Chapter Four

Map the solution space – Explore alternatives

So far, we have framed the problem in the form of a quest that clearly specifies the hero, the treasure and the dragon. At this point, it can be immensely tempting to jump into pursuing the treasure using whichever solution that first occurs to us. But, often, the obvious solution isn’t the best one, and letting our autopilot (our System 1 thinking) take the lead would result in a suboptimal approach.1

Consider the example of a global business services company with operations in Australia. The country manager wanted $20 million from headquarters to pursue a new business opportunity. When her proposal was turned down, her initial reaction was to resign. But her team persuaded her to explore other ways of pursuing the business opportunity, such as partnering with another organisation, which eventually proved successful. Stepping out to look beyond the obvious solutions can be valuable.2

This chapter shows how to avoid this common pitfall, providing a systematic approach to explore wide-ranging options that can be developed into concrete alternatives.3

The process is the same as the one we used for uncovering root causes.4 First, we use divergent thinking to generate options, drawing a how map. Once we feel that we have exhausted our creativity, we use convergent thinking by summarising the potential options into a set of concrete alternatives that we feel have the greatest potential. We’ll then compare the benefits and drawbacks of the alternatives in a systematic manner (see Chapter 6).

 MOVE LEFT TO RIGHT BY APPLYING THE FOUR MAP RULES

Effective how maps obey the same four map rules as effective why maps with only minor changes owed to the different type of question asked. Let’s review them.

Mapping rule 1: How maps answer a single how question

The how map answers a single question, typically of the form: ‘How may [the hero] get [the treasure].’ For instance, ‘How may we increase our company’s profitability, given that . . . ?’ Notice the delicate phrasing of the question: ‘How may we’ or ‘How might we’ but not ‘How should we’. This is to promote exploring ideas, even seemingly absurd ones, by delaying their evaluation to a later stage. We’ve stolen this approach from design thinkers, who deliberately choose their words to create space for maximum freedom of thinking.5

A tree diagram for how question.

An important implication is that every single node in the map – the options – must answer the full question without the help of another node, that is, independently. To explain, let’s look at an example. If you answer the question ‘How may I go from NYC to London?’ with ‘By travelling by sea/air/ground’, each of these options is independent: it answers the question without requiring the support from another option. You can think of them as channels.

A diagram shows the steps and channels for a question.

In contrast, you might be tempted to answer the same question by listing what you would need to do to get from NYC to London; say, choosing a means of transportation, purchasing a ticket, and going to the airport. But those steps aren’t independent: to get from NYC to London, you need to do each one of them. In other words, those aren’t options but steps in a process. Successful how maps use channels, not steps in a process.

Mapping rule 2: How maps go from the question to alternatives

To draw your map, use two questions. Horizontally, ask how, typically three times or more. Vertically, create new branches by asking what else? This will lead you to chart out the solution space, identifying ever more precise (from left to right) and ever more creative (up and down) options. Continue asking ‘how’ until the options are concrete enough for you to envision how they could be implemented. For instance, one way how to get from NYC to London is to fly in an economy seat on BA 1511.

Just like with why maps, write each node in a how map as a full declarative sentence so that it states a complete idea that answers the question, not just a title. For example, if you want to increase the number of clients that your company has, instead of just saying ‘competitors’ clients’, be more precise by stating: ‘by acquiring the clients of our competitors’. A node’s structure is always ‘By [action verb]-ing . . . ’ Abiding by this rule might add a few minutes to the process, but we have found that it brings a precision that helps avoid confusion and misunderstandings later on, so you’re likely to save time overall.

A tree diagram shows the question with alternatives.

Mapping rule 3: How maps have a MECE structure

A how map has two key functions. The first is to help explore the solution space, to think of new ideas. The second is to systematically organise that space so that you consider all potential answers exactly once. And, yes, that means using a MECE structure.

In case you’re questioning the necessity of actually mapping your solution space, consider this: By representing a physical space, a geographic map helps you choose your route to your destination. No one will argue the value of a map when placed in an unfamiliar location. Well, by helping you explore and organise alternatives, a how map fulfils the same function for the solution space, so that you can choose how to get to your treasure.

Making the structure of your map MECE can be challenging. To help you do so, follow the same approach as when developing your why map (see Chapter 3). In addition, using a few more ideas will help you for both types of maps:

Two diagrams for the question 'How may we increase our revenues from new clients?'
  • Limit the sub-nodes under any given node to 3–5: When a node has lots of sub-nodes, it becomes difficult to keep the structure MECE or validate MECEness. We can all remember being presented a slide with 15 bullet points that triggers us to immediately check out mentally (and turn to our smart phones) because it was impossible to make sense of the mess.

    Limiting the number of sub-nodes doesn’t mean that you don’t present concrete ideas! All it means is that instead of aggregating all your ideas on one level, you progress more gradually. At the same time, don’t leave any node with a single sub-node, as this is indicative of a problem: Either your sub-node isn’t CE (it needs at least one sibling) or the node and sub-node can be combined into a single node.

  • Use logic to promote ideation: In our experience, using a map with a MECE structure can unleash your creativity by putting logic to work. For instance, if one of your nodes says ‘by converting people who currently buy from our competitors to buy from us’, you can use that node to identify other sources of new clients. If we can get new clients by ‘stealing’ them from our competitors, where else could we get new clients from? Maybe ‘By converting people who are not currently buying this kind of product/service (ours or our competitors’) to buy from us’. In this case, putting logic to work for you means that you’ll be looking for all sources of new clients. Creating nodes, you set empty ‘mental buckets’ that prompt your mind with a directed stimulus to fill them up with ideas. In our experience, this prompted ideation is much more efficient and leads to a broader range of ideas than only working with a blank sheet.

    Now, don’t fool yourself: Most ideas in the map will not be feasible or desirable, so you’ll end up abandoning most, but don’t let that stop you from thinking more innovatively. Remember, developing the map, you generate ideas. You’ll evaluate them later.

  • Let the nodes be ICE (independent and collectively exhaustive): It is the structure of the map that is MECE. So if an idea is in one part of the map, that precludes it from being in another (the structure is ME) and the map encompasses all potential ideas (CE). However, the nodes in the map, the ideas, are independent and collectively exhaustive, or ICE. Here, ‘independent’ means that an idea can be pursued without the help of another idea in the map. So several ideas might be pursued concomitantly, but no idea needs another one (see section ‘how maps answer a single how question’, above).

Mapping rule 4: How maps are insightful

A good how map doesn’t just contain lots of ideas in a MECE structure. It also helps you get to promising alternatives. That means that they need to be insightful: logically correct and adding value. Let’s look at the travelling-from-NYC-to-London example again. You could start your map in a variety of ways, including highlighting the means of transportation:

  • Type: say, ‘by travelling by [ground/air/sea]’
  • Price: say, ‘by travelling using a [free/paying] means of transportation’
  • Carbon footprint: ‘by travelling using a means of transportation that has a [negative/neutral/positive] carbon footprint’
  • Riskiness: ‘by travelling using a means of transportation that has an associated [low/neutral/high] risk’

Or its speed, convenience, comfort, flexibility, anonymity, . . . . Indeed, there are numerous ways to start your map! So, how should you start your map? Well, using the most insightful, of course! But even within our definition of insightfulness (logically valid and useful; see Chapter 3), insightfulness means different things to different people.

For instance, perhaps you are extremely environmentally conscious and, like Greta Thunberg who sailed across the Atlantic to go to a UN climate summit, you’ll only consider renewable means of transportation.6 Here, the third structure might be most helpful to help you zero in on the avenues worth considering further. Or you might be like most business and tourism travellers, preferring more conventional approaches; then the first approach probably provides the most useful categorisation. Whatever the case, you won’t know how insightful a first cut is until you compare it to another, so try to consider at least two first cuts, and then expand the map.

A map for the question 'how may I go from NYC to London?'

Another way to help you be more insightful is to refrain from using ‘other’, particularly in the first levels. Using ‘other’ automatically makes that level of your map CE, which seems great at first sight. But another critical value of a map is to surface concrete ideas, which don’t appear when you use ‘other’; at least not at that level of the map. To test your map’s MECEness, you would have to integrate ideas coming from two levels of the map, which is harder to do. Therefore, you are better off skipping the use of ‘other’ for the sake of insightfulness.

Two diagrams for the question 'How may I go from NYC to London?'

One exception to the don’t-use-other guideline is when you want to create a placeholder to return to later. Another exception is when you are already at higher levels, so any part of the map only influences a limited portion of the solution space.

 MOVE RIGHT TO LEFT TO CREATE ­ADDITIONAL OPTIONS

Psychologist Alex Osborn, who popularised brainstorming, said that ‘the best way to have a good idea is to have many ideas’. Similarly, Nobel-Prize laureate Linus Pauling pointed out that ‘the way to get good ideas is to get lots of ideas and throw the bad ones away’. For an illustration of the approach in practice, consider Edison’s famous experiments of passing electricity through hundreds of materials for several years before selecting carbon filaments. He is often quoted as saying, ‘I have not failed 10,000 times – I’ve successfully found 10,000 ways that will not work’. Empirical evidence also supports this claim that having more ideas helps having better ideas.7

The primary function of a how map is to assist in this divergent-thinking task by enabling you to systematically explore and organise the solution space. In the overwhelming majority of cases, developing an effective map entails progressing both from left to right – that is, using a structure to identify ideas – and from right to left – that is, using an unstructured laundry list of ideas to identify an insightful structure. Start from whichever side you prefer, but you’ll probably benefit from doing both during your analysis.

A diagram shows a tree diagram and it reads: 1, use a structure to identify other potential options, 2, use a laundry list of options to identify potential structures, and 3 shows a loop.

We have discussed the left-to-right way of developing how maps at length. Let’s now take a brief look at three concrete ways to generate novel ideas: applying the solution of a similar problem, reframing your problem, or relaxing some of your pre-imposed constraints.

Promote (constructive!) dissent8

In some cultures, particularly in those with high Power Distance, groups can easily default to the HiPPO – the Highest Paid Person’s Opinion – or other forms of undesirable consensus. Why should consensus be undesirable? Well, the self-censorship of lower-ranking group members prevents the team from benefiting from the friction of different perspectives to innovate.

A diverse group of stakeholders can help avoid group members thinking too much alike. Diversity includes identity diversity, which encompasses the age, gender, and cultural and ethnicity identity of the people; and functional diversity, which captures how people represent and solve problems.9 Identity diversity can help reduce the harmful effect of correlated experiences while functional diversity might help bring about a more exhaustive search of the solution space.10 Research has shown that the latter has positive impact on a team’s performance.11

Overall, it is desirable to assemble a team with diverse perspectives and complementary expertise.12 Vigorous debates ahead of the decision are useful and dissent can be an effective means to avoid groupthink (that is, group members becoming less independent13) or other suboptimal convergences of opinions.14

In addition, if you are the most senior person in the team, consider staying out of the idea-generation process altogether. Not because you won’t have good ideas, but because your presence might limit the creativity of other team members.15

Various approaches exist to promote dissent, including instructed dissent, which consists of asking a subset of the team to adopt a position opposite to the consensus (playing devil’s advocate) regardless of their personal opinion.16 These approaches can help improve the quality of the discussion.17

Apply the solution of a similar problem

You might wonder how to jump-start your idea generation. Well, to begin with, you can learn from others who are in your field or from problem solvers in different areas whose solutions you can transfer to your problem.

Imagine a high-school principal who wants to speed up the cafeteria’s lunch line. She can check if some lines move faster than others, check if lines are now moving slower than before, or look at other schools for best practices to transfer. More broadly, she can also look at other organisations that managed checkout processes – convenience stores, airport check-in lines, or public pools. She can also talk to people who manage crowds in general, such as managers of sports stadiums, amusement parks or shopping malls. But why stop there?

Sometimes you can get ideas from seemingly unrelated sources, such as looking at nature to help with engineering design – a practice called ­biomimicry. That’s what the engineers of the famous Japanese bullet train Shinkansen did. Their previous design suffered from harsh sound waves whenever a train left a tunnel at high speed. For inspiration, the design team looked for something in nature that could cope with sudden changes in air resistance. They found that the kingfisher’s special beak enables it to dive from air, a low resistance medium, into water, a high resistance medium, with minimal energy loss. This insight inspired the development of the Shinkansen distinctive cone-shaped nose, reminiscent of a ­kingfisher’s beak.18

Even though most of the problems we face might look unique on the surface, a biomimicry-inspired approach can be helpful because many problems share structural similarities with other problems, sometimes of a completely different nature. One such common problem is the so-called congestion one. ‘Congestion’ refers to a mismatch between something that we want more of with something we want less of. Our profitability problem is a congestion one (we want more revenues and less costs). The structure of that how map may provide a useful blueprint to address problems that look completely different but have a similar structure (so-called isomorphic problems), such as fitting cars in our parking lot or helping Louis XIV with his fountains (see Chapter 1).19

Solutions for four questions.

Reframe your problem

To illustrate some of the significant reframing effects that the right-to-left way of ideation can yield, imagine that you’re the manager of a building where people complain that the elevators are too slow. Initially, you might start left to right by asking: ‘How may we speed up the elevators?’ Take a minute to draw an initial how map.

Maybe your map looks something like ours, separating the current elevators from adding new ones before diving into details in each branch.

A diagram maps the branches for how may we speed up the elevators.

However, with now switching to right-to-left idea generation, you might find your initial framing overly constraining. For instance, it might occur to you to distract elevator users to make them feel that the elevators are speedier. How? Well, there are many ways: give them a TV to look at, a mirror in which they can admire themselves, a newspaper they can read, a radio station they can listen to, an internet access on which they can surf the net – you name it.20 The bottom line is: None of these ideas would fit in your original how map.

Now, if you believe that this line of thinking might be worth pursuing, you can go back and broaden the quest so that it accommodates these and other options. For instance, you might reframe your quest to state: ‘How can we make our users happy with the speed of our elevators?’ This new line of thinking opens fantastic avenues; after all, installing a few mirrors would cost a lot less than swapping the elevators’ motors or installing new elevators!

The key point is that sometimes, an (in this case) engineering problem isn’t best solved with an (in this case) engineering solution. Reframing our problem in a broader or a narrower scope can drastically improve our problem solving. And although this idea might look trivial, make no mistake, seeing that your current frame is overly narrow or broad is usually far from trivial.

A second observation is that problem framing and option generation are closely interlinked. One informs the other and it can therefore pay off to iterate between the two as new evidence helps us gain new insights into our problem.

Relax constraints

We all have mental filters that automatically weed out the ‘overly crazy ideas’ whenever solving a problem. Although these filters help us be pragmatic, they can also interfere with our creativity, leading us to prematurely weed out options because they seem too far out.

A diagram maps the branches for how may we make our users happy with the speed of our elevators?

To broaden your option space, think about what holds you back from generating ideas. And then, ask ‘what if?’ What if we didn’t care about cost? What if our key stakeholders were onboard? What if we could partner with our top competitor? Relaxing constraints might take you back to the set-up of your logistics (see Chapter 1). For instance, you might ask: ‘What if we had twice or three times the budget?’ or ‘What if we could work on this problem for six months instead of just four weeks?’

Thinking MECE, we’ve already exercised our ‘what else?’ muscle, which helped us identify alternative answers. Asking ‘what if?’ takes this exercise even further by questioning assumed constraints, the traditional practices that we take for granted because that’s how things are done around here. Asking ‘what if?’ enables you to break free from the straitjackets of convention and habit.

And, to re-emphasise, many of these ideas won’t be feasible or desirable. Many will be branded absurd; after all, budgets are limited and getting a project completed on time is important. But, time permitting, there’s nothing wrong with having absurd ideas. An absurd idea may be the starting point of a good idea that incorporates the desirability of the absurd idea with the feasibility of something more realistic to implement.

Combine the left-to-right and right-to-left approaches

The left-to-right and the right-to-left approaches to idea generation are not mutually exclusive but, rather, complementary. So it usually pays off to combine them. If you start with a laundry list, at some point structure your ideas to clean up the list by eliminating overlapping or even identical ideas. Similarly, if you start with a structure, you will inevitably wonder at some point how to generate further ideas within a specific category. Then, it is useful to not just rely on logic but to tap into bottom-up tools – such as brainwriting – to develop ideas.

No matter what your preferred approach, you need to manage an important tension: On the one hand, you want to shepherd the process through, building momentum in your problem-solving process. On the other hand, you also want to have the patience necessary to appreciate the value of bad ideas. Why? Because it is often impossible to determine at the outset if an idea is absurd.

Even seemingly absurd ideas might contain the seed for something great, so give your subconscious time to do its job. In fact, research has shown that creative ideas tend to pop up seemingly out of nowhere when you are doing something completely different, such as taking a shower, exercising, meditating or dreaming.21 For instance, Berkeley neuroscientist Matthew Walker explains that our brains make non-obvious connections during the REM phases of sleep that lead to unexpected creative insights.22 Wanna solve that tough problem? Sleep more, take more showers, or do whatever else that relaxes you!

Decide when to quit looking

So, you need to explore different options, which will help you avoid premature closure. But exploring options could go on indefinitely! After all, you can never be sure that your option set is collectively exhaustive. Time is scarce in most problem-solving projects, so when should you stop looking?

Exploration is looking for new options that are unproven but might be potentially rewarding; exploitation is sticking with an available good option. There is no known optimal solution for the explore-exploit dilemma, and a general solution might not even exist.23 However the literature provides some insights.

We often restrict our search to a subset of potential solutions, particularly when our experience is not rich enough to guide our search.24 So it might be useful to evaluate the diversity of your options: If all of them are of the same kind, or closely related, you may want to continue challenging yourself.

How long to spend searching also depends on the cost of opportunity: What else could you be doing if you were not spending more effort on exploring? If further exploration comes at the expense of thinking through the decision or convincing stakeholders, both of which are critical and time consuming, now might be a good moment to move on. Note, however, that we often see managers close off their search quickly – arguably much too quickly. These observations are in line with research findings on exploration without reward.25

Conversely, some teams are reluctant to stop exploring. The hope, whether conscious or not, is that more exploration will lead them to discover a magic bullet that will only have upsides. In our experience, however, magic bullets don’t exist – no matter how much exploration is involved. Rather than focusing on finding an alternative that would entail no trade-offs, teams might be better off working through the trade-offs. Realising that the alternatives on the table are the only ones there are can help the team shift from exploration to the next step.

In sum, it might be beneficial to remember that you will probably be better served spreading your limited time to get to a good-enough result for each of the frame, explore, and decide activities than investing it all in one of the three and leaving the other two barely thought through.

 USE YOUR OPTIONS TO CREATE ALTERNATIVES

Now that your divergent thinking has fuelled the development of your how map, it might contain 20, 30 or even more ideas with varying degrees of detail. Because you’ve included all ideas independently of their desirability, some of these options are more promising than others. And even though you do not want to make a final call right away on which solution to implement (we’ll do so in Chapter 6), it is helpful to converge your thinking onto a manageable set of concrete alternatives that you can evaluate. This is where exploring switches from divergent thinking to convergent thinking.

What constitutes a good set of alternatives is somewhat problem dependent, but a few general rules apply:

  • Each alternative is a logically valid answer to the question. Each alternative has the potential to answer the full problem without needing the support of another alternative. To take up an already familiar example, re-skim the box on page 64: In Peugeot’s case, since the question asks how to fulfil distribution needs, defined as selling and providing maintenance, each alternative must be a complete distribution solution. So ‘by selling only’ wouldn’t be a valid alternative, because it only addresses the selling part of the challenge but gives no direction on how to distribute.

    Note that an alternative may be composed of a collection of fractional solutions, each of which might be small but, as a whole, constitute a group that gets the job done.26 So it might be that an alternative to increase your profitability will be increasing revenues from return clients in one of your target markets and reducing your variable costs for one line of product.

  • The set has at least two alternatives and not too many. If you only have one alternative, then there’s no decision, so you need at least two. Considering multiple alternatives has benefits beyond increasing the likelihood of finding better potential solutions, as it also gives you fallback solutions in case your preferred alternative does not work out.27 Also, working with various alternatives might reduce politics within the team. In our experience, as people reflect on a wider range of alternatives, they tend to get less invested in a specific one, which enables them to change opinions more easily. Including multiple alternatives also enables you to integrate the perspectives of stakeholders who might prefer different ways forward. Considering their preferences will help you think through the decision’s trade-offs, which will help you prepare for the potentially difficult conversations ahead. But, beware: taking more alternatives ahead isn’t necessarily better. There are decreasing returns to having more alternatives and, at some point, the returns can become negative: having too many alternatives might lead us to suffer from choice overload.28
  • The alternatives are reasonably mutually exclusive. If you can pursue more than one alternative at a time, then you don’t need to choose! So alternatives must be reasonably mutually exclusive: pursuing one should preclude you from pursuing others. In the words of management scholar Roger Martin: ‘true choice requires giving up one thing in order to reap the strategic benefits of the other. If multiple options can be pursued simultaneously or there is but one sensible option, the firm does not face a true strategic choice.’29

    In short, for most decisions, we can’t have it all – even though we often think that we do. The difficult reality of solving complex problems is that there are trade-offs among different benefit-cost constellations: pursuing one alternative that gets you some of what you value comes at the price of foregoing something else that you value.

  • The alternatives are concrete. As long as your alternatives remain conceptual or abstract, it is difficult to assess them. Making your alternatives as concrete as possible will improve your thinking. When you develop an alternative, ask yourself: Is this something I can do, buy, sell, etc.? One way to do so is to use the simple method we already used in framing our problem: show your prototype alternative to someone unfamiliar with it. Ask them to read it out loud in front of you so you can see where they’re struggling, and ask them to explain it back to you after reading it only once so you know if it’s concrete enough.
  • The alternatives are promising. Developing our how map, our goal was to create lots of options. Obviously, we won’t be able to implement all of them; in fact, we might not even want to. Although our formal evaluation will take place in the next step, we can already start filtering out the solutions that do not look promising now. When converting options into alternatives, throw out those that are obviously either not feasible or desirable. Validate that you have real alternatives (not pseudo alternatives that make the real alternative look better in comparison). Also, throw out those that look overly similar. In our experience, if team members disagree about alternatives, you probably are in good shape.30 As a rule of thumb, keep looking for alternatives until you or your team members fall in love with at least two.
A diagram maps the solutions for the question 'how should Peugeot fulfil its distribution needs in the US.'

In practice, alternatives can come from anywhere in your map. To help conceptualise this, consider an analogy: our quest is to prepare a great dish for our dinner guests. In this analogy, the options in the map are the ingredients that we have to prepare the dish. Our map helps us account for each exactly once (we don’t forget any, we don’t double-list some). And the alternatives are the recipes. So, our decision is to find the recipe that we think will work best. Some recipes (alternatives) might use one single ingredient (option) whereas others use various.

 CHAPTER TAKEAWAYS

Don’t run off implementing whatever alternative first occurs to you. Instead, as everywhere else in the process, start with divergent thinking. You can do so by developing a how map in which you systematically identify and organise the various ways of solving your problem.

Good how maps follow the same four rules as good why maps:

  • Mapping rule 1: They answer a single how question.
  • Mapping rule 2: They go from the question to potential solutions.
  • Mapping rule 3: They use a MECE structure.
  • Mapping rule 4: They are insightful.

Don’t let thinking MECE and insightful get in your way! If you can’t think of a great structure for your map, no problem, start by developing a laundry list of ideas. In the end, your how map does indeed need to have a MECE and insightful structure, but that doesn’t mean that you need to start with the structure.

Don’t develop solutions on your own if you can involve stakeholders; in fact, aim to co-create the solution space!

Don’t auto-censure too much: a how map is useful to explore the solution space. By definition, it will include lots of dumb ideas, and that’s fine. Use the map to ideate, keep the evaluation for later.

 CHAPTER 4 NOTES

  1.   1See, for instance, Richards, L. G. (1998). Stimulating creativity: Teaching engineers to be innovators. FIE’98. 28th Annual Frontiers in Education Conference. Moving from ’Teacher-Centered’ to ’Learner-Centered’ ­Education. Conference Proceedings (Cat. No. 98CH36214), IEEE.
  2.   2See Bouquet, C. and J. Barsoux (2009). ’Denise Donovan (A): Getting Head Office Support for Local Initiatives.’ IMD Case Series IMD-3-2103, Lausanne, Switzerland.
  3.   3Alternative- vs. value-focused thinking. Although FrED isn’t linear, we offer to explore alternatives before exploring criteria (what is called ‘­value-focused thinking’). Both approaches are valid. For more, see p. 55 of Goodwin, P. and G. Wright (2014). Decision analysis for management judgment, John Wiley & Sons; Keeney, R. L. (1992). ­Value-focused thinking: A path to creative decision making. Cambridge, Massachusetts, Harvard University Press; Wright, G. and P. ­Goodwin (1999). ‘Rethinking value elicitation for personal consequential ­decisions. Journal of Multi-Criteria Decision Analysis 8(1): 3–10.
  4.   4Divergent and convergent thinking occur at all stages of the ­problem-solving process. See Basadur, M. (1995). ’Optimal ­ideation-evaluation ratios.’ Creativity Research Journal 8(1): 63 –75.
  5.   5See, for instance, Siemon, D., F. Becker and S. Robra-Bissantz (2018). ’How might we? From design challenges to business innovation.’ Innovation 4.
  6.   6UN News. (2019). ’Teen activist Greta Thunberg arrives in New York by boat, putting ‘climate crisis’ in spotlight.’ Retrieved April 21, 2021, from https://news.un.org/en/story/2019/08/1045161.
  7.   7See Girotra, K., C. Terwiesch and K. T. Ulrich (2010). ’Idea generation and the quality of the best idea.’ Management Science 56(4): 591605.
  8.   8Let me tell you everything that’s wrong with you. One possible explanation as to why dissent helps improve outcomes is that people tend to be more demanding when evaluating arguments than they are when formulating them. Therefore, the more debate and conflict between opinions, the more argument evaluation prevails over production ­(Mercier, H. (2016). ’The argumentative theory: Predictions and empirical evidence.’ Trends in Cognitive Sciences 20(9): 689–700).
  9.   9Hong, L. and S. E. Page (2004). ’Groups of diverse problem solvers can outperform groups of high-ability problem solvers.’ Proceedings of the National Academy of Sciences of the United States of America 101(46): 1638516389.
  10. 10For a brief discussion, see Bang, D. and C. D. Frith (2017). ’Making better decisions in groups.’ Royal Society Open Science 4(8): 170–193.
  11. 11Horwitz, S. K. and I. B. Horwitz (2007). ’The effects of team diversity on team outcomes: A meta-analytic review of team demography.’ Journal of Management 33(6): 9871015.
  12. 12See p. 61 of National Research Council (2011). Intelligence ­analysis for tomorrow: Advances from the behavioral and social sciences. ­Washington, DC, National Academies Press.
  13. 13Bang, D. and C. D. Frith (2017). ’Making better decisions in groups.’ Royal Society Open Science 4(8): 170–193. Schulz-Hardt, S., F. C. Brodbeck, A. Mojzisch, R. Kerschreiter and D. Frey (2006). ’Group decision making in hidden profile situations: Dissent as a facilitator for decision quality.’ Journal of Personality and Social Psychology 91(6): 1080–1093.
  14. 14See, for instance, pp. 64–66 of National Research Council (2014). Convergence: Facilitating transdisciplinary integration of life sciences, physical sciences, engineering, and beyond. Washington, DC, The National Academies Press.
  15. 15Keum, D. D. and K. E. See (2017). ’The influence of hierarchy on idea generation and selection in the innovation process.’ Organization Science 28(4): 653669.
  16. 16See, for instance, Herbert, T. T. and R. W. Estes (1977). ’Improving executive decisions by formalizing dissent: The corporate devil’s advocate.’ Academy of Management Review 2(4): 662667.
  17. 17Greitemeyer, T., S. Schulz-Hardt, F. C. Brodbeck and D. Frey (2006). ’Information sampling and group decision making: The effects of an advocacy decision procedure and task experience.’ Journal of Experimental Psychology: Applied 12(1): 31.
  18. 18Lim, C., D. Yun, I. Park and B. Yoon (2018). ’A systematic approach for new technology development by using a biomimicry-based TRIZ contradiction matrix.’ Creativity and Innovation Management 27(4): 414430.
  19. 19This is called analogical problem solving; for a primer, see Holyoak, K. J. (2012). Analogy and relational reasoning. The Oxford handbook of thinking and reasoning. K. J. Holyoak and R. G. Morrison. New York, Oxford University Press: 234–259. Kahneman, D. and D. Lovallo (1993). ’Timid choices and bold forecasts: A cognitive perspective on risk taking.’ Management Science 39(1): 17–31. Gick, M. L. and K. J. Holyoak (1980). ’Analogical problem solving.’ Cognitive Psychology 12(3): 306–355. See also pp. 99–119 of Epstein, D. (2020). Range: How generalists triumph in a specialized world, Pan Books. Lovallo, D., C. Clarke and C. Camerer (2012). ’Robust analogizing and the outside view: Two empirical tests of case-based decision making.’ Strategic Management Journal 33(5): 496512.
  20. 20See p. 25 of Mason, R. O. and I. I. Mitroff (1981). Challenging strategic planning assumptions: Theory, cases, and techniques, Wiley New York.
  21. 21For more on creative problem solving techniques, see p. 23 of Reeves, M. and J. Fuller (2021). Imagination machine: How to spark new ideas and create your company’s future, Harvard Business Review Press.
  22. 22For a summary of the impact of sleep on human functioning (including creativity), see Walker, M (2018). Why we sleep, Penguin. For a more detailed study on the role of sleep for ideation, see Gish, J. J., D. T. Wagner, D. A. Grégoire and C. M. Barnes (2019). ’Sleep and entrepreneurs’ abilities to imagine and form initial beliefs about new venture ideas.’ Journal of Business Venturing 34(6): 105943.
  23. 23Explore/exploit and optimise/satisfice. Nobel Prize laureate Herbert Simon coined the term satisficing by combining satisfying and sufficing. We satisfice when we stop looking for a solution after we’ve identified one that is good enough. This contrasts with optimising, which consists of always looking for a better solution (Simon, H. A. (1990). ’Invariants of human behavior.’ Annual Review of Psychology 41(1): 1–20). Our drive to be collectively exhaustive relates to optimising, but we can never be sure that we are collectively exhaustive (because no matter what we’ve identified, there might be another possibility out there). Cohen, J. D., S. M. McClure and A. J. Yu (2007). ’Should I stay or should I go? How the human brain manages the trade-off between exploitation and exploration.’ Philosophical Transactions of the Royal Society B: Biological Sciences 362(1481): 933–942. Song, M., Z. Bnaya and W. J. Ma (2019). ’Sources of suboptimality in a minimalistic explore–exploit task.’ Nature Human Behaviour 3(4): 361–368.
  24. 24Sanborn, A. N. and N. Chater (2016). ’Bayesian brains without probabilities.’ Trends in Cognitive Sciences 20(12): 883–893.
  25. 25Exploration without reward, the secretary problem. An interesting subset of the explore/exploit dilemma is when exploration doesn’t provide any reward, a situation known as the secretary problem. Imagine a searcher (employer) interviewing secretarial candidates one at a time. The searcher’s goal is to identify the single best candidate. After each interview, the searcher must decide whether to make an offer. If the offer is made, the exploration ceases. If the searcher doesn’t make an offer, there won’t be a chance to make that offer again to the candidate later. How many candidates should the searcher interview before making an offer? An optimal solution exists: 37%. The searcher should not make an offer to the first candidates but, instead, use them to calibrate expectations. Then, after interviewing the first 37% candidates, the searcher should make an offer to the first candidate who is better than any the previous ones. In one study, participants at first failed to search long enough but learned to extend their search in subsequent trials. See Sang, K., P. M. Todd, R. L. Goldstone and T. T. Hills (2020). ’Simple threshold rules solve explore/exploit trade-offs in a resource accumulation search task.’ Cognitive Science 44(2): e12817; Seale, D. A. and A. Rapoport (1997). ’Sequential decision making with relative ranks: An experimental investigation of the ”secretary problem”.’ Organizational Behavior and Human Decision Processes 69(3): 221–236.
  26. 26A collection of piecemeal solutions also works. Talking at a recent event at IMD, Swiss explorer Bertrand Piccard called these piranha solutions because each, on its own, would take a long time to get the job done but, as a group, they are extremely effective.
  27. 27Alternatives come in all numbers. For some problems – so-called choice problems – the set of alternatives is naturally small and finite; for others, it might be large or perhaps infinite, as is the case in design or optimisation problems (Wallenius, J., J. S. Dyer, P. C. Fishburn, R. E. Steuer, S. Zionts and K. Deb (2008). ’Multiple criteria decision making, multiattribute utility theory: Recent accomplishments and what lies ahead.’ Management Science 54(7): 1336–1349).
  28. 28More choice is not necessarily better: no matter whether it’s salad dressings in the supermarket, stereo systems at the consumer electronics store, or colleges to go to, too many alternatives can lead to detrimental outcomes as our mental decision system gets overloaded. For an excellent overview of negative implications of having too much choice, see Schwartz, B. (2005). The paradox of choice, Harper Perennial. Schwartz, B. (2004). The paradox of choice: Why more is less, New York, Ecco New York.
  29. 29Martin, R. (1997). Strategic choice structuring: A set of good choices positions a firm for competitive advantage.
  30. 30Can we disagree, please? During a meeting where the top management of General Motors was considering a difficult decision, chairman Alfred P. Sloan made a final comment, ‘Gentlemen, I take it we are all in complete agreement on the decision here?’ He waited for each person to confirm. ‘Then, I propose we postpone further discussion of this matter until our next meeting to give ourselves time to develop disagreement and perhaps gain some understanding of what this decision is about.’ (Burkus, D. (2013). ’How criticism creates innovative teams.’ Harvard Business Review Blog.)
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