Engineering Skills for Life: The Decision Matrix

Some things I learned in my engineering classes I can safely forget after the test, like whether Faraday came before Oersted, or after.  Other things I’ll want to remember not only for my [theoretical] future engineering career, but also for life.  Things like how to make a two-liter bottle fly as far as possible, or the steps for completing a complex team project by the deadline.  This second category is the kind of things I want to share with you.

The decision matrix is a tool for making complex choices.  It does this by laying out all the relevant criteria, how well each possible solution fulfills each, and how important they are relative to each other, kind of like an in-depth pros and cons list.  Once complete, decision matrices generate scores to compare.  Decision matrices work best when you have only a few options and lots of criteria.  Since personal preferences factor into the decisions we make, one person’s decision matrix will look different from anothers, even if they’re considering the same choice with the same options.  Here I’m going to use the example of deciding what kind of pet to get.

1.  Figure out what options you’re choosing between.  List every serious option.  With open-ended decisions, a brainstorming session can help generate creative solutions to consider.

Let’s evaluate a rabbit, a goldfish, and a parakeet.  We put these at the head of columns in the decision matrix:

Rabbit Goldfish Parakeet

2.  Figure out what the null option is.  The null option is what happens if you don’t make a decision, or if you leave things how they are currently.  This might not be a serious option, but you want to be able to compare it to actual options.  It also explicitly shows that not making a choice is, itself, a choice.

The null option here is not getting a pet.  We add that as an option, alongside the options we’ve already listed.

Rabbit Goldfish Parakeet No pet

3.  List all the relevant criteria you want to evaluate your options by.  Make sure to actually include everything you want to consider.  If you finish your decision matrix and find yourself saying, “Yeah, but I don’t feel like…” or “Sure, but this doesn’t take into account…” then your decision matrix is not functioning properly.  Take everything into account, including subjective things like how you feel.  Feelings are a legitimate part of decision making, so it’s appropriate to include criteria for desire, nostalgia, general impressions, etc.

We want to include both objective criteria, such as cost and time commitment, as well as subjective criteria, such as cuteness.  The criteria go in a column on the far left.

Criteria Rabbit Goldfish Parakeet No pet
Cost
Allowed
Time commitment
Smell
Cuteness
Playfulness
Trainability
Number of legs
Travel

4.  Some criteria should be more important than others.  To reflect this, assign a numerical weight to each criterion.  More important criteria should have a higher weight than less important ones.  Technically, the math works out using numbers of any size, but I recommend using whole numbers between 0-20.  Assigning a criterion a weight of zero indicates that this criterion has no impact whatsoever on your decision.  The results would be the same if you left the criterion off the matrix entirely, but you may choose to write it down with a weight of zero to show that you didn’t forget about it, you just decided it had no importance.

Weights go in another column, directly to the right of the Criteria column.  We have lots of free time to spend caring for and playing with our pet, so we care a lot about being able to train it, and not so much about the size of the time commitment.  A different person might have different priorities.  We also decide that we don’t have any reason to care how many legs our pet has, so we give that criterion a weight of zero.

Criteria Weight Rabbit Goldfish Parakeet No pet
Cost 15
Allowed
Time commitment 5
Smell 12
Cuteness 18
Playfulness 20
Trainability 18
Number of legs 0
Travel 3

5.  If one of your criteria isn’t just more important than the others, but is absolutely necessary for a viable solution, you will have a hard time assigning it a weight.  One way to deal with this problem is to just assign it a ridiculously high weight (like 100).  Otherwise, you can mark it specially, and remember at the end to eliminate any options that don’t satisfy the requirement.

We can’t have any pet that isn’t allowed in our building.  Instead of assigning a weight to the Allowed category, we mark it with a star to indicate that it is a requirement.

Criteria Weight Rabbit Goldfish Parakeet No pet
Cost 15
Allowed  *
Time commitment 5
Smell 12
Cuteness 18
Playfulness 20
Trainability 18
Number of legs 0
Travel 3

6.  Consider how to translate the criteria you’ve chosen into numerical scores.  For each criterion, you will have to assign each option a score from 0-10, with ten being the best, based on how well it fulfills that criterion.  It is very important to be consistent in assigning these scores;  if Option A has a higher score for one criterion than Option B, that should definitely always mean that Option A is that much better at that criterion than Option B.  To ensure consistency, some people write out ahead of time how each criterion should be evaluated, e.g. “Distances from 0-12m are assigned 1, 13-15m are assigned 3, 16m are assigned 10, and 17+m are assigned 6.”  Make sure that the lowest score possible is zero and the highest score possible is ten.  If a criterion is binary rather than gradient (if a thing can either succeed or fail, without any shades in the middle,) then give successes a 10 and failures a 0.

We’ve filled in scores from 0-10 for each type of pet, as well as the null option of not getting a pet.  Notice that because a higher score is always better, and we want a small time commitment, that pets with larger time commitments get lower scores.  The same is true for cost.

Pets are either allowed or not, so all the scores in the Allowed row are either 10 (allowed) or 0 (not allowed.)  Also notice that the null option of not getting a pet usually either completely succeeds or completely fails at each, so its scores are all 10’s and 0’s.

Criteria Weight Rabbit Goldfish Parakeet No pet
Cost 15  4  8  5  10
Allowed *  0  10  10  10
Time commitment 5  6  9  4  10
Smell 12  7  10  9  10
Cuteness 18  6  2  10  0
Playfulness 20  7  1  8  0
Trainability 18  5  0 8  0
Number of legs 0  10  3  7  0
Travel 3  8  0  4  10

7.  Now that you’ve done all the hard work, it’s time to see your final scores!  For each option, multiply each score by its weight, then sum the products.  If you chose to mark any requirements with a star, skip these when calculating the final score.

Here is just the Rabbit option, by itself, showing the weight times the score.  The weight times the score isn’t shown in the full results because there’s not room for it, but that column is the one we’re actually adding together.

Criteria Weight Rabbit [Weight x Score]
Cost 15 4  60
Allowed * 0
Time commitment 5 6  30
Smell 12 7  84
Cuteness 18 6  108
Playfulness 20 7  140
Trainability 18 5  90
Number of legs 0 10  0
Travel 3 8  24
Total  536

And here is everything all together:

Criteria Weight Rabbit Goldfish Parakeet No pet
Cost 15 4 8 5 10
Allowed * 0 10 10 10
Time commitment 5 6 9 4 10
Smell 12 7 10 9 10
Cuteness 18 6 2 10 0
Playfulness 20 7 1 8 0
Trainability 18 5 0 8 0
Number of legs 0 10 3 7 0
Travel 3 8 0 4 10
Total  536  341  699  350

8.  Evaluate the decision matrix.  First, if you marked any required criteria with stars, eliminate all the options that do not meet the requirement.  Next, look at the total scores for the remaining options.  If everything up to this point has been correct, the option with the highest total score is the one that best fits your criteria, and should therefore be the best option.

Because rabbits are not allowed in our building, we eliminate rabbits as an option for a pet.  The remaining options are goldfish, parakeet, and [no pet].  Comparing the total scores, we find that the parakeet has the highest score, with 699, and therefore is, overall, best at the things we value most in a pet.  We decide to get a parakeet.  We also notice:

  • Even if rabbits had not been eliminated, parakeets would still have been the better choice, since their score of 699 is higher than the rabbits’ score of 536.
  • Parakeets did not beat rabbits in every category, but the categories rabbits scored better in were not weighted as highly as others.
  • Having a parakeet or a rabbit is much better than not having any pet, but having a goldfish is actually worse than having no pet.  Looking at the scores, we see this is because a goldfish takes time and money, but cannot be played with or trained and is a travel concern.
  • Although we assigned scores for how many legs each type of pet has (apparently four legs is ideal,) these scores had no impact on the final scores, because the category has a weight of zero, and anything multiplied by zero is zero.
  • The highest possible score is 10x the sum of the weights, or in this case, 910.  None of the options even got close to this, but that’s to be expected, since a perfect score would indicate a pet that costs nothing, requires no care, smells like daisies, is the cutest, smartest, most playful animal, and can travel anywhere without problems.  This is one reason it makes more sense to compare the options to a null option, no pet, than to a perfect score, which is virtually unattainable.

 

If, at this point, you look back on your decision matrix and think to yourself, “This doesn’t value … highly enough,” or “I should have considered the impact of …” then it’s okay to go back and adjust weights, or add criteria you forgot about.  But be wary of doing this too much.  Decision matrices are meant to be used as a tool to make the best choice, not a way to justify the choice you were going to make anyway.

If, at this point, you’re thinking to yourself, “This may be a logical way to make a decision, but it’s so cold and objective, and there’s all kinds of important feelings that come into buying a pet…” then you’ve misunderstood.  Go back to step 3 and list everything important about making this decision, including all of your feelings, and weigh them according to how important you actually think they are.  If you’ve done that, the end results do show you your best option.  This requires you to be brutally honest with yourself.  If you value your instincts in decision-making, then include “instincts” or “gut feeling” as a criterion, and weigh it appropriately.  If you don’t actually care how eco-friendly your solution is, give that category a weight of zero.  Arguing that the results of a decision matrix don’t reflect your values is equivalent to saying that you lied when you wrote down what was important to you.  Decision matrices don’t give cold, logical results unless you tell them to, but they do give objective ones.

Thanks for reading!  I hope that this tool is helpful for you.

— S. Jack

One thought on “Engineering Skills for Life: The Decision Matrix

  1. Awesome blog. I added the RSS feed to my reader so I’ll get all your posts.

    I had a super long question that would prove I read this thoroughly, but I answered it in the process of writing it out. So all I can say is, this is a great idea that I badly needed for a decision I have to make in the next couple of days. Thank you so much.

    Like

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