Multi-Attribute Decision Matrices, Done Right

decision matrices (MADM) are a useful methodology for comparing multiple alternatives and choosing the alternative that most closely fits your needs and budget. By evaluating a set of criteria for every option, you’ll be able to be confident that you’ve got a transparent understanding of the choice space.

They’re, nonetheless, often misinterpreted or misapplied. This text explains methods to utilize multi-attribute decision matrices and avoid pitfalls commonly related to their use. It also lays the groundwork for a distinct method that borrows vital concepts from MADM without falling into its implicit traps.

A Motivating Example: Tent Selection

My family is out there for a brand new tent. As such, we did what we normally do: we googled “best tent for automotive camping.” One in every of the primary results was a GearLab article called “The Best Camping Tents | Tested and Ranked.”

Within the article, GearLab rates 16 tents on a scale of 1 to 10 across five attributes. They weigh those attributes, after which rank the tents 1-16 based on the weighted scores. This is a simple example of a multi-attribute decision matrix.

The Purpose of MADM

MADM is usually treated as a way for data to make a call on behalf of a stakeholder. Within the GearLab article, they recommend the one “best” tent based on their MADM findings. I would like to emphasise that MADM doesn’t the choice;it it.

It may best be understood as a great tool for structuring comparisons across all alternatives, eliminating clearly inferior options, and revealing the highest contenders. Used appropriately, it helps decision-makers see the landscape of accessible decisions slightly than pointing them to a single “correct” alternative.

When misused, it might probably steer a call into the bottom and leave the choice maker with a foul taste of their mouth about “data-driven” decision-making.

In brief, MADM’s purpose is to present decision-makers a greater grasp of their options, eliminate poor options, and present value propositions, to not automate the choice.

Easy methods to Properly Use MADM

Here is my basic guide to MADM:

1. Discover the decision-maker, decision space, and attributes.
2. Define the weights for every attribute.
3. Collect the info and calculate the weighted scores.
4. Plot the products against the value and find the efficient frontier.
5. Present the findings and suggestions to the choice maker.

Briefly, I’ll describe each in just a little more detail.

First, determine who the choice maker is. Are you doing this evaluation for another person’s decision, or for your individual? For this instance, let’s assume that it’s for your individual decision.

Defining the choice space is usually fairly straightforward. That you must know the variety of item (resembling a tent) being considered and discover the highest n options. Be sure you fairly sample all options, not only those that come to mind first.

Then, assign several attributes. Give you an inventory of things that may make the product more useful or beneficial.

After you define the attributes, I like to recommend speaking with the decision-maker. Once you begin talking to the decision-maker, ensure you utilize their priorities, not yours.

Rank the attributes by importance, and consider the tradeoffs. Tradeoff questions like “Would I trade an inch of headspace from 71 inches to 70 inches for a tent that’s just a little more wind-proof?” Then, assign attribute weights in accordance with these responses and place them in a table for later use. These won’t ever be perfect, even when the evaluation is for your individual use.

Now you’ve got something that appears like this.

Collecting the info can vary in difficulty. In this example, it’s relatively straightforward. Seek for each tent, go to “tech specs” to seek out most information, and reviews to seek out the remainder. Record that data in your decision matrix. If it’s not straightforward, it’s possible you’ll have to subjectively assign a worth to every attribute, but you’ll want to define your criterion, or at the very least your general pondering, when you do that.

For the tents on GearLab, they rated each attribute on a scale of 1 to 10, as shown below.

Now, your decision matrix looks like this. Note that to maintain the chart readable, I actually have omitted the “quality” attribute.

All that continues to be is to calculate the weighted scores. To do that, take the sum product of the weights and the values for every item. You now have your accomplished decision matrix. I actually have also included the value for reference.

Next, plot the weighted rating of every item against its price, orient yourself to the plot, and plot the efficient frontier:

From this, we are able to discover eight tents on the efficient frontier. Being on the efficient frontier means we cannot get a greater weighted rating at the identical or lower cost. That is the important thing insight MADM provides: identifying which options are strictly dominated and which involve meaningful trade-offs between quality and value.

If this plot looks familiar, it is probably going because you’ve got seen an identical plot on a financial risk-return efficient frontier. One axis is something you would like less of (price/risk), and the opposite is something you would like more of (rating/return).

So which to recommend? If my budget is $600 and I would like the highest-quality tent I can afford, I might go for the North Face Wawona 6.

See here: I drew a line on the budget, then selected the primary tent to the left of that line on the efficient frontier. I could do an identical thing if I had a “quality budget” and drew a line, then selected the primary point on the efficient frontier above the road.

All that continues to be now could be to present your findings to the decision-maker. When doing this, I like to recommend orienting them to the plot and mentioning and explaining the efficient frontier. Something so simple as “for every of those points, you can not get a greater rating for a similar price” will suffice. Call attention to the highest-rated option. In case you know their budget prematurely, make the suitable suggestion.

Note that if we use a ratio of the weighted rating to cost, we lose a whole lot of information and can’t determine which tent to decide on. It is suitable to incorporate this information, but not mandatory, because it sometimes tells a misleading story. For instance, if a tent costs only $5 at a garage sale and is just as large as one of the best competitor, but leaks when it rains, it is just not an actual contender. Nonetheless, the ratio would likely show it because the “best value” alternative. For an identical reason, price needs to be kept separate from the attributes in MADM and used only as a constraint or tradeoff.

Conclusion

Now that you just understand how MADM works, its shortcomings are easier to see. It has a bent to overlook certain details in decision-making by generalizing every part right into a single rating and assuming linearity across all attributes (i.e., a rise from 70 inches to 71 inches is treated as equally beneficial as a rise from 40 inches to 41 inches, which might be not the case).

It’s essential to know the mechanics of MADM to understand the advance achieved by adopting this next method. Within the second a part of this two-part series, I’ll propose a substitute for MADM that preserves its strengths while yielding recommendations more closely aligned with decision makers’ priorities.

Creator Note

In case you enjoyed this, I write about analytical reasoning, decision science, optimization, and data science. I also share latest work and related thoughts on LinkedIn.