Posts Tagged ‘matrix’

How to: Completing a tradeoff analysis

Friday, July 8th, 2011


You Are What You Decide asked: “So, how do you decide? Based on your gut intuition, a formal analysis of trade-offs, your core beliefs, multiple criteria, the alignment to your vision for a preferred future? Or something else?” There are many approaches to completing a formal analysis of trade-offs. This post will summarize two.

Important decisions include multiple, sometimes competing factors. A trade-off is the giving up of one thing in return for another. Just about every complex decision requires that you accept having less of one thing in order to get more of something else.

Ben Franklin’s trade-off tool


Ben Franklin’s trade-off tool provides a simple, intuitive way to weigh trade-offs. Create two vertical columns, one labeled “Pros” and one “Cons.” Brainstorm the two lists. Then pair an item or items from each list with an item or items of equal weight from the other list. These similarly weighted combinations of pros and cons cancel each other out. In the sample graphic, the pros outweigh the cons in the tradeoff “algebra.” No need for a more sophisticated tool to make the decision. The methodology could be taught to a young child.

Visualizing trades in a decision matrix


The beauty of a decision matrix is that you can easily manage the tradeoff analysis because you can see where the trade-offs are.

A previous three-part post described how to complete a multi-criteria analysis. Part 3 illustrated how to construct a decision matrix using the example of the college selection process.

The matrix above displays the final results of assessing three colleges against a set of weighted criteria. The cells with the red border represent the highest score on each criterion. The “Total Benefit” is the sum of the weighted scores. As you can see, the matrix helps to clarify the decision’s specific trade-offs by individual criterion.

These results might lead a family to decide to select Syracuse because it has the highest Total Benefit score and scores highest on three criteria: Distance, Clubs and Food. However, the trade-offs are also clear. Delaware is superior on two criteria: Social Life and Facilities. Temple, on one: Major. The decision framework creates clarity: by selecting Syracuse, the family achieves the greatest Total Benefit but gives up on superior Facilities, Social Life and Major.

The challenge of any complex decision is how to clarify, manage and evaluate the trade offs. Ben Franklin’s trade-off tool and a decision matrix each complete the task in different ways. How do you manage trades in your decision-making?

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How to: Multi-criteria Analysis – Part 3

Thursday, May 19th, 2011


A multi-criteria analysis is a formal decision process you might use when making a weighty decision. This is the final of a three-part post that walks you through the process, step-by-step.

Part 1:

  • Step 1: Complete your research
  • Step 2: Generate and weight criteria (i.e., define your desired outcome)

Part 2:

  • Step 3: Identify and/or create options, alternatives or solutions
  • Step 4: Complete a side-by-side comparison

Part 3:

  • Step 5: Objectively assess each option against each weighted criterion
  • Step 6: Make your decision


Step 5: Assess each option against each weighted criterion

Having completed your research, articulated a set of weighted criteria, converged on a rich set of options, and completed your side-by-side comparison, you now need to objectively assess each option against each weighted criterion. Let’s continue with the example of the Elmsford facilities task force.

First, task force members reviewed their completed side-by-side comparison and used a 1 to 9 scale to score the three facilities options against the 11 criteria on a worksheet. Then, in subgroups, they shared their worksheets and began to converge on reasonable, evidence-based scoring for each cell. Finally, the whole group used Prism’s group decision support system to vote all the cells in the decision matrix. After all 33 cells were complete, the system automatically calculated the weighted scores in each cell and the total benefit (i.e., the sum of the weighted scores) for each option. See chart below.



Returning to the example of college selection: if you do not have access to sophisticated decision support technology, you can complete your decision matrix using a chart and calculator or a spreadsheet. For your convenience, you can download a working spreadsheet.

Simply follow the directions on the spreadsheet to enter your

  • Decision criteria across the top row of the matrix (completed in Step 2)
  • Criteria weights (completed in Step 2)
  • Options down the first column (completed in Step 3)

While referring closely to your side-by-side comparison, score each option against each criterion in the appropriate cell. You can use a 1-9 scale or you can limit your scale to the total number of options (e.g., if you had four options, the scale would be 1-4). By the way, the download does all the matrix calculations automatically. See sample completed matrix below.


Step 6: Make your decision

With your decision matrix complete, you should now be prepared to make a confident, sound decision. You can

  • Compare the total benefit of each option against the set of weighted criteria
  • Examine the specific trade-offs
  • Create scenarios by changing the decision criteria weights

Regarding trade-offs: a trade-off is the giving up of one thing in return for another. Just about every complex decision requires that you accept having less of one thing in order to get more of something else. The beauty of a decision matrix is that you can easily manage the tradeoff analysis because you can see where the trade-offs are.

In the college selection example, a family might decide to select Syracuse because it has the highest Total Benefit score and scores highest on three criteria: Distance, Clubs and Food. However, the trade-offs are also clear. Delaware is superior on two criteria: Social Life and Facilities. Temple, on one: Major. The decision framework creates clarity: by selecting Syracuse, the family achieves the greatest Total Benefit but gives up on superior Facilities, Social Life and Major. (See annotated chart below, highlighting the trades.)


Of course, the matrix above begs a powerful question: Is Syracuse University, a private institution, worth the more than 40% premium it charges in tuition, room and board and fees over public institutions such as Temple and Delaware? Put in quantitative terms, is it worth spending a 40% premium to attend Syracuse instead of Delaware if Syracuse only provides an 18% additional Total Benefit (236 points versus 200 points)?

Returning to our other example, the Elmsford facilities task force could not make a decision based solely on their multiple criteria matrix. They needed to take one more step and complete a cost-benefit analysis. A family looking to maximize its return on their college investment may want to do the same.

A future post will describe how to complete a cost-benefit analysis.



“Decide” image credit mattw1ls0n

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How to: Multi-criteria Analysis – Part 2

Tuesday, May 3rd, 2011


A multi-criteria analysis is a formal decision process you might use when making a weighty decision. This is the second of a three-part post that walks you through the process, step-by-step.

Part 1:

  • Step 1: Complete your research
  • Step 2: Generate and weight criteria (i.e., define your desired outcome)

Part 2:

  • Step 3: Identify and/or create options, alternatives or solutions
  • Step 4: Complete a side-by-side comparison

Part 3:

  • Step #5: Objectively assess each option against each weighted criterion
  • Step #6: Make your decision

Step 3: Identify and/or create options


Having completed your research and articulated a set of weighted criteria, you now need to converge on a rich set of options. Let’s continue with the example of selecting a college.

Whenever you are generating alternatives, always diverge broadly. Avoid what psychologist refer to as “premature closure.” That is, you don’t want to converge on a set of options before you have explored all possibilities; otherwise, you risk leaving an optimal choice off the table.

As mentioned in Part 1, no decision-making process is linear. Therefore, the reality is that options are being explored during research (Step 1) and while generating and weighting the criteria (Step 2). For example, an aspiring college student and her family may begin the decision process with a preliminary list of possible colleges. That list may then grow to a dozen and perhaps as many as 20 colleges as they complete research and begin to articulate criteria.

Once all options are on the table, apply your decision criteria as a “first sort” to filter out suboptimal choices and to begin to converge on the final set of options that will require more intense scrutiny. During the research and criteria generation phase, my daughter’s list grew to as many as 16 colleges and then was slowly pared to just three schools.

Returning to the example of the Elmsford facilities task force case study: whereas they began by considering five robust facilities scenarios, they quickly converged on three final options:

  • Demo the old Dixson primary and build a new one
  • Renovate Dixson primary
  • Renovate the grade 2 – 6 Grady Elementary to accommodate all students PK-6

Step 4: Complete a side-by-side comparison


Creating a side-by-side comparison is not rocket science. Simply build a table with your options listed across the top and your criteria listed down the side. From your research, add quantitative and qualitative evidence of each option’s “contribution” to each criterion. The Elmsford task force created an evidence-based side-by-side comparison of their three options against the 11 criteria (see sample below).

The side-by side comparison template is generic and can be used for any multi-criteria decision. For the college selection decision, simply place the names of the institutions still in the running across the top and the decision criteria down the side. Then complete the side-by-side comparison by entering factual data, either quantitative or qualitative, that objectively demonstrates how each option contributes to each criterion.

At this point, you have a solid decision framework that includes your final options, weighted criteria and clear evidence of the contribution of each option to each criterion. In How to: Multi-criteria Analysis – Part 3, we discuss how to advance this framework by assessing each of the options numerically against the weighted criteria and then making the decision!

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How to: Multi-criteria Analysis – Part 1

Monday, April 18th, 2011


You Are What You Decide asked: So, how do you decide? Based on your gut intuition, a formal analysis of trade-offs, your core beliefs, multiple criteria, the alignment to your vision for a preferred future? Or something else?

This three-part post will walk step-by-step through a multi-criteria analysis, a formal decision process you might use when making a weighty decision. Here are the steps:

Part 1:

  • Step 1: Complete your research
  • Step 2: Generate and weight criteria (i.e., define your desired outcome)

Part 2:

  • Step 3: Identify and/or create options, alternatives or solutions
  • Step 4: Complete a side-by-side comparison

Part 3:

  • Step #5: Objectively assess each option against each weighted criterion
  • Step #6: Make your decision

The steps are listed linearly for ease of understanding. But rarely does a decision process unfold without iteration. Thoughtful multi-criteria analysis leads you to loop back-and-forth between steps, clarifying and refining your thinking as you go. For example, although you may begin with an initial set of options, that set will likely be refined and enriched as you complete your research, generate and weight criteria, apply the criteria and move to decision-making.

Step 1: Complete your research


Whether buying a car or house, choosing a college or making some other consequential choice, you need first to become well informed.

  • What do I need to know?
  • What are my requirements?
  • Are there constraints?
  • What are the options?
  • How can I compare those options fairly?

In my experience, folks make two critical mistakes at this phase of decision-making. They do not invest sufficient time or resources in research, and they move to decision-making before they have investigated a wide range of options.

Consider the college search process. In terms of financial investment, it is one of the more significant decisions a typical family will make. In New York State, the total four-year investment at a public institution approaches $80,000 and at a private institution often exceeds $200,000. In some cases it tops out at $250,000.

Nonetheless, it is common for overwhelmed families to skimp on or rush through the information gathering phase. I have heard parents remark that they couldn’t afford to purchase the standard college guides, such as the Princeton Review ($22.99), because they are too expensive! I know students who neglected to use amortization calculators to determine the true cost of their student loans, both in terms of monthly payments and total payback with interest. Families often visit few college campuses before making their final selection. The consequences of these short-cuts are predictable. For example, after dropping her child off at college for the first time, a mom I know lamented: I was surprised how rural it was.

Multi-criteria case study

Consider this case study. Prism recently facilitated a diverse team of school district stakeholders through a successful multi-criteria decision. The Elmsford Union Free School District facilities planning task force was grappling with a complex decision. Elmsford’s Dixson Primary, a PK-1 building built in 1894, enjoys the love of many community stakeholders but is considered woefully inadequate to serve the needs of its students. The issue is emotional and many task force members arrived with preconceived notions: some, that the building needs to be closed; others, that building should be renovated. There was conflict and disagreement.

The planning process required that the team step back from their preconceived notions and thoroughly research the issue. For example, they spent considerable time walking through the facilities and researching state education law, financing and other issues. They needed to build a shared knowledge base so that their conversations — including their disagreements — could be informed by fact wherever possible. As shared knowledge grew and many untested assumptions proven invalid, the conversation became less polarized and more informed.

Step 2a: Generate criteria


Once they were well-informed, the task force began to list its criteria. A criterion is a standard, rule, or test on which a judgment or decision can be based. For example, if you are buying a house, a criterion might be “number of bedrooms” or “size of the yard.”

The Elmsford task force went through a creative process, diverging to consider many criteria and then converging on a final set of eleven. They defined their criteria clearly and simply, using a few words, like a book title, followed by a succinct definition. They agreed to eleven criteria, including “Multi-purpose: there is a large, multi-purpose room that has a stage and that can accommodate the school population” and “Flexibility: the facility has the flexibility to accommodate short- and long-term growth,” among others.

A family selecting the best college can use a similar process. Using 3 x 5 cards, articulate one criterion per card until all possible criteria have been listed. As a family, share, clarify, combine and refine your criteria. Then converge on a final set. Like the Elmsford task force, you will have defined your desired outcome and now know explicitly what you want to achieve. In the parlance of IT professionals, you will have completed your requirements analysis. Or, simply put, now that you know what you want, you just might get it.

Step 2b: Weight criteria


With the decision criteria agreed to, you can now weight them. First, order the final set of 3 X 5 cards in declining order of relative importance. Then assign a weight (between 0 – 100) to each criterion, making sure that the sum of all weights totals 100. Then begin to build a decision matrix, either using a table or, preferably, a spreadsheet. Place the weighted criteria in the top row. Later, you will add the options into the first column. See the sample decision matrix above. Or feel free to download the working spreadsheet.

The Elmsford task force used Prism’s Group Decision Support System to weight their criteria by completing a paired comparison analysis. View their results in the chart below.

Having identified and weighted your criteria, you are well on your way to creating a sound decision framework. In How to: Multi-criteria Analysis – Part 2, we discuss how to advance this framework by adding a set of options and completing a side-by-side comparison.




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Channel Your Inner Crayfish Brain

Monday, June 28th, 2010


When making decisions, do you struggle with cost-benefit anaylses? Well, here is motivation for you to improve that skill: According to ScienceDaily, “Crayfish make surprisingly complex, cost-benefit calculations.” The findings are from a University of Maryland study.

A crayfish has two defense mechanisms against predators: to freeze and hope the predator does not recognize it as a food source or to escape quickly by flipping its tail and swimming backwards. The Maryland study offered the crayfish “stark decisions — a choice between finding their next meal and becoming a meal for an apparent predator.” The crayfish could freeze and “remain close to a food source while at risk of being eaten by the predator” or it could flip its tail and escape the predator but put “critical distance” between it and its next meal.

How did the crayfish do when confronted with this clear cost-benefit dilemma?

The study concluded that crayfish are decisive decision-makers and adept at making trade-offs. “They carefully weighed the risk of attack against the expected reward” and took action “in a matter of milliseconds.” Their risk-benefit calculus was clear: when a predator was “moving too rapidly for escape,” the crayfish would not tail flip but freeze in order to remain close to the food source. On the other hand, when a threatening predator moved more slowly, the crayfish would tail flip to escape while sacrificing proximity to the food source.

Hey, if a crustacean can do it, we can do it! How do you calculate costs and benefits when making a decision? What is your decision calculus? Here’s a formula for you to consider:

Value = (Benefit – Cost)

When making decisions, you should always seek the highest value solution — that is, the solution that delivers the greatest benefit for its cost. Put simply, a good solution is worth more than it costs, and a bad solution costs more than it is worth. For example, let’s say you have three solutions to a challenge or opportunity:

- Solution A provides the greatest benefit at a cost of $X.
- Solution B provides 93% of the benefit but at 60% of the cost of Solution A.
- Solution C provides 60% of the benefit at 55% of the cost of Solution A.

What would you do? In this simple example, Solution B is the highest value option:

- Solution B provides 93% of the benefit but at 60% of the cost of Solution A.
- Solution B provides significantly greater benefit than Solution C at about the same cost.

Easy in concept; harder in execution. I know.

A future blog post will discuss the value formula above in greater detail. In the meantime, please see two current posts, Ben Franklin’s Trade-off Tool and The Matrix, for additional information on managing trade-offs and making cost-benefit decisions.

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The Matrix

Thursday, February 11th, 2010


Struggling with a tough decision? Wavering back and forth, unable to make up your mind? Very likely your frustration results from thinking about a complex problem—like buying a house—one factor at a time. To attack a complex problem and keep track of its multiple factors, create a decision matrix:

  • Down the left side, enter your options. Across the top, list your decision criteria. A criterion is an objective test upon which a judgment can be made.
  • Assign a weight to each criterion to indicate its importance to a good decision. The weight is usually a number between 0.0 and 1.0 with the sum of the weights equaling 1.0.
  • Then, one column at a time, ask: “To what degree does option 1..2..3 contribute to criterion A..B..C?” Use a simple scale where 5 = Highest Contribution and 1 = Lowest Contribution.
  • Multiply the score in each cell by the criterion’s weight.
  • Then add across the rows to determine a total, weighted score for each option.

You should now have a deeper understanding of the relative value of each option. Hey, maybe you’ll even be able to make the decision!

Use the illustration below to build your decision matrix. For a comprehensive explanation, see our three-part post on multi-criteria decision-making. Alternatively, visit “Let Simon Decide,” a pretty effective online tool for matrix decision-making.


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