complex problem solving

What It Takes to Think Deeply About Complex Problems

by Tony Schwartz

Summary .   

The problems we’re facing often seem as complex as they do intractable. And as Albert Einstein is often quoted as saying, “We cannot solve our problems with the same level of thinking that created them.” So what does it take to increase the complexity of our thinking?

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CONCEPTUAL ANALYSIS article

Complex problem solving: what it is and what it is not.

• 1 Department of Psychology, University of Bamberg, Bamberg, Germany
• 2 Department of Psychology, Heidelberg University, Heidelberg, Germany

Computer-simulated scenarios have been part of psychological research on problem solving for more than 40 years. The shift in emphasis from simple toy problems to complex, more real-life oriented problems has been accompanied by discussions about the best ways to assess the process of solving complex problems. Psychometric issues such as reliable assessments and addressing correlations with other instruments have been in the foreground of these discussions and have left the content validity of complex problem solving in the background. In this paper, we return the focus to content issues and address the important features that define complex problems.

Succeeding in the 21st century requires many competencies, including creativity, life-long learning, and collaboration skills (e.g., National Research Council, 2011 ; Griffin and Care, 2015 ), to name only a few. One competence that seems to be of central importance is the ability to solve complex problems ( Mainzer, 2009 ). Mainzer quotes the Nobel prize winner Simon (1957) who wrote as early as 1957:

The capacity of the human mind for formulating and solving complex problems is very small compared with the size of the problem whose solution is required for objectively rational behavior in the real world or even for a reasonable approximation to such objective rationality. (p. 198)

The shift from well-defined to ill-defined problems came about as a result of a disillusion with the “general problem solver” ( Newell et al., 1959 ): The general problem solver was a computer software intended to solve all kind of problems that can be expressed through well-formed formulas. However, it soon became clear that this procedure was in fact a “special problem solver” that could only solve well-defined problems in a closed space. But real-world problems feature open boundaries and have no well-determined solution. In fact, the world is full of wicked problems and clumsy solutions ( Verweij and Thompson, 2006 ). As a result, solving well-defined problems and solving ill-defined problems requires different cognitive processes ( Schraw et al., 1995 ; but see Funke, 2010 ).

Well-defined problems have a clear set of means for reaching a precisely described goal state. For example: in a match-stick arithmetic problem, a person receives a false arithmetic expression constructed out of matchsticks (e.g., IV = III + III). According to the instructions, moving one of the matchsticks will make the equations true. Here, both the problem (find the appropriate stick to move) and the goal state (true arithmetic expression; solution is: VI = III + III) are defined clearly.

Ill-defined problems have no clear problem definition, their goal state is not defined clearly, and the means of moving towards the (diffusely described) goal state are not clear. For example: The goal state for solving the political conflict in the near-east conflict between Israel and Palestine is not clearly defined (living in peaceful harmony with each other?) and even if the conflict parties would agree on a two-state solution, this goal again leaves many issues unresolved. This type of problem is called a “complex problem” and is of central importance to this paper. All psychological processes that occur within individual persons and deal with the handling of such ill-defined complex problems will be subsumed under the umbrella term “complex problem solving” (CPS).

Systematic research on CPS started in the 1970s with observations of the behavior of participants who were confronted with computer simulated microworlds. For example, in one of those microworlds participants assumed the role of executives who were tasked to manage a company over a certain period of time (see Brehmer and Dörner, 1993 , for a discussion of this methodology). Today, CPS is an established concept and has even influenced large-scale assessments such as PISA (“Programme for International Student Assessment”), organized by the Organization for Economic Cooperation and Development ( OECD, 2014 ). According to the World Economic Forum, CPS is one of the most important competencies required in the future ( World Economic Forum, 2015 ). Numerous articles on the subject have been published in recent years, documenting the increasing research activity relating to this field. In the following collection of papers we list only those published in 2010 and later: theoretical papers ( Blech and Funke, 2010 ; Funke, 2010 ; Knauff and Wolf, 2010 ; Leutner et al., 2012 ; Selten et al., 2012 ; Wüstenberg et al., 2012 ; Greiff et al., 2013b ; Fischer and Neubert, 2015 ; Schoppek and Fischer, 2015 ), papers about measurement issues ( Danner et al., 2011a ; Greiff et al., 2012 , 2015a ; Alison et al., 2013 ; Gobert et al., 2015 ; Greiff and Fischer, 2013 ; Herde et al., 2016 ; Stadler et al., 2016 ), papers about applications ( Fischer and Neubert, 2015 ; Ederer et al., 2016 ; Tremblay et al., 2017 ), papers about differential effects ( Barth and Funke, 2010 ; Danner et al., 2011b ; Beckmann and Goode, 2014 ; Greiff and Neubert, 2014 ; Scherer et al., 2015 ; Meißner et al., 2016 ; Wüstenberg et al., 2016 ), one paper about developmental effects ( Frischkorn et al., 2014 ), one paper with a neuroscience background ( Osman, 2012 ) 1 , papers about cultural differences ( Güss and Dörner, 2011 ; Sonnleitner et al., 2014 ; Güss et al., 2015 ), papers about validity issues ( Goode and Beckmann, 2010 ; Greiff et al., 2013c ; Schweizer et al., 2013 ; Mainert et al., 2015 ; Funke et al., 2017 ; Greiff et al., 2017 , 2015b ; Kretzschmar et al., 2016 ; Kretzschmar, 2017 ), review papers and meta-analyses ( Osman, 2010 ; Stadler et al., 2015 ), and finally books ( Qudrat-Ullah, 2015 ; Csapó and Funke, 2017b ) and book chapters ( Funke, 2012 ; Hotaling et al., 2015 ; Funke and Greiff, 2017 ; Greiff and Funke, 2017 ; Csapó and Funke, 2017a ; Fischer et al., 2017 ; Molnàr et al., 2017 ; Tobinski and Fritz, 2017 ; Viehrig et al., 2017 ). In addition, a new “Journal of Dynamic Decision Making” (JDDM) has been launched ( Fischer et al., 2015 , 2016 ) to give the field an open-access outlet for research and discussion.

This paper aims to clarify aspects of validity: what should be meant by the term CPS and what not? This clarification seems necessary because misunderstandings in recent publications provide – from our point of view – a potentially misleading picture of the construct. We start this article with a historical review before attempting to systematize different positions. We conclude with a working definition.

Historical Review

The concept behind CPS goes back to the German phrase “komplexes Problemlösen” (CPS; the term “komplexes Problemlösen” was used as a book title by Funke, 1986 ). The concept was introduced in Germany by Dörner and colleagues in the mid-1970s (see Dörner et al., 1975 ; Dörner, 1975 ) for the first time. The German phrase was later translated to CPS in the titles of two edited volumes by Sternberg and Frensch (1991) and Frensch and Funke (1995a) that collected papers from different research traditions. Even though it looks as though the term was coined in the 1970s, Edwards (1962) used the term “dynamic decision making” to describe decisions that come in a sequence. He compared static with dynamic decision making, writing:

In dynamic situations, a new complication not found in the static situations arises. The environment in which the decision is set may be changing, either as a function of the sequence of decisions, or independently of them, or both. It is this possibility of an environment which changes while you collect information about it which makes the task of dynamic decision theory so difficult and so much fun. (p. 60)

The ability to solve complex problems is typically measured via dynamic systems that contain several interrelated variables that participants need to alter. Early work (see, e.g., Dörner, 1980 ) used a simulation scenario called “Lohhausen” that contained more than 2000 variables that represented the activities of a small town: Participants had to take over the role of a mayor for a simulated period of 10 years. The simulation condensed these ten years to ten hours in real time. Later, researchers used smaller dynamic systems as scenarios either based on linear equations (see, e.g., Funke, 1993 ) or on finite state automata (see, e.g., Buchner and Funke, 1993 ). In these contexts, CPS consisted of the identification and control of dynamic task environments that were previously unknown to the participants. Different task environments came along with different degrees of fidelity ( Gray, 2002 ).

According to Funke (2012) , the typical attributes of complex systems are (a) complexity of the problem situation which is usually represented by the sheer number of involved variables; (b) connectivity and mutual dependencies between involved variables; (c) dynamics of the situation, which reflects the role of time and developments within a system; (d) intransparency (in part or full) about the involved variables and their current values; and (e) polytely (greek term for “many goals”), representing goal conflicts on different levels of analysis. This mixture of features is similar to what is called VUCA (volatility, uncertainty, complexity, ambiguity) in modern approaches to management (e.g., Mack et al., 2016 ).

In his evaluation of the CPS movement, Sternberg (1995) compared (young) European approaches to CPS with (older) American research on expertise. His analysis of the differences between the European and American traditions shows advantages but also potential drawbacks for each side. He states (p. 301): “I believe that although there are problems with the European approach, it deals with some fundamental questions that American research scarcely addresses.” So, even though the echo of the European approach did not enjoy strong resonance in the US at that time, it was valued by scholars like Sternberg and others. Before attending to validity issues, we will first present a short review of different streams.

Different Approaches to CPS

In the short history of CPS research, different approaches can be identified ( Buchner, 1995 ; Fischer et al., 2017 ). To systematize, we differentiate between the following five lines of research:

(a) The search for individual differences comprises studies identifying interindividual differences that affect the ability to solve complex problems. This line of research is reflected, for example, in the early work by Dörner et al. (1983) and their “Lohhausen” study. Here, naïve student participants took over the role of the mayor of a small simulated town named Lohhausen for a simulation period of ten years. According to the results of the authors, it is not intelligence (as measured by conventional IQ tests) that predicts performance, but it is the ability to stay calm in the face of a challenging situation and the ability to switch easily between an analytic mode of processing and a more holistic one.

(b) The search for cognitive processes deals with the processes behind understanding complex dynamic systems. Representative of this line of research is, for example, Berry and Broadbent’s (1984) work on implicit and explicit learning processes when people interact with a dynamic system called “Sugar Production”. They found that those who perform best in controlling a dynamic system can do so implicitly, without explicit knowledge of details regarding the systems’ relations.

(c) The search for system factors seeks to identify the aspects of dynamic systems that determine the difficulty of complex problems and make some problems harder than others. Representative of this line of research is, for example, work by Funke (1985) , who systematically varied the number of causal effects within a dynamic system or the presence/absence of eigendynamics. He found, for example, that solution quality decreases as the number of systems relations increases.

(d) The psychometric approach develops measurement instruments that can be used as an alternative to classical IQ tests, as something that goes “beyond IQ”. The MicroDYN approach ( Wüstenberg et al., 2012 ) is representative for this line of research that presents an alternative to reasoning tests (like Raven matrices). These authors demonstrated that a small improvement in predicting school grade point average beyond reasoning is possible with MicroDYN tests.

(e) The experimental approach explores CPS under different experimental conditions. This approach uses CPS assessment instruments to test hypotheses derived from psychological theories and is sometimes used in research about cognitive processes (see above). Exemplary for this line of research is the work by Rohe et al. (2016) , who test the usefulness of “motto goals” in the context of complex problems compared to more traditional learning and performance goals. Motto goals differ from pure performance goals by activating positive affect and should lead to better goal attainment especially in complex situations (the mentioned study found no effect).

To be clear: these five approaches are not mutually exclusive and do overlap. But the differentiation helps to identify different research communities and different traditions. These communities had different opinions about scaling complexity.

The Race for Complexity: Use of More and More Complex Systems

In the early years of CPS research, microworlds started with systems containing about 20 variables (“Tailorshop”), soon reached 60 variables (“Moro”), and culminated in systems with about 2000 variables (“Lohhausen”). This race for complexity ended with the introduction of the concept of “minimal complex systems” (MCS; Greiff and Funke, 2009 ; Funke and Greiff, 2017 ), which ushered in a search for the lower bound of complexity instead of the higher bound, which could not be defined as easily. The idea behind this concept was that whereas the upper limits of complexity are unbound, the lower limits might be identifiable. Imagine starting with a simple system containing two variables with a simple linear connection between them; then, step by step, increase the number of variables and/or the type of connections. One soon reaches a point where the system can no longer be considered simple and has become a “complex system”. This point represents a minimal complex system. Despite some research having been conducted in this direction, the point of transition from simple to complex has not been identified clearly as of yet.

Some years later, the original “minimal complex systems” approach ( Greiff and Funke, 2009 ) shifted to the “multiple complex systems” approach ( Greiff et al., 2013a ). This shift is more than a slight change in wording: it is important because it taps into the issue of validity directly. Minimal complex systems have been introduced in the context of challenges from large-scale assessments like PISA 2012 that measure new aspects of problem solving, namely interactive problems besides static problem solving ( Greiff and Funke, 2017 ). PISA 2012 required test developers to remain within testing time constraints (given by the school class schedule). Also, test developers needed a large item pool for the construction of a broad class of problem solving items. It was clear from the beginning that MCS deal with simple dynamic situations that require controlled interaction: the exploration and control of simple ticket machines, simple mobile phones, or simple MP3 players (all of these example domains were developed within PISA 2012) – rather than really complex situations like managerial or political decision making.

As a consequence of this subtle but important shift in interpreting the letters MCS, the definition of CPS became a subject of debate recently ( Funke, 2014a ; Greiff and Martin, 2014 ; Funke et al., 2017 ). In the words of Funke (2014b , p. 495):

It is funny that problems that nowadays come under the term ‘CPS’, are less complex (in terms of the previously described attributes of complex situations) than at the beginning of this new research tradition. The emphasis on psychometric qualities has led to a loss of variety. Systems thinking requires more than analyzing models with two or three linear equations – nonlinearity, cyclicity, rebound effects, etc. are inherent features of complex problems and should show up at least in some of the problems used for research and assessment purposes. Minimal complex systems run the danger of becoming minimal valid systems.

Searching for minimal complex systems is not the same as gaining insight into the way how humans deal with complexity and uncertainty. For psychometric purposes, it is appropriate to reduce complexity to a minimum; for understanding problem solving under conditions of overload, intransparency, and dynamics, it is necessary to realize those attributes with reasonable strength. This aspect is illustrated in the next section.

Importance of the Validity Issue

The most important reason for discussing the question of what complex problem solving is and what it is not stems from its phenomenology: if we lose sight of our phenomena, we are no longer doing good psychology. The relevant phenomena in the context of complex problems encompass many important aspects. In this section, we discuss four phenomena that are specific to complex problems. We consider these phenomena as critical for theory development and for the construction of assessment instruments (i.e., microworlds). These phenomena require theories for explaining them and they require assessment instruments eliciting them in a reliable way.

The first phenomenon is the emergency reaction of the intellectual system ( Dörner, 1980 ): When dealing with complex systems, actors tend to (a) reduce their intellectual level by decreasing self-reflections, by decreasing their intentions, by stereotyping, and by reducing their realization of intentions, (b) they show a tendency for fast action with increased readiness for risk, with increased violations of rules, and with increased tendency to escape the situation, and (c) they degenerate their hypotheses formation by construction of more global hypotheses and reduced tests of hypotheses, by increasing entrenchment, and by decontextualizing their goals. This phenomenon illustrates the strong connection between cognition, emotion, and motivation that has been emphasized by Dörner (see, e.g., Dörner and Güss, 2013 ) from the beginning of his research tradition; the emergency reaction reveals a shift in the mode of information processing under the pressure of complexity.

The second phenomenon comprises cross-cultural differences with respect to strategy use ( Strohschneider and Güss, 1999 ; Güss and Wiley, 2007 ; Güss et al., 2015 ). Results from complex task environments illustrate the strong influence of context and background knowledge to an extent that cannot be found for knowledge-poor problems. For example, in a comparison between Brazilian and German participants, it turned out that Brazilians accept the given problem descriptions and are more optimistic about the results of their efforts, whereas Germans tend to inquire more about the background of the problems and take a more active approach but are less optimistic (according to Strohschneider and Güss, 1998 , p. 695).

The third phenomenon relates to failures that occur during the planning and acting stages ( Jansson, 1994 ; Ramnarayan et al., 1997 ), illustrating that rational procedures seem to be unlikely to be used in complex situations. The potential for failures ( Dörner, 1996 ) rises with the complexity of the problem. Jansson (1994) presents seven major areas for failures with complex situations: acting directly on current feedback; insufficient systematization; insufficient control of hypotheses and strategies; lack of self-reflection; selective information gathering; selective decision making; and thematic vagabonding.

The fourth phenomenon describes (a lack of) training and transfer effects ( Kretzschmar and Süß, 2015 ), which again illustrates the context dependency of strategies and knowledge (i.e., there is no strategy that is so universal that it can be used in many different problem situations). In their own experiment, the authors could show training effects only for knowledge acquisition, not for knowledge application. Only with specific feedback, performance in complex environments can be increased ( Engelhart et al., 2017 ).

These four phenomena illustrate why the type of complexity (or degree of simplicity) used in research really matters. Furthermore, they demonstrate effects that are specific for complex problems, but not for toy problems. These phenomena direct the attention to the important question: does the stimulus material used (i.e., the computer-simulated microworld) tap and elicit the manifold of phenomena described above?

Dealing with partly unknown complex systems requires courage, wisdom, knowledge, grit, and creativity. In creativity research, “little c” and “BIG C” are used to differentiate between everyday creativity and eminent creativity ( Beghetto and Kaufman, 2007 ; Kaufman and Beghetto, 2009 ). Everyday creativity is important for solving everyday problems (e.g., finding a clever fix for a broken spoke on my bicycle), eminent creativity changes the world (e.g., inventing solar cells for energy production). Maybe problem solving research should use a similar differentiation between “little p” and “BIG P” to mark toy problems on the one side and big societal challenges on the other. The question then remains: what can we learn about BIG P by studying little p? What phenomena are present in both types, and what phenomena are unique to each of the two extremes?

Discussing research on CPS requires reflecting on the field’s research methods. Even if the experimental approach has been successful for testing hypotheses (for an overview of older work, see Funke, 1995 ), other methods might provide additional and novel insights. Complex phenomena require complex approaches to understand them. The complex nature of complex systems imposes limitations on psychological experiments: The more complex the environments, the more difficult is it to keep conditions under experimental control. And if experiments have to be run in labs one should bring enough complexity into the lab to establish the phenomena mentioned, at least in part.

There are interesting options to be explored (again): think-aloud protocols , which have been discredited for many years ( Nisbett and Wilson, 1977 ) and yet are a valuable source for theory testing ( Ericsson and Simon, 1983 ); introspection ( Jäkel and Schreiber, 2013 ), which seems to be banned from psychological methods but nevertheless offers insights into thought processes; the use of life-streaming ( Wendt, 2017 ), a medium in which streamers generate a video stream of think-aloud data in computer-gaming; political decision-making ( Dhami et al., 2015 ) that demonstrates error-proneness in groups; historical case studies ( Dörner and Güss, 2011 ) that give insights into the thinking styles of political leaders; the use of the critical incident technique ( Reuschenbach, 2008 ) to construct complex scenarios; and simulations with different degrees of fidelity ( Gray, 2002 ).

The methods tool box is full of instruments that have to be explored more carefully before any individual instrument receives a ban or research narrows its focus to only one paradigm for data collection. Brehmer and Dörner (1993) discussed the tensions between “research in the laboratory and research in the field”, optimistically concluding “that the new methodology of computer-simulated microworlds will provide us with the means to bridge the gap between the laboratory and the field” (p. 183). The idea behind this optimism was that computer-simulated scenarios would bring more complexity from the outside world into the controlled lab environment. But this is not true for all simulated scenarios. In his paper on simulated environments, Gray (2002) differentiated computer-simulated environments with respect to three dimensions: (1) tractability (“the more training subjects require before they can use a simulated task environment, the less tractable it is”, p. 211), correspondence (“High correspondence simulated task environments simulate many aspects of one task environment. Low correspondence simulated task environments simulate one aspect of many task environments”, p. 214), and engagement (“A simulated task environment is engaging to the degree to which it involves and occupies the participants; that is, the degree to which they agree to take it seriously”, p. 217). But the mere fact that a task is called a “computer-simulated task environment” does not mean anything specific in terms of these three dimensions. This is one of several reasons why we should differentiate between those studies that do not address the core features of CPS and those that do.

What is not CPS?

Even though a growing number of references claiming to deal with complex problems exist (e.g., Greiff and Wüstenberg, 2015 ; Greiff et al., 2016 ), it would be better to label the requirements within these tasks “dynamic problem solving,” as it has been done adequately in earlier work ( Greiff et al., 2012 ). The dynamics behind on-off-switches ( Thimbleby, 2007 ) are remarkable but not really complex. Small nonlinear systems that exhibit stunningly complex and unstable behavior do exist – but they are not used in psychometric assessments of so-called CPS. There are other small systems (like MicroDYN scenarios: Greiff and Wüstenberg, 2014 ) that exhibit simple forms of system behavior that are completely predictable and stable. This type of simple systems is used frequently. It is even offered commercially as a complex problem-solving test called COMPRO ( Greiff and Wüstenberg, 2015 ) for business applications. But a closer look reveals that the label is not used correctly; within COMPRO, the used linear equations are far from being complex and the system can be handled properly by using only one strategy (see for more details Funke et al., 2017 ).

Why do simple linear systems not fall within CPS? At the surface, nonlinear and linear systems might appear similar because both only include 3–5 variables. But the difference is in terms of systems behavior as well as strategies and learning. If the behavior is simple (as in linear systems where more input is related to more output and vice versa), the system can be easily understood (participants in the MicroDYN world have 3 minutes to explore a complex system). If the behavior is complex (as in systems that contain strange attractors or negative feedback loops), things become more complicated and much more observation is needed to identify the hidden structure of the unknown system ( Berry and Broadbent, 1984 ; Hundertmark et al., 2015 ).

Another issue is learning. If tasks can be solved using a single (and not so complicated) strategy, steep learning curves are to be expected. The shift from problem solving to learned routine behavior occurs rapidly, as was demonstrated by Luchins (1942) . In his water jar experiments, participants quickly acquired a specific strategy (a mental set) for solving certain measurement problems that they later continued applying to problems that would have allowed for easier approaches. In the case of complex systems, learning can occur only on very general, abstract levels because it is difficult for human observers to make specific predictions. Routines dealing with complex systems are quite different from routines relating to linear systems.

What should not be studied under the label of CPS are pure learning effects, multiple-cue probability learning, or tasks that can be solved using a single strategy. This last issue is a problem for MicroDYN tasks that rely strongly on the VOTAT strategy (“vary one thing at a time”; see Tschirgi, 1980 ). In real-life, it is hard to imagine a business manager trying to solve her or his problems by means of VOTAT.

What is CPS?

In the early days of CPS research, planet Earth’s dynamics and complexities gained attention through such books as “The limits to growth” ( Meadows et al., 1972 ) and “Beyond the limits” ( Meadows et al., 1992 ). In the current decade, for example, the World Economic Forum (2016) attempts to identify the complexities and risks of our modern world. In order to understand the meaning of complexity and uncertainty, taking a look at the worlds’ most pressing issues is helpful. Searching for strategies to cope with these problems is a difficult task: surely there is no place for the simple principle of “vary-one-thing-at-a-time” (VOTAT) when it comes to global problems. The VOTAT strategy is helpful in the context of simple problems ( Wüstenberg et al., 2014 ); therefore, whether or not VOTAT is helpful in a given problem situation helps us distinguish simple from complex problems.

Because there exist no clear-cut strategies for complex problems, typical failures occur when dealing with uncertainty ( Dörner, 1996 ; Güss et al., 2015 ). Ramnarayan et al. (1997) put together a list of generic errors (e.g., not developing adequate action plans; lack of background control; learning from experience blocked by stereotype knowledge; reactive instead of proactive action) that are typical of knowledge-rich complex systems but cannot be found in simple problems.

Complex problem solving is not a one-dimensional, low-level construct. On the contrary, CPS is a multi-dimensional bundle of competencies existing at a high level of abstraction, similar to intelligence (but going beyond IQ). As Funke et al. (2018) state: “Assessment of transversal (in educational contexts: cross-curricular) competencies cannot be done with one or two types of assessment. The plurality of skills and competencies requires a plurality of assessment instruments.”

There are at least three different aspects of complex systems that are part of our understanding of a complex system: (1) a complex system can be described at different levels of abstraction; (2) a complex system develops over time, has a history, a current state, and a (potentially unpredictable) future; (3) a complex system is knowledge-rich and activates a large semantic network, together with a broad list of potential strategies (domain-specific as well as domain-general).

Complex problem solving is not only a cognitive process but is also an emotional one ( Spering et al., 2005 ; Barth and Funke, 2010 ) and strongly dependent on motivation (low-stakes versus high-stakes testing; see Hermes and Stelling, 2016 ).

Furthermore, CPS is a dynamic process unfolding over time, with different phases and with more differentiation than simply knowledge acquisition and knowledge application. Ideally, the process should entail identifying problems (see Dillon, 1982 ; Lee and Cho, 2007 ), even if in experimental settings, problems are provided to participants a priori . The more complex and open a given situation, the more options can be generated (T. S. Schweizer et al., 2016 ). In closed problems, these processes do not occur in the same way.

In analogy to the difference between formative (process-oriented) and summative (result-oriented) assessment ( Wiliam and Black, 1996 ; Bennett, 2011 ), CPS should not be reduced to the mere outcome of a solution process. The process leading up to the solution, including detours and errors made along the way, might provide a more differentiated impression of a person’s problem-solving abilities and competencies than the final result of such a process. This is one of the reasons why CPS environments are not, in fact, complex intelligence tests: research on CPS is not only about the outcome of the decision process, but it is also about the problem-solving process itself.

Complex problem solving is part of our daily life: finding the right person to share one’s life with, choosing a career that not only makes money, but that also makes us happy. Of course, CPS is not restricted to personal problems – life on Earth gives us many hard nuts to crack: climate change, population growth, the threat of war, the use and distribution of natural resources. In sum, many societal challenges can be seen as complex problems. To reduce that complexity to a one-hour lab activity on a random Friday afternoon puts it out of context and does not address CPS issues.

Theories about CPS should specify which populations they apply to. Across populations, one thing to consider is prior knowledge. CPS research with experts (e.g., Dew et al., 2009 ) is quite different from problem solving research using tasks that intentionally do not require any specific prior knowledge (see, e.g., Beckmann and Goode, 2014 ).

More than 20 years ago, Frensch and Funke (1995b) defined CPS as follows:

CPS occurs to overcome barriers between a given state and a desired goal state by means of behavioral and/or cognitive, multi-step activities. The given state, goal state, and barriers between given state and goal state are complex, change dynamically during problem solving, and are intransparent. The exact properties of the given state, goal state, and barriers are unknown to the solver at the outset. CPS implies the efficient interaction between a solver and the situational requirements of the task, and involves a solver’s cognitive, emotional, personal, and social abilities and knowledge. (p. 18)

The above definition is rather formal and does not account for content or relations between the simulation and the real world. In a sense, we need a new definition of CPS that addresses these issues. Based on our previous arguments, we propose the following working definition:

Complex problem solving is a collection of self-regulated psychological processes and activities necessary in dynamic environments to achieve ill-defined goals that cannot be reached by routine actions. Creative combinations of knowledge and a broad set of strategies are needed. Solutions are often more bricolage than perfect or optimal. The problem-solving process combines cognitive, emotional, and motivational aspects, particularly in high-stakes situations. Complex problems usually involve knowledge-rich requirements and collaboration among different persons.

The main differences to the older definition lie in the emphasis on (a) the self-regulation of processes, (b) creativity (as opposed to routine behavior), (c) the bricolage type of solution, and (d) the role of high-stakes challenges. Our new definition incorporates some aspects that have been discussed in this review but were not reflected in the 1995 definition, which focused on attributes of complex problems like dynamics or intransparency.

This leads us to the final reflection about the role of CPS for dealing with uncertainty and complexity in real life. We will distinguish thinking from reasoning and introduce the sense of possibility as an important aspect of validity.

CPS as Combining Reasoning and Thinking in an Uncertain Reality

Leading up to the Battle of Borodino in Leo Tolstoy’s novel “War and Peace”, Prince Andrei Bolkonsky explains the concept of war to his friend Pierre. Pierre expects war to resemble a game of chess: You position the troops and attempt to defeat your opponent by moving them in different directions.

“Far from it!”, Andrei responds. “In chess, you know the knight and his moves, you know the pawn and his combat strength. While in war, a battalion is sometimes stronger than a division and sometimes weaker than a company; it all depends on circumstances that can never be known. In war, you do not know the position of your enemy; some things you might be able to observe, some things you have to divine (but that depends on your ability to do so!) and many things cannot even be guessed at. In chess, you can see all of your opponent’s possible moves. In war, that is impossible. If you decide to attack, you cannot know whether the necessary conditions are met for you to succeed. Many a time, you cannot even know whether your troops will follow your orders…”

In essence, war is characterized by a high degree of uncertainty. A good commander (or politician) can add to that what he or she sees, tentatively fill in the blanks – and not just by means of logical deduction but also by intelligently bridging missing links. A bad commander extrapolates from what he sees and thus arrives at improper conclusions.

Many languages differentiate between two modes of mentalizing; for instance, the English language distinguishes between ‘thinking’ and ‘reasoning’. Reasoning denotes acute and exact mentalizing involving logical deductions. Such deductions are usually based on evidence and counterevidence. Thinking, however, is what is required to write novels. It is the construction of an initially unknown reality. But it is not a pipe dream, an unfounded process of fabrication. Rather, thinking asks us to imagine reality (“Wirklichkeitsfantasie”). In other words, a novelist has to possess a “sense of possibility” (“Möglichkeitssinn”, Robert Musil; in German, sense of possibility is often used synonymously with imagination even though imagination is not the same as sense of possibility, for imagination also encapsulates the impossible). This sense of possibility entails knowing the whole (or several wholes) or being able to construe an unknown whole that could accommodate a known part. The whole has to align with sociological and geographical givens, with the mentality of certain peoples or groups, and with the laws of physics and chemistry. Otherwise, the entire venture is ill-founded. A sense of possibility does not aim for the moon but imagines something that might be possible but has not been considered possible or even potentially possible so far.

Thinking is a means to eliminate uncertainty. This process requires both of the modes of thinking we have discussed thus far. Economic, political, or ecological decisions require us to first consider the situation at hand. Though certain situational aspects can be known, but many cannot. In fact, von Clausewitz (1832) posits that only about 25% of the necessary information is available when a military decision needs to be made. Even then, there is no way to guarantee that whatever information is available is also correct: Even if a piece of information was completely accurate yesterday, it might no longer apply today.

Once our sense of possibility has helped grasping a situation, problem solvers need to call on their reasoning skills. Not every situation requires the same action, and we may want to act this way or another to reach this or that goal. This appears logical, but it is a logic based on constantly shifting grounds: We cannot know whether necessary conditions are met, sometimes the assumptions we have made later turn out to be incorrect, and sometimes we have to revise our assumptions or make completely new ones. It is necessary to constantly switch between our sense of possibility and our sense of reality, that is, to switch between thinking and reasoning. It is an arduous process, and some people handle it well, while others do not.

If we are to believe Tuchman’s (1984) book, “The March of Folly”, most politicians and commanders are fools. According to Tuchman, not much has changed in the 3300 years that have elapsed since the misguided Trojans decided to welcome the left-behind wooden horse into their city that would end up dismantling Troy’s defensive walls. The Trojans, too, had been warned, but decided not to heed the warning. Although Laocoön had revealed the horse’s true nature to them by attacking it with a spear, making the weapons inside the horse ring, the Trojans refused to see the forest for the trees. They did not want to listen, they wanted the war to be over, and this desire ended up shaping their perception.

The objective of psychology is to predict and explain human actions and behavior as accurately as possible. However, thinking cannot be investigated by limiting its study to neatly confined fractions of reality such as the realms of propositional logic, chess, Go tasks, the Tower of Hanoi, and so forth. Within these systems, there is little need for a sense of possibility. But a sense of possibility – the ability to divine and construe an unknown reality – is at least as important as logical reasoning skills. Not researching the sense of possibility limits the validity of psychological research. All economic and political decision making draws upon this sense of possibility. By not exploring it, psychological research dedicated to the study of thinking cannot further the understanding of politicians’ competence and the reasons that underlie political mistakes. Christopher Clark identifies European diplomats’, politicians’, and commanders’ inability to form an accurate representation of reality as a reason for the outbreak of World War I. According to Clark’s (2012) book, “The Sleepwalkers”, the politicians of the time lived in their own make-believe world, wrongfully assuming that it was the same world everyone else inhabited. If CPS research wants to make significant contributions to the world, it has to acknowledge complexity and uncertainty as important aspects of it.

For more than 40 years, CPS has been a new subject of psychological research. During this time period, the initial emphasis on analyzing how humans deal with complex, dynamic, and uncertain situations has been lost. What is subsumed under the heading of CPS in modern research has lost the original complexities of real-life problems. From our point of view, the challenges of the 21st century require a return to the origins of this research tradition. We would encourage researchers in the field of problem solving to come back to the original ideas. There is enough complexity and uncertainty in the world to be studied. Improving our understanding of how humans deal with these global and pressing problems would be a worthwhile enterprise.

Author Contributions

JF drafted a first version of the manuscript, DD added further text and commented on the draft. JF finalized the manuscript.

Authors Note

After more than 40 years of controversial discussions between both authors, this is the first joint paper. We are happy to have done this now! We have found common ground!

Conflict of Interest Statement

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Acknowledgments

The authors thank the Deutsche Forschungsgemeinschaft (DFG) for the continuous support of their research over many years. Thanks to Daniel Holt for his comments on validity issues, thanks to Julia Nolte who helped us by translating German text excerpts into readable English and helped us, together with Keri Hartman, to improve our style and grammar – thanks for that! We also thank the two reviewers for their helpful critical comments on earlier versions of this manuscript. Finally, we acknowledge financial support by Deutsche Forschungsgemeinschaft and Ruprecht-Karls-Universität Heidelberg within their funding programme Open Access Publishing .

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Keywords : complex problem solving, validity, assessment, definition, MicroDYN

Citation: Dörner D and Funke J (2017) Complex Problem Solving: What It Is and What It Is Not. Front. Psychol. 8:1153. doi: 10.3389/fpsyg.2017.01153

Received: 14 March 2017; Accepted: 23 June 2017; Published: 11 July 2017.

Reviewed by:

Copyright © 2017 Dörner and Funke. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY) . The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

*Correspondence: Joachim Funke, am9hY2hpbS5mdW5rZUBwc3ljaG9sb2dpZS51bmloZWlkZWxiZXJnLmRl

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How To Solve Complex Problems

In today’s increasingly complex world, we are constantly faced with ill-defined problems that don’t have a clear solution. From poverty and climate change to crime and addiction, complex situations surround us. Unlike simple problems with a pre-defined or “right” answer, complex problems share several basic characteristics that make them hard to solve. While these problems can be frustrating and overwhelming, they also offer an opportunity for growth and creativity. Complex problem-solving skills are the key to addressing these tough issues.

In this article, I will discuss simple versus complex problems, define complex problem solving, and describe why it is so important in complex dynamic environments. I will also explain how to develop problem-solving skills and share some tips for effectively solving complex problems.

How is simple problem-solving different from complex problem-solving?

Solving problems is about getting from a currently undesirable state to an intended goal state. In other words, about bridging the gap between “what is” and “what ought to be”. However, the challenge of reaching a solution varies based on the kind of problem that is being solved. There are generally three different kinds of problems you should consider.

Simple problems have one problem solution. The goal is to find that answer as quickly and efficiently as possible. Puzzles are classic examples of simple problem solving. The objective is to find the one correct solution out of many possibilities.

Problems are different from puzzles in that they don’t have a known problem solution. As such, many people may agree that there is an issue to be solved, but they may not agree on the intended goal state or how to get there. In this type of problem, people spend a lot of time debating the best solution and the optimal way to achieve it.

Messes are collections of interrelated problems where many stakeholders may not even agree on what the issue is. Unlike problems where there is agreement about what the problem is, in messes, there isn’t agreement amongst stakeholders. In other words, even “what is” can’t be taken for granted. Most complex social problems are messes, made up of interrelated social issues with ill-defined boundaries and goals.

Problems and messes can be complicated or complex

Puzzles are simple, but problems and messes exist on a continuum between complicated and complex. Complicated problems are technical in nature. There may be many involved variables, but the relationships are linear. As a result, complicated problems have step-by-step, systematic solutions. Repairing an engine or building a rocket may be difficult because of the many parts involved, but it is a technical problem we call complicated.

On the other hand, solving a complex problem is entirely different. Unlike complicated problems that may have many variables with linear relationships, a complex problem is characterized by connectivity patterns that are harder to understand and predict.

Characteristics of complex problems and messes

So what else makes a problem complex? Here are seven additional characteristics (from Funke and Hester and Adams ).

• Lack of information. There is often a lack of data or information about the problem itself. In some cases, variables are unknown or cannot be measured.
• Many goals. A complex problem has a mix of conflicting objectives. In some sense, every stakeholder involved with the problem may have their own goals. However, with limited resources, not all goals can be simultaneously satisfied.
• Unpredictable feedback loops. In part due to many variables connected by a range of different relationships, a change in one variable is likely to have effects on other variables in the system. However, because we do not know all of the variables it will affect, small changes can have disproportionate system-wide effects. These unexpected events that have big, unpredictable effects are sometimes called Black Swans.
• Dynamic. A complex problem changes over time and there is a significant impact based on when you act. In other words, because the problem and its parts and relationships are constantly changing, an action taken today won’t have the same effects as the same action taken tomorrow.
• Time-delayed. It takes a while for cause and effect to be realized. Thus it is very hard to know if any given intervention is working.
• Unknown unknowns. Building off the previous point about a lack of information, in a complex problem you may not even know what you don’t know. In other words, there may be very important variables that you are not even aware of.
• Affected by (error-prone) humans. Simply put, human behavior tends to be illogical and unpredictable. When humans are involved in a problem, avoiding error may be impossible.

What is complex problem-solving?

“Complex problem solving” is the term for how to address a complex problem or messes that have the characteristics listed above.

Since a complex problem is a different phenomenon than a simple or complicated problem, solving them requires a different approach. Methods designed for simple problems, like systematic organization, deductive logic, and linear thinking don’t work well on their own for a complex problem.

And yet, despite its importance, there isn’t complete agreement about what exactly it is.

How is complex problem solving defined by experts?

Let’s look at what scientists, researchers, and system thinkers have come up with in terms of a definition for solving a complex problem. 

As a series of observations and informed decisions

For many employers, the focus is on making smart decisions. These must weigh the future effects to the company of any given solution. According to Indeed.com , it is defined as “a series of observations and informed decisions used to find and implement a solution to a problem. Beyond finding and implementing a solution, complex problem solving also involves considering future changes to circumstance, resources, and capabilities that may affect the trajectory of the process and success of the solution. Complex problem solving also involves considering the impact of the solution on the surrounding environment and individuals.”

As using information to review options and develop solutions

For others, it is more of a systematic way to consider a range of options. According to O*NET ,  the definition focuses on “identifying complex problems and reviewing related information to develop and evaluate options and implement solutions.”

As a self-regulated psychological process

Others emphasize the broad range of skills and emotions needed for change. In addition, they endorse an inspired kind of pragmatism. For example, Dietrich Dorner and Joachim Funke define it as “a collection of self-regulated psychological processes and activities necessary in dynamic environments to achieve ill-defined goals that cannot be reached by routine actions. Creative combinations of knowledge and a broad set of strategies are needed. Solutions are often more bricolage than perfect or optimal. The problem-solving process combines cognitive, emotional, and motivational aspects, particularly in high-stakes situations. Complex problems usually involve knowledge-rich requirements and collaboration among different persons.”

As a novel way of thinking and reasoning

Finally, some emphasize the multidisciplinary nature of knowledge and processes needed to tackle a complex problem. Patrick Hester and Kevin MacG. Adams have stated that “no single discipline can solve truly complex problems. Problems of real interest, those vexing ones that keep you up at night, require a discipline-agnostic approach…Simply they require us to think systemically about our problem…a novel way of thinking and reasoning about complex problems that encourages increased understanding and deliberate intervention.”

A synthesis definition

By pulling the main themes of these definitions together, we can get a sense of what complex problem-solvers must do:

Gain a better understanding of the phenomena of a complex problem or mess. Use a discipline-agnostic approach in order to develop deliberate interventions. Take into consideration future impacts on the surrounding environment.

Why is complex problem solving important?

Many efforts aimed at complex social problems like reducing homelessness and improving public health – despite good intentions giving more effort than ever before – are destined to fail because their approach is based on simple problem-solving. And some efforts might even unwittingly be contributing to the problems they’re trying to solve. 

Einstein said that “We can’t solve problems by using the same kind of thinking we used when we created them.” I think he could have easily been alluding to the need for more complex problem solvers who think differently. So what skills are required to do this?

What are complex problem-solving skills?

The skills required to solve a complex problem aren’t from one domain, nor are they an easily-packaged bundle. Rather, I like to think of them as a balancing act between a series of seemingly opposite approaches but synthesized. This brings a sort of cognitive dissonance into the process, which is itself informative.

It brings F. Scott Fitzgerald’s maxim to mind: 

“The test of a first-rate intelligence is the ability to hold two opposing ideas in mind at the same time and still retain the ability to function. One should, for example, be able to see that things are hopeless yet be determined to make them otherwise.” 

To see the problem situation clearly, for example, but also with a sense of optimism and possibility.

Here are the top three dialectics to keep in mind:

Thinking and reasoning

Reasoning is the ability to make logical deductions based on evidence and counterevidence. On the other hand, thinking is more about imagining an unknown reality based on thoughts about the whole picture and how the parts could fit together. By thinking clearly, one can have a sense of possibility that prepares the mind to deduce the right action in the unique moment at hand.

As Dorner and Funke explain: “Not every situation requires the same action,  and we may want to act this way or another to reach this or that goal. This appears logical, but it is a logic based on constantly shifting grounds: We cannot know whether necessary conditions are met, sometimes the assumptions we have made later turn out to be incorrect, and sometimes we have to revise our assumptions or make completely new ones. It is necessary to constantly switch between our sense of possibility and our sense of reality, that is, to switch between thinking and reasoning. It is an arduous process, and some people handle it well, while others do not.”

Analysis and reductionism combined with synthesis and holism

It’s important to be able to use scientific processes to break down a complex problem into its parts and analyze them. But at the same time, a complex problem is more than the sum of its parts. In most cases, the relationships between the parts are more important than the parts themselves. Therefore, decomposing problems with rigor isn’t enough. What’s needed, once problems are reduced and understood, is a way of understanding the relationships between various components as well as putting the pieces back together. However, synthesis and holism on their own without deductive analysis can often miss details and relationships that matter.  

What makes this balancing act more difficult is that certain professions tend to be trained in and prefer one domain over the other. Scientists prefer analysis and reductionism whereas most social scientists and practitioners default to synthesis and holism. Unfortunately, this divide of preferences results in people working in their silos at the expense of multi-disciplinary approaches that together can better “see” complexity.

Situational awareness and self-awareness 

Dual awareness is the ability to pay attention to two experiences simultaneously. In the case of complex problems, context really matters. In other words, problem-solving exists in an ecosystem of environmental factors that are not incidental. Personal and cultural preferences play a part as do current events unfolding over time. But as a problem solver, knowing the environment is only part of the equation. 

The other crucial part is the internal psychological process unique to every individual who also interacts with the problem and the environment. Problem solvers inevitably come into contact with others who may disagree with them, or be advancing seemingly counterproductive solutions, and these interactions result in emotions and motivations. Without self-awareness, we can become attached to our own subjective opinions, fall in love with “our” solutions, and generally be driven by the desire to be seen as problem solvers at the expense of actually solving the problem.

By balancing these three dialectics, practitioners can better deal with uncertainty as well as stay motivated despite setbacks. Self-regulation among these seemingly opposite approaches also reminds one to stay open-minded.

How do you develop complex problem-solving skills?

There is no one answer to this question, as the best way to develop them will vary depending on your strengths and weaknesses. However, there are a few general things that you can do to improve your ability to solve problems.

Ground yourself in theory and knowledge

First, it is important to learn about systems thinking and complexity theories. These frameworks will help you understand how complex systems work, and how different parts of a system interact with each other. This conceptual understanding will allow you to identify potential solutions to problems more quickly and effectively.

Practice switching between approaches

Second, practice switching between the dialectics mentioned above. For example, in your next meeting try to spend roughly half your time thinking and half your time reasoning. The important part is trying to get habituated to regularly switching lenses. It may seem disjointed at first, but after a while, it becomes second nature to simultaneously see how the parts interact and the big picture.

Focus on the specific problem phenomena

Third, it may sound obvious, but people often don’t spend very much time studying the problem itself and how it functions. In some sense, becoming a good problem-solver involves becoming a problem scientist. Your time should be spent regularly investigating the phenomena of “what is” rather than “what ought to be”. A holistic understanding of the problem is the required prerequisite to coming up with good solutions.

Stay curious

Finally, after we have worked on a problem for a while, we tend to think we know everything about it, including how to solve it. Even if we’re working on a problem, which may change dynamically from day to day, we start treating it more like a puzzle with a definite solution. When that happens, we can lose our motivation to continue learning about the problem. This is very risky because it closes the door to learning from others, regardless of whether we completely agree with them or not.

As Neils Bohr said, “Two different perspectives or models about a system will reveal truths regarding the system that are neither entirely independent nor entirely compatible.”

By staying curious, we can retain our ability to learn on a daily basis.

Tips for how to solve complex problems

Focus on processes over results.

It’s easy to get lost in utopian thinking. Many people spend so much time on “what ought to be” that they forget that problem solving is about the gap between “what is” and “what ought to be”. It is said that “life is a journey, not a destination.” The same is true for complex problem-solving. To do it well, a problem solver must focus on enjoying the process of gaining a holistic understanding of the problem. 

Adaptive and iterative methods and tools

A variety of adaptive and iterative methods have been developed to address complexity. They share a laser focus on gaining holistic understanding with tools that best match the phenomena of complexity. They are also non-ideological, trans-disciplinary, and flexible. In most cases, your journey through a set of steps won’t be linear. Rather, as you think and reason, analyze and synthesize, you’ll jump around to get a holistic picture.

In my online course , we generally follow a seven-step method:

• Get clear sight with a complex problem-solving frame
• Establish a secure base of operation
• Gain a deep understanding of the problem
• Create an interactive model of the problem
• Develop an impact strategy
• Create an action plan and implement
• Embed systemic solutions

Of course, each of these steps involves testing to see what works and consistently evaluating our process and progress.

Resolution is about systematically managing a problem over time

One last thing to keep in mind. Most social problems are not just solved one day, never to return. In reality,  most complex problems are managed, not solved. For all practical purposes, what this means is that “the solution” is a way of systematically dealing with the problem over time. Some find this disappointing, but it’s actually a pragmatic pointer to think about resolution – a way move problems in the right direction – rather than final solutions.

Problem solvers regularly train and practice

If you need help developing your complex problem-solving skills, I have an online class where you can learn everything you need to know. 

Sign up today and learn how to be successful at making a difference in the world!

SoftwareDominos

Complex Problems: What Does the Nature of the Problem Tell Us About Its Solution

1. Overview

In The 7 Timeless Steps to Guide You Through Complex Problem Solving , we discussed a generic approach that could be systematically applied to solving complex problems. Since not all problems are complex, and many gradations of complexity exist, it is probably a good idea to start by defining what complex problem-solving involves and what categories of problems are most suitable to tackle using that approach. For this reason, understanding complex problems made the top position on the list.

Practically all living organisms deal with complex problems, from single-celled amebas to societies of Homo sapiens , and surprisingly, the solution-creation process can be very similar, at least on the conceptual level. This article will elaborate on this point further, articulating the terminology and ideas often associated with how complex adaptive systems solve complex problems. More specifically, we will answer the following questions:

This article is part of a series on complex problem-solving. The list below will guide you through the different subtopics.

Complex Problem-Solving Guide in 7 Steps

The 7 Timeless Steps to Guide You Through Complex Problem Solving

The Nature of Complex Problems

What Does the Nature of the Problem Tell Us About Its Solution

Gaussian Distributions vs Power Laws

Your Ultimate Guide to Making Sense of Natural and Social Phenomena

Complex Problem-Solving in Groups

An Exploratory Overview of ProbleSolving Processes in Groups

The Power of Critical Thinking

An Essential Guide for Personal and Professional Development

Group-Decision Making

6 Modes That Tell Us How Teams Decide

3. An Intuitive Definition of Complex Problems

We all intuitively grasp the characteristics of challenging problems, at least at their fundamental levels. For instance, we can promptly recognize that fixing a faulty washing machine is relatively simple. First, we need basic technical skills to identify the faulty part. Next, we would read the code on the back, order a spare part, and finally replace it.

In simple problems, there is no uncertainty around the root cause or the solution.

On the other hand, deciding whether or not to accept a job offer is anything but simple. Firstly, you will never have sufficient information to make an optimal decision . Secondly, you cannot predict the consequences of such a decision. Finally, whichever choice you make will change your worldview, rendering any forecasts you have made of the future almost instantly obsolete.

The following characteristics distinguish complex problems.

So, what are complex problems?

Complex problems — an intuitive guide.

Non-triviality

Complex problems generally admit non-trivial solutions. In addition to strong field expertise and solid analytical skills, they require a high cognitive load to formulate.

Uncertainty

Solutions to complex problems cannot be guaranteed as the behaviour of the system to which the solution is applied is always unpredictable.

Diagnosing complex problems is especially challenging because consensus on facts, root causes, and solutions can be difficult to obtain, especially in large groups.

3. Challenges of Working With Complex Problems

Experts like Nassim Taleb, Gerd Gigerenzer, and Daniel Kahnemann insist that solving complex problems is relatively easy once we understand which tools to apply. In their view, failures come from applying engineering methods like optimization rather than intuition , heuristics, biases, imitation, and many other techniques refined over millennia of evolution and accumulated wisdom.

4. Complex Problems in the Literature

Experts have extensively researched topics associated with intuition, cognitive psychology , risk management , organisational behaviour , and decision-making under uncertainty. This has left us with a rich body of knowledge popularized by best-selling authors such as Daniel Kahneman and Nassim Taleb, which will be reviewed next.

4.1 Fooled by Randomness (Taleb, 2001)

Fooled by Randomness is one of Taleb’s best-selling books , and its central story revolves around the hidden role of chance in our lives. In Taleb’s view, we grossly and routinely overestimate our capabilities to forecast future events ( the turkey problem ) and cope with that failure through mechanisms like the narrative fallacy and our ability to reconstruct past events based on new information.

Key takeaways from Fooled By Randomness

• In social , financial, economic, and political systems, Gaussian distributions mislead at best by providing a comforting but shifting ground for modelling events.
• Power laws like Pareto’s provide more suitable models for examining complex systems .
• Time-tested heuristics, formulated through a long knowledge acquisition and refinement period, are more valuable for decision-making under uncertainty than optimisation techniques, which require a well-behaved underlying model (such as the Gaussian).

4.2 Thinking, Fast and Slow (Kahneman, 2011)

Thinking, Fast and Slow is a best-selling book by Daniel Kahneman popularizing his work in cognitive psychology about the mechanism and efficiency of human judgment and decision-making under conditions of uncertainty. His original idea revolves around modelling the human mind as two systems, which he refers to as System 1 and System 2.

Key takeaways from Thinking, Fast and Slow

• Systems 1 and 2 perfectly cover our decision-making needs for simple and complex problems.
• System 1 is fast and inexpensive, allowing us to make critical decisions with imperfect or unreliable data .
• System 1 relies on heuristics and biases to compensate for unreliable information and processing time.
• System 2 is slow and expensive but more accurate, allowing us to make decisions requiring a high cognitive load and processing larger amounts of information.

4.3 Process Consultation (Schein, 1969)

Professor Edgar Schein is a leading authority in organizational behaviour, culture , and psychology. His short but insightful book Process Consultation: Its Role in Organizational Development dedicates a full chapter to group problem-solving and decision-making. Schein explores how leaders and their groups tackle complex problems in this chapter.

Key takeaways from Process Consultation

• Group problem-solving presents challenges and dynamics that differ from those of individuals and is a subject in its own right.
• In both cases, events that cause tension and anxiety trigger a solution-finding process that culminates in applying changes to the environment or the individual or group’s interactions with it.
• However, problem formulation, solution creation and implementation differ significantly between the two cases.

5. The Information Sufficiency Problem

5.1 how much data is enough.

During the Newtonian age, physicists believed that once the initial conditions of a physical system were precisely determined, its future evolution could be predicted with arbitrary precision. For example, the laws of dynamics allow us to calculate the infinite trajectory of a point mass given its initial position and velocity.

What happens when the system consists of innumerable particles, each with a different initial speed and position? For practical reasons, we substitute the individual particles with a unit of volume where its macro properties can be calculated by averaging over its constituent particles. For example, instead of registering the speed and position of every molecule in a gas container, we substitute those numbers with temperature and pressure calculated on a coarse-grained subvolume. This coarse-graining allows us to explore the system’s physical properties without drowning in data.

5.2 The Rise of Statistical Mechanics and Probabilistic Models

The coarse-graining method and the impracticality of precise calculations on the molecular level gave rise to statistical mechanics , which Boltzmann and others pioneered. Under statistical mechanics, physical systems are governed by the laws of thermodynamics. The second law of thermodynamics is the most famous, dictating that a system’s entropy (or disorder) must always increase.

The practical advantages of using coarse-graining came at a cost, as a probabilistic model replaced the classic view of deterministic evolution. In this new paradigm, a physical system is predisposed to evolve into one of numerous states. We can only predict the probability that it will be in a given future state, but we can never be sure which one.

But all is not lost. Even with the probabilistic model, we can still calculate a system’s future state and create contingency plans for each scenario. We might even be able to influence the outcome by applying pressure on known system levers. This assumption forms the basis of Strategic Choice Theory .

Strategic choice theory, in the realm of organizational theory, emphasizes the influence of leaders and decision-makers on an organization’s direction. It contrasts with earlier views that saw organizations solely responding to external forces.

Managing Probabilistic Systems

In probabilistic models, we assume that the system’s future states are well-defined and their probabilities are calculable. Given this information, adequate planning and optimization processes can be applied to maximize a specific utility function.

5.3 Probabilistic Models Cannot Account for Innovation

Any physical, chemical, or biological system that shows innovation cannot, by definition, be analyzed using probability models, as the latter assumes all future states are static and knowable in advance. Also, the probabilities for reaching any of those states are either fixed or vary according to well-specified rules.

Therefore, probabilistic models are not good enough to predict the future behaviour of human systems. This also spells trouble for Strategic Choice Theory, which relies on simple causal relationships between leaders’ interventions and desired consequences to achieve progress or resolve conflicts.

If a system can produce novel behaviour, it is unpredictable and, therefore, hard to manage. Ecologies of living organisms can only be understood through complexity theory and managed by principles that consider that.

Complex systems presenting complex problems will never offer sufficient information, and managers must make choices under uncertain conditions.

Even if we consider every atom (or elementary particle) in the universe , we still would not be able to predict the rich diversity of phenomena (including biodiversity on Earth) that we currently observe. Quantum mechanics and symmetry breaking ensure enough randomness is injected into the system to produce rich but unpredictable results.

The same applies when we try to understand the source of consciousness in our brains. Would it help to incorporate every neuron and synapse in a gigantic mathematical model? Even if this becomes practical someday, experts seem to believe that emerging consciousness in the inanimate matter is far away.

In summary, there seems to be a hard limit on how much useful information, in principle and practice, can be gleaned by observing a complex system .

6. Problem Classification

6.1 maximizing utility functions.

Problems can present themselves in many different ways. However, we are interested in those characterized by a utility function.

A utility function is a concept primarily used in economics, decision theory, and game theory to represent an individual’s preferences over different outcomes or states of the world. It assigns a numerical (or utility) value to each possible outcome or combination, reflecting the individual’s subjective satisfaction or preference associated with those outcomes.

How Are Utility Functions Used?

Here are some key points about utility functions:

Using utility functions, people can compare complex options involving chance or risk and make decisions based on their preferences and risk tolerance.

6.2 Ordered, Chaotic, Complex, and Random Systems

Imagine that you have the following problem. You are required to configure an air conditioning system for a data centre. The system is composed of two machines: a cooling engine and a computer connected to it. The computer has temperature and humidity sensors and various switches and dials that allow operators to set control parameters such as maximum temperature or humidity.

The engineer setting up the system must configure it to minimize power consumption while keeping the room at a given temperature and humidity level. The only issue is that the system does not have an operations guide, and the engineer has to figure out how to set it up using trial and error.

Four scenarios are possible: Ordered, Random, Complex, and Chaotic.

Ordered Systems

• Changes in the switches or dials produce a clear response in the cooling machine.
• Although some settings may impact others, the engineer can, through trial and error, understand the relationship between the controls and the outcomes.
• Ordered systems have direct causal relationships and hard constraints between their components.
• Problems in an ordered system can be resolved through the relationships between control parameters and the utility function.
• Computers, watches, and washing machines are examples of such systems.

Random Systems

• Changes in the switches or dials produce different responses every time. There seems to be no correlation between the settings and the outcomes.
• Random systems have no causal links and no constraints between their components.
• Random systems present problems that cannot be resolved; they are, by definition, unmanageable.
• A reward system based on rolling two dice is a random system.

Chaotic Systems

• Small changes in the switches or dials produce wild responses. Although the system appears random and unpredictable, it shows regular behavioural patterns over the long term.
• Chaotic systems have causal links and hard constraints between their components in addition to non-linear dynamics.
• Chaotic systems are also challenging to manage. However, causes can be linked to effects, and regularities can be leveraged.
• The weather, a turbulent water flow , and three bodies rotating around each other in gravitational fields are examples of chaotic systems.

Complex Systems

• Changes in the switches or dials produce different responses every time. Slight correlations can be measured between the settings and the outcomes.
• Complex systems have indirect causal links and loose constraints between their components.
• Complex systems come in two varieties: adaptive and non-adaptive.
• An example of a non-adaptive complex system is the Brusselator . An example of a complex adaptive system is a microbiome.
• Complex systems present problems that can be resolved through heuristics, safe-to-fail experimentation, and managing in the present rather than towards a desirable future state.

7. Small Worlds, Optimization, and Unknown Unknowns

7.1 leonard j. savage’s “small world”.

Leonard Jimmie Savage (1917-1971) was an American statistician and economist who significantly contributed to statistics , decision theory, and econometrics.

“Savage’s Small World” refers to a thought experiment proposed by the statistician and economist Leonard Jimmie Savage. This concept is often cited in discussions about subjective probability and decision theory.

Decision-Making in a Simple World

L. J. Savage’s “Small World”

• In Savage’s Small World, imagine a small society where everyone knows each other’s preferences, capabilities, and the outcomes of their decisions.
• Within this world, individuals can communicate freely and exchange information about their beliefs, desires, and experiences.
• In such a setting, decision-making becomes more transparent and informed, as individuals can access comprehensive knowledge about each other’s perspectives and choices.

The significance of Savage’s Small World lies in its implications for decision theory. It illustrates an idealized scenario where uncertainty is minimized, and individuals have perfect knowledge about the consequences of their actions. In reality, however, decision-makers often face uncertainty and incomplete information, prompting probabilistic reasoning and subjective judgment.

By contrasting Savage’s Small World with the complexities of real-world decision-making, Savage highlighted the importance of subjective probability for navigating uncertainty and making rational choices. Subjective probability allows individuals to express their beliefs and uncertainty in a formal framework, facilitating reasoned decision-making even when complete information is lacking.

7.2 Optimization Techniques

Optimization techniques can be effectively applied in a Small World scenario where all outcomes and probabilities can be precisely computed beforehand. This is because decision-makers have complete knowledge of the system, allowing them to accurately assess the consequences of their actions and choose the optimal course of action based on predetermined criteria.

In contrast, in the real world, uncertainty, complexity, and incomplete information often make it challenging to compute outcomes and probabilities beforehand precisely. As a result, optimization techniques may not be as effective, as they rely on accurate information to generate optimal solutions. Decision-makers must contend with uncertainty and imperfect knowledge, which can lead to suboptimal outcomes even when applying optimisation techniques.

One example where optimization relies on known outcomes and their probabilities is in the context of inventory management.

In inventory management, a retailer determines the optimal inventory level for each product to minimize costs while ensuring that customer demand is met. In this case, the utility function represents the retailer’s objective, which typically involves minimizing inventory holding costs and stockouts.

Optimisation Process in Inventory Management

Here’s a rigorous breakdown of the optimization process:

• 1 – Identify outcomes and probabilities :
• 2- Define the utility function :
• 3- Formulate the optimization problem :
• 4- Solve the optimization problem :

By incorporating known outcomes (demand scenarios) and their probabilities into the utility function and using optimization techniques, retailers can manage their inventory effectively, minimizing costs while ensuring customer satisfaction and maintaining adequate product availability.

7.3 Optimisation in Complex Worlds

Optimization techniques may encounter challenges in complex situations, particularly those governed by power laws (see discussion on Gaussian Distributions vs Power Laws: Your Ultimate Guide to Making Sense of Natural and Social Phenomena and their impact on our understanding of complex natural phenomena), due to several reasons:

Practical challenges of estimating model parameters in power laws versus Gaussians

Comparing the practical difficulties of estimating model parameters such as mean and variance in power laws versus Gaussians:

• Mean estimation
• Variance estimation

7.4 Unknown Unknowns

The concept of “ unknown unknowns” refers to phenomena or factors that are not only unknown but also unknowable.

In Savage’s “Small World,” which represents an idealized scenario where decision-makers have perfect knowledge of outcomes and their probabilities, the concept of “unknown unknowns” highlights the limitations of this idealization. In a Small World, nothing new ever happens, and there can be no “Unknown Unknowns”.

In contrast, complex adaptive systems constantly display emergent behaviour; patterns that could not have been anticipated. A leader managing such a system cannot list all possible outcomes, let alone assign each probability.

8. Subjectivity and the Role of the Observer

In decision-making, a leader’s subjective experience contrasts with their role as an objective observer. For example, in systems thinking and cybernetics, the leader must diagnose problems based on data and evidence and formulate a logical and rational solution.

A leader working on complex problems in a social group is an integral part of the system. As we have seen in previous sections, the leader is unable to gather sufficient information about the system in principle and practice, and whatever data they gather will be coloured by their subjective experience

Systems Thinking in a Nuntshell

Systems Thinking is a holistic approach to understanding complex systems by examining their interconnectedness, interdependencies, and dynamics. It views the leader’s role in an organization as crucial for effective strategy formulation and decision-making by emphasizing the following principles:

• Holistic Perspective :
• Interconnectedness :
• Feedback Loops :

Systems Thinking addresses the paradox of the leader being part of the system being managed by acknowledging the leader’s dual role as both a participant within the system and an external observer guiding its direction. Several key principles help resolve this conflict:

Exploring problem-solving reveals that not all problems are created equal. Distinguishing between simple and complex problems reveals the underlying nature of the systems they belong to. Simple problems are typically found within ordered systems, whereas complex problems are inherent to complex systems. These systems extend beyond biological ecologies to encompass social groups and organizations, where intricate interactions and emergent behaviours define their complexity.

One defining characteristic of complex systems is their governance by power laws, rendering traditional optimization techniques ineffective. Unlike in ordered systems, where linear solutions may suffice, complex systems defy such neat categorizations. Applying optimization strategies proves futile due to the non-linear, unpredictable dynamics governed by power laws.

Heuristics emerge as promising alternatives to optimization in navigating the labyrinth of complex systems. These intuitive, rule-of-thumb approaches allow for adaptive decision-making, acknowledging complex systems’ inherent uncertainty and non-linearity.

10. References

• Thinking, Fast and Slow — by Daniel Kahneman , 2011
• Fooled by Randomness — by Nassim Nicholas Taleb , 2001
• Process Consultation — by Edgar Schein , 1969
• The Quark and the Jaguar — by Murray Gell-Mann , 1994

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Complex Problem Solving

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Dealing with uncertainty ; Dynamic decision making ; Problem solving in dynamic microworlds

Complex problem solving takes place for reducing the barrier between a given start state and an intended goal state with the help of cognitive activities and behavior. Start state, intended goal state, and barriers prove complexity, change dynamically over time, and can be partially intransparent. In contrast to solving simple problems, with complex problems at the beginning of a problem solution the exact features of the start state, of the intended goal state, and of the barriers are unknown. Complex problem solving expects the efficient interaction between the problem-solving person and situational conditions that depend on the task. It demands the use of cognitive, emotional, and social resources as well as knowledge (see Frensch and Funke 1995 ).

Theoretical Background

Since 1975 there has been started a new movement in the psychology of thinking that is engaged in complex...

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Brehmer, B., & Dörner, D. (1993). Experiments with computer-simulated microworlds: Escaping both the narrow straits of the laboratory and the deep blue sea of the field study. Computers in Human Behavior, 9 , 171–184.

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Dörner, D. (1997). The logic of failure. Recognizing and avoiding error in complex situations . New York: Basic Books.

Frensch, P. A., & Funke, J. (Eds.). (1995). Complex problem solving: The European perspective . Hillsdale: Lawrence Erlbaum Associates.

Funke, J. (2003). Problemlösendes Denken . Stuttgart: Kohlhammer.

Osman, M. (2010). Controlling uncertainty: A review of human behavior in complex dynamic environments. Psychological Bulletin, 136 , 65–86.

Wenke, D., Frensch, P. A., & Funke, J. (2005). Complex problem solving and intelligence: Empirical relation and causal direction. In R. J. Sternberg & J. E. Pretz (Eds.), Cognition and intelligence: Identifying the mechanisms of the mind (pp. 160–187). New York: Cambridge University Press.

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Funke, J. (2012). Complex Problem Solving. In: Seel, N.M. (eds) Encyclopedia of the Sciences of Learning. Springer, Boston, MA. https://doi.org/10.1007/978-1-4419-1428-6_685

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