculate the final value gets more complex, I would strongly recommend using spreadsheets. The fact that they already have rows and columns that form a matrix, and their math capabilities make them the go-to tool in most cases.
Final Thoughts
Decision matrices come in many shapes, and each has its place. Whether you’re after a quick comparison, a discussion starter, or a detailed analysis based on data, there’s a matrix that fits.
As you may have noticed, we can get different results based on the matrix we use and how we use it. Decision matrices are tools that help us make decisions, but they can’t do it without our clear guidance, otherwise they become random number we are not better off than when we started.
The next time you’re feeling stuck between options, try a decision matrix. It might just make your decision a lot easier.
Cheers!
José Miguel
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