I’ll immediately explain my irony about 2×2 matrices, but before a little bit of context: last week, a friend of mine lent me a book to read; he had it in his (anti-)library for years and never read it. Since he knows my study addiction, he just said, “You’ve already read dozens of books on critical thinking and decision-making, then read this one too”. So I opened it and “studied” in more or less half day. It’s not that I am a kind of learning master, just above the average, but I knew already most of the models and, moreover, the basic ideas behind them: the idea of drawing things (physical objects or abstract concepts) while displaying values of 2 or more “parameters”. This is something pretty common in Engineering (STEM in general) and I love infographics and data visualization, I really consider some dashboards/plots as a masterpiece or as a great way to disrupt your previous point of view on some topics.
“The decision book”, wrote by Mikael Krogerus and Roman Tschäppeler, tries to summarize/list some of the major schemes/matrices known in the field (the authors are in consulting sector). Actually, if you’re interested even a little bit on the topic, probably you found some of these pictures styles even during shopping. For example, if you like single malt Scotch whisky, you may have seen this map before, to help you decide which bottle you want to taste:
The concept behind the construction of these charts is easy and immediate: with 2 dimensions, you can represent a space where you can put points representing a couple of values (thank you René Descartes).
Honestly, if I have to talk about my flavors (I mean, in general, not about whisky), I prefer multi-dimensional schemes, since I want to compare multiple features at once, not only 2, that’s why I already showed some scheme in my decision process, like the ones I suggest when you may want to see if it’s time to change a job or some aspect of your life (e.g.: Searching for a job…) – some radar diagrams can be useful for the scope.
Important notice before drowning in all the matrixes: sometimes better having more “resolution” rather than just 4 boxes, more like “a continuum” in x and y axis – same way as the whisky chart above, not just inserted in the boxes, but with relative weight/positions, since Oban and Cragganmore are much more similar compared to the difference, in the same 2 quadrants, between Ardbeg and Lagavulin.
IMPORTANT: I recap here the first edition of the book (2008) and, as always, what you’ll find between parenthesis are just my opinion/notes/ramblings/delusions/… – and, as I always write: please, remember that this is just a quick recap of the book, go and buy it (possibly, the last edition, fully revisited as the authors wrote).
1. What is a decision making-model
Models are great, remembering that “Map is not the territory” (see The Great Mental Models – General Thinking Concepts), they can be used to faster visualize options (specially when you’re paralyzed in “The paradox of choice”).
The authors remember that models they presented follow these criteria: they:
- simplify, focusing on certain features/aspects of reality;
- are pragmatic;
- sum up, like executive summaries;
- are visual;
- organize, providing structures;
- are methods, so they can’t automatically come up to a conclusion, rather they facilitate questions.
The authors grouped the models in 4 sections, I can draw them in a map:
2. How to improve yourself
2.1 The Eisenhower matrix
One of the most famous matrices, used to group tasks in the 4 quadrants, depending if they are urgent or not, important or not: don’t confuse importance with urgency!
2.2 The SWOT analysis
Another 2×2 famous matrix, to spot Strengths, Weakness, Opportunities, Threats – hence the acronym.
2.3 The BCG box
Again 2×2 matrix, grouped on market growth low/high and relative market share low/high, to evaluate cost and benefits.
For more details, here.
2.4 The project portfolio matrix
If you are a slasher, like Marci Alboher described people doing multiple things/jobs (like “Multipotentiate”, but actually doing something for real, not just dreaming), you can use another 2×2 matrix again, to visualize your activities in costs – including effort, time, etc. – and results. Or you can even represent two costs variables, like money in an axis and time in the other one.
2.5 The John Whitmore model
Since S.M.A.R.T. was not enough (even if I kindly remind you that sometimes is better to Be smart: set some NON-SMART goals!), other 2 words aside, so 3 words for a total of 14 points – it’s worth noting that often better the KISS approach: Keep It Simple, Stupid.
- SMART (Specific, Measurable, Attainable, Realistic, Time bounded);
- PURE (Positively stated, Understood, Relevant, Ethical);
- CLEAR (Challenging, Legal, Environmentally sound, Agreed, Recorded)
2.6 The rubber band model
When dealing with pros and cons in a choice, think yourself like trapped by two elastic bands, one forward and one backward (or as psychologists can say: the two levers, e.g.: running from pain and searching for pleasure – or: both desire and fear to change).
2.7 The feedback model
To deal with others’ compliments and criticism, you can divide – yes another 2×2 matrix – in advice, criticism, compliment and suggestion. Focusing on suggested actions and ignoring the non-actionable comments.
2.8 The family tree model
Humans are social animals etc… So you can use this model for company brand (or personal brand) to improve/expand your reach, since some people/customers will discover your product and will speak to others, but you may want to expand your customers’ network/chain the most (in other words: maximize/diversify your circles to expand more and limit “concentration”/”intersections”). Try to distance/expand toward more distant targets, since they will grow/expand in different directions, reaching different people.
2.9 The morphological box and scamper
In 1930, Swiss physicist developed a problem solving method involving combination of what exist to create a new solution (see also: “Range” by Epstein). Bob Eberle and Alex Osborn created an acronym to help you “dealing with things” to guide a little bit your creativity: SCAMPER (Substitute, Combine, Adapt, Modify, Put to other use, Eliminate, Reverse).
2.10 The Esquire gift model
Another 2-axis graph, from Esquire magazine, to evaluate how much spend for a gift/present to someone for some events, considering time you know the person
2.11 The consequences model
Yes, another 2-axis graph, x=time and y=extent (I am curious on how you can quantify it) by Kreiner and Christensen to show that at the beginning of a project/activity you know little but it’s often at that time that your decisions can have a big impact; going forward in time, you’ll know probably more but decisions will probably have little impact.
2.12 The conflict resolution model
To resolve a conflict there are usually up to 6 ways to act: Flight (lose lose), Fight (win lose), Give up (resulting often in lose-win situation), Evade responsibility (lose lose involving others), Compromise (win lose, win lose – both partially), Reach a consensus (win win… sure?). These actions are represented as moving from emotional to rational reaction (not so sure, think about reach consensus in nationalism).
2.13 The crossroads model
Inspired by The Grove’s “the personal compass”.
A mix between values, goals, etc… considering:
where have you come from, what it’s important to you, which people are important to you, what is hindering you (preventing you to do something), what are your fears.
You can then follow: something you always wanted to try, the wildest dream, the road you feel more sensible (according to your values and “global” values), a road not travelled, keep going, going back to a place you felt safe.
3. How to understand yourself better
3.1 The flow model
Taken by Mihaly Csikszentmihalyi’s concept of desirable difficulty when we’re in a flow, involving usually: intense focus, our choice, not too much and not too few difficult, with clear objective and immediate feedback. So we can draw a diagonal line between the 2-axis challenges vs. abilities: below is under-challenged, above is over-challenged.
3.2 The Johari window
See this famous… another 2×2 matrix.
3.3 The cognitive dissonance
People smoke even if they know is unhealthy, as Leon Festinger used the term “cognitive dissonance” to describe when we live not accordingly to our principles/beliefs. We can escape this dissonance by changing either our behavior or our attitude (see How (yet another book on) Atomic Habits made me think and a lot of other books/courses).
3.3 The music matrix
Another 4 quadrants space, where to classify artists from mainstream to avantgarde and from authentic (?) to designed.
(this is not too accurate since some artists are not “points” but rather “areas” or multiple-spots since they can produce different kind of music, let’s think of a lot of progressive rock bands or prolific experimental artists like Frank Zappa).
3.4 The unimaginable model
We can put theories/models in a 4 quadrants chart again, from provable to not-provable and from unimaginable (e.g: quantum physics, black matter) to imaginable.
3.5 The Uffe Elbaek model
This is about perceptions of ourselves, either by ourselves: how we see it now and how we would like to be in the future; plus how we are seen by other: how they see us now and how they would like to see (their expectations).
We can draw values in a radar diagram (finally, more features) and move toward the right direction to “fill the gap” between current state and desired one.
3.6 The fashion model
2-axis, past to future, reality to appearance (the last two are basically the percentage of cost for signaling).
Another: 2-axis, casual to formal, hip to old school.
3.7 The energy model
Are you living in the here and now?
We can draw us, a group or even a State, in percentage of how much we’re living thinking of the past, present and future. Basically 3 models: memory-driven if allocating more percentage to past; dream-driven if orientating to future; reality-driven if focusing on the present.
(In my humble opinion, this is way too semplicisitic!).
3.8 The supermemo model
How to remember stuff?
Piotr Wozniak plotted a 2-axis chart with curves on likelihood to remember vs days from something learnt, the so-called “curves of forgetting” (Important note here: actually studied before, started at least with Hermann Ebbinghaus, see also Spaced Repetition).
3.9 The political compass
Another 2-axis, liberalism/anarchy to authoritarianism/fascism, left/communist to right/neo-liberalism.
(If you’re interested, there’s even a website where you can check where are you in the political spectrum).
3.10 The personal performance model
3-axis diagram, to put 0 to 10 on each to find your shape on: have to, able to, want to (see: my post on how to find the “right” job for us, Deep Work, Ikigai, and many others).
3.11 The making of model
To determine your future, first understand your past.
Instead of creating a future from scratch, try to bind it to your past creating a link. So let go what you want to change and leave all the rest, focusing on what was involved at that time: people involved, goals at that time, successes, obstacles you overcame, what you learn.
3.12 The personal potential trap
“Such a promising kid!” (see also “Multipotentiate”).
Track: your personal expectations, people’s expectations of you, your actual achievements. Try to draw the 3 curves together in a timeline, with y-axis representing “the amount” (again this struggle to fake quantitative).
3.13 The hype cycle
When thinking about the “next big thing”, try to focus on: technology trigger, peak or inflated expectations, trough of disillusionment, slope of enlightenment (hype is over), plateau of productivity.
See all the graphs about it, e.g.: on Gartner.
3.14 The subtle signals model
Another 2×2 matrix, frequency vs effect of communication, to identify people you speak more/less with and that produce more effect on your work.
(I find it highly debatable).
3.15 The network target model
Think about your social circles: family, friends, colleagues, acquaintances. Then, the frequency you meet them. Finally, notice who of them are richer/poorer than you, younger/older, uglier/more attractive and so on.
(This is linked to the concept “you’re the sum of the 5 people you interact more”).
3.16 The superficial knowledge model
Another 2-axis chart, to put topics, from embarrassing to impressive, from easy to difficult.
(Ideally, you may want to go deeper and toward interesting and difficult topics, even if it’s not always the case).
4. How to understand others better
4.1 The Swiss cheese model
James Reason described some error results as the results of something (e.g.: security vector attack) going through several slices of Swiss cheese (e.g.: holes are human errors or vulnerabilities).
The are 3 types of mistakes: real mistakes, black-outs (e.g.: part of process forgotten or not-thought about the specific case, blindspots), slip-ups (bad implementation).
3 various levels: skill-based, rule-based, knowledge-based.
Various factors, involving: people, technical, organization, outside influence, etc.
4.2 The Maslow pyramids
Everyone who studied a few pages on Psychology knows it).
4.3 Thinking outside the box
(Not much to add, more than the title).
4.4 The Sinus Milieu and Bourdieu models
Useful to represent/describe groups, with axis like: social status from lower to upper classes; basic orientation from tradition to experiments-prone. It can be used to define also target for our product. Another 2-axis on groups: economical capital vs cultural capital
4.5 The double loop learning model
Reflecting from actions and learning from them. Focus on second-order (and/or to meta in the processes, see 2nd order and first principles in The Great Mental Models – General Thinking Concepts).
4.6 The AI model
AI = Appreciative Inquiry. In short: focus on what is going well and good attributes rather than weakness.
In a 2×2 matrix with destructive-constructive and negative-positive, we’ll have: the fault finder, like “idea is good, but…”; the dictator “no!”; the schoolteacher “the idea isn’t good because…”; the AI thinker “Yes and we can also…”.
(but please don’t fall into “The Stupidity Paradox”).
4.7 The small world model
The maximum 6-degrees of separation, by Milgram.
4.8 The Pareto principle
80/20 and its variations.
4.9 The long-tail model
More than just Pareto, see in general distributions that may have long-tail
(see also Taleb on fat-tails in his books like “Antifragile”).
4.10 The Montecarlo simulation
We can only approx a definitive outcome (see: often we discretize/quantize, with errors).
4.11 The black swan model
(See again Taleb, based on Popper/Russell turk).
4.12 The chasm – the diffusion model
Some ideas and objects spread, other no.
(See more in “The Tipping Point” and in Sociological theory of diffusion, Diffusion of innovations, and so on, remembering that develop can’t wait too much, etc).
4.13 The black box model
With growing complexity, we understand less and less of what we use. In a 2-axis chart of complexity and dynamic, we can move toward positive values in both direction, growing the study required to understand (otherwise: everything too complex become undistinguishible from magic, as better said here).
4.14 The status model
You can recognize a winner (?) in looking at spending habits of people and how they earned money: 2-axis, earned to inherited and altruistic to egoistic. You can find children of rich parents, new rich, and so on.
4.15 The prisoner’s dilemma
This is the classic about when it’s worth trusting someone
5. How to improve others
5.1 The Drexler-Sibbet team performance level
It can be used to align different people to a project/model, so you can lead a group to become a real team. Ask periodically (see: military style) how far is each one from the supposed level and what that person needs to reach that level.
5.2 The team model
This can be used to identify “levels” at each part of a project, e.g.: asking “Do i have the right people and resource?”, “Do we have the soft and hard skills required?”, “Are we capable of doing what I am expecting?” and then track over time the performance of each member, to identify strength and weakness. E.g.: Radar diagrams on each one on the required skill and see which person fit better for each task.
5.3 The gap in the market model
To recognize a good market idea, 3D graph on products’ aspects: cost-effectiveness, prestige and awareness. The last one is “how loud” is it (marketing, branding, …). You can identify a certain spot that is not yet “crowded” with objects in your sector.
5.4 The Hersey-Blanchard model
Situational leadership (different “progressive” styles when moving toward a certain direction over time, assuming growing in expertise).
Instructing in initial phase; then coaching; then supporting; finally delegating.
5.5 The 6 hats
To change your point of view, you can imagine to adopt, on same problem, 6 PoVs eah time wearing a different colored hat:
white: analytical; red: emotional; black: critical/risk; yellow: optimistic, best-case; green: creative; blue: structured, process, big picture.
In a team, there can be also 9 different profiles:
action oriented: doer, implementer, perfectionist;
communications-oriented: coordinator, team player, trailblazer;
knowledge-oriented: innovator, observer, specialist.
5.6 The result optimization model
Working in loops (rather than in fixed Gantt)
(See all the frameworks you may know, including Agile, Waterfall, continuous delivery and many others).
5.7 The world’s next top model
“When you only have a hammer…”.
Importance of data, simulation, beta-testing, but we still confront with reality.
(See also the new way of doing stuff without understanding the underlying formulas and models, like we do now like monkeys querying AI/ML).
Final consideration
Sure it’s a book you may find useful if you really never saw a 2×2 matrix in your life applied to critical thinking or decision making. But if you’re a seasoned professional like me, chances are that books like this are just too simple, it’s like having a 7th grade book between college books in your library (no offense here: just trying to help you to identify the best target).
(To my friend G.: you probably knew it! Thank you for making me waste half day, so I slowed down my race toward the knowledge :P).
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