Dr. Mark L. Mitchell

The Five Ordered Steps of Problem-Solving

Step 1: Define the problem.

Why is this step is the most important step?

     Because defining the problem defines the solution. That is, the diagnosis determines the treatment (if you are diagnosed with the flu, you get a different treatment than if you are diagnosed with a cold). 

    Quotes illustrating the importance of this step:

    Examples of insights due to re-defining the problem

       

6 pitfalls in defining the problem.

  1. Narrowly defining the problem results eliminates options.
    • When confronted with COVID-19, Trump apparently framed the problem as "Can we have a good economy OR fight COVID?"-- when he could have framed the problem as "How can we have a good economy AND fight COVID?"
    • Trump has also been accused of asking "How can we have a good economy by wrecking the environment?"-- when  he could have asked "How can we have a good economy AND improve the environment?"
    • Similarly, many people define problems in "all or none" terms, such as "Should we stay married or should we get a divorce?"
    • Experience a simple example of defining the problem too narrowly: The nine-dot problem

                  Ways to avoid defining the problem too narrowly

                   A longer look at reframing the problem

  2. Biases may cause us to deny the problem ("Denial is not just a river in Egypt): "It's not a problem because I don't want it to be a problem." Examples:
    • Denying the smoking causes cancer.
    • Denying global warming.
    • Denying the threat caused by COVID-19.
    • Denying that there are problems with our policing and justice systems.
  3. Biases may cause us to misidentify the cause of the problem. As Maslow wrote, "it is tempting, if the only tool you have is a hammer, to treat everything as if it were a nail." Examples:
    • Republicans seem to think, despite the evidence, that all problems are caused by taxes and all problems can be solved by cutting taxes.
    • Republicans seem to think that budget deficits are bad--when there is a Democratic president.
    • Bigots see the U.S. immigration problem as that there are too many immigrants when, in fact, the problem is that we have too few--a fact that threatens social security and our future economic growth.
    Two particularly common and powerful biases:

    1. The "Not me" bias: We often don't take responsibility for our contribution to the problem. For example, you have heard people say things like:

      • "It's not my fault." 
      • "Look at what you made me do!"
      • "You are making me mad"
      • "That's a nasty question"
      • "Fake news!"
      One way to deal with this bias is suggested by Timothy Ferris: "...tell my story to myself from the perspective of a victim, then I tell the exact same story from a place of 100 percent responsibility."
    2. The fundamental attribution error. Personalizing problems: Blaming people rather than situations. As anyone who has been stuck in traffic or in a bad job knows, bad environments can make even mature, rational people do immature, irrational things.
  4. Mistaking symptoms or effects for causes: In our chaotic, complex world, isolating the cause of an effect is difficult. Consequently, not only we may mistake effects or symptoms for causes. Furthermore, what we think is an important source of the problem may be unimportant (our ancestors would not believe that tiny things like viruses and bacteria could make us sick) whereas a factor that we think is unimportant may turn out to be very important. So, we may need to rely on scientists and experts to determine the most important causes of a problem. Many people refuse to do so; consequently, we have people arguing that cigarettes don't cause cancer and that humans are not contributing to global warming.
  5. Incorrectly identifying what  kind of problem we have, so we try to solve one type of problem when we should be trying to solve a different type of problem.
  6.               Example 1:

                         What rule is determining the sequence of these numbers?    8,5, 4, 9, 1, 6, 7, 10, 3, 2

                          Two other examples: Think of the last time you applied the wrong formula to a word-problem or heard of a friend who was misdiagnosed by a doctor.

    Sometimes, we misidentify the kind of problem we have because of the representativeness heuristic: a general rule used when people decide whether something is an example of a category. If  what we are looking at  matches our memory of a typical instance of a category, we will classify that  thing as being a member of that category. For example, you determine whether someone is a child or an adult based on their appearance matching your memorized examples of children and adults. The advantage of the representativeness heuristic is that people can take advantage of their experiences and their expertise. For example, a doctor can quickly diagnose a patient who has a disease that the doctor has seen hundreds of times before. However, problems may look similar, but be different. So, the representativeness heuristic may lead not only to stereotyping, but to misdiagnosing the problem by overlooking key differences between this new problem and old problems.

    The representativeness heuristic may also cause us to ignore important information. For example, a doctor might, seeing that the patient's symptoms matched malaria, use the representativeness heuristic to diagnose the patient as having malaria, even though the patient probably didn't have malaria given one important fact: There hadn't been a malaria case where the patient lived in over 50 years.

  7. Defining the problem in a way that is too vague. Example: A student says "they are having trouble with the course" or "did not do well on the last exam."

Step 2: Generate options

Using existing solutions:

1. Algorithms: a problem-solving strategy that--if all the steps are followed--is guaranteed to eventually lead to a solution.

Two problems with algorithms:

1. They involve many steps (and doing many steps takes time and uses up the limited space in short-term memory)

2. They only fit problems where there is one right answer. Thus, there are algorithms for solving some math problems and playing certain simple games like tic-tac-toe, but not for problems with human relationships.

2. Heuristics: a general rule that guides problem-solving, but does not guarantee a perfect solution. You can think of heuristics as mental shortcuts, hunches, or as educated guesses. (Click here for a weather-related heuristic.)  Examples of useful heuristics:

Barriers to generating new solutions

  1. Ignoring the problem and hoping that it will magically go away

            Examples: "COVID will magically go away."

  2.                           "COVID is a hoax."

                             "Global warming is a hoax."

    2. Fixation/Set: a rigidity in problem-solving due to wanting to continue to do things the old way. Examples:

    3. STM's limits-- Because STM is limited, we can't think of many options at once. One way to get around this problem is to force yourself to write down at least 3 options. 

    4. "All-or-nothing" thinking. Examples

    5. Prematurely dismissing solutions   The generating ideas step should not be disrupted by evaluating ideas: Evaluation should  be the next step.


Step 3:  Evaluate options

("For every problem, there is a solution that is simple, quick, and wrong" -- Paul Ylvisaker. True, even before Trump suggested the COVID could be cured with chloroquine or reportedly suggested that hurricanes should be nuked.)

Why we "satisfice" (choose the first satisfactory option)

rather than "optimize" (choose the best [optimum] option)

What it takes to optimize:

1. Consider all the options

2. Consider all the pros and cons of all the options

3. Determine the probabilities of each of those prose and cons

4.  Correctly weight the importance of all those pros and cons

5. Combine all the  information about the pros and cons of all the options to arrive at the best (optimal) choice

 

Table illustrating complexity of making an optimal choice: An oversimplified example of choosing among apartments. Note that there are probably more than 3 places that you could consider and that you probably care about more than price, proximity to campus, and landlord. For example, you probably care about how quiet it is, how safe it is, how big it is, and how nice it is. However, even this oversimplified example shows you how complicated optimizing is.

 

Options Price Score on Price Price's Importance Location Location's Score Location's Importance Landlord's Reputation Landlord's Score Landlord's ImportanceTotal score
1 500/month 3 4 2 miles from campus 2 2 Excellent 5 4 36 (3 * 4) + (2 * 2) + (5 * 4)
2 400/month 4 4 5 miles from campus 1 2 Average 3 4 30 (4 * 4) + (1 * 2) + (3 * 4)
3 700/month 1 4 next to campus 5 2 Poor 1 4 18 (1 * 4) + (5 * 2) + (1 * 4)

Why we fail to optimize (besides the fact that optimizing is stressful):

  1. Because of the limits of STM, we do poorly at:

    Considering all the options

    Considering all the pros and cons of each option

    Combining all that information

  2. To get around some of the limits of short-term memory, you might just write down all your options as well as their pros and cons (Example).

    To get around more of the limits of short-term memory, you could use this decision making program to help you make decisions.

  3. We are bad at estimating the frequency of events because of the availability heuristic:  using the rule that  how often something happens is based on how easy it is to remember examples of that event happening. The problem is that some events, even if they don't occur very often, are easy to recall (e.g., airplane crashes).

    How politicians and some in the media have used the availability heuristic against us.

    • In 2016, Trump ran on a vision of America being unsafe due to violent crime, but, in fact, America's violent crime rate was almost half of what it had been in 1990.
    • Trump acted like cities near the Mexican border are extremely dangerous places, largely due to undocumented immigrants from Mexico. In fact, it seems that immigrants are less likely to commit crimes and that some southern border towns (e.g., El Paso) are among the safest cities in the country whereas cities far from the Mexican border (e.g., Baltimore and Detroit) are among the most dangerous U.S. cities.
    • Trump has convinced some people that ANTIFA are a bunch of murderers. In fact, as of this writing,  ANTIFA is responsible for only one death (and that may have been in self-defense).  In general, right wing extremists are responsible for much more violence than the left-wing extremists. (link to more recent data).
    • Some have argued that police are being gunned down at high rates and that COVID-19 is a hoax. However, recent figures show 101 police officers died from  COVID-19 and 82 died from all other causes combined (e.g., car accidents, being shot, etc.).
    • Police are about 3/4 as likely to die from a car crash as from a shooting; yet many officers do not wear seat belts.
    • Being a police officer is a dangerous job. However, there are at least 18 jobs that are more dangerous. Jobs that are more than 2X as dangerous as being a police officer include commercial fisherman and fisherwomen (more than 7X as dangerous as the police officer job), loggers (more than 6X as dangerous), pilots (more than 3X as dangerous), roofers, steel workers, truck drivers, and garbage collectors.
    • As Kristoff (March 23, 2021)writes, "In a typical year in the U.S., more preschoolers are shot dead in America (about 75) than police officers are."

    *Note that the availability heuristic also fools us about whether we have a problem--or what the problem is. For example, many people think the U.S. has an immigration problem due to having too many immigrants. In fact, the U.S. does have an immigration problem due to a lack of immigrants. The number of Americans who were born in a foreign country has shrunk by more than half since the 1990s--and, if not fixed, this immigrant shortage will have dramatic negative effects on social security (and, probably, on the entire economy--Japan has learned how a lack of immigrants sinks an economy)

     

  4. Satisficing: Going with the first option that is satisfactory rather than optimizing: going for the best (optimum) option.
  5. Decision fatigue: If we are tired of making decisions, we may not look at all our options jor evaluate them carefully.
  6. Looking at only one criteria when many factors have to be taken into account: Examples:
    • "I will take the one with the lowest price"--disregarding quality, convenience, and other criteria.
    • "I will take Dr. X's class because it fits into my schedule."
  7. Looking only at the solution's effect on your immediate problem. That is, not engaging in systems thinking--realizing that everything is connected to everything else. The good systems thinker is thinking several steps ahead.
    • We look at short-term effects rather than long term effects.
    • We don't consider side effects and unintended consequences.
      • People may change their behavior in ways that defeat our solution (e.g., they may find loopholes in rules, rebel against rules, or retaliate against sanctions imposed for breaking the rules).
      • Your solution affects more people than you considered (e.g., eliminating homelessness might hurt hotel and other business owners)
      • Heroine was once considered a solution to opium addiction.
      • President Trump urged people to take chloroquine, arguing, essentially, "what do you have to lose." However, chloroquine has side effects and at least one study suggested that people taking chloroquine were more likely to die than those not taking that drug.
      • We may exercise more to try to lose weight but end up eating more (because we are hungrier or because we "earned it"), so we end up gaining weight.
  8. "All or nothing" thinking: We see a solution as all good or all bad. The result may be that we see all the options as terrible. For example, since both Democrats and Republicans have some dishonest members, we may say, "They are all terrible." As the saying goes, "the perfect is the enemy of the good."
  9. Overconfidence: We are not nearly as accurate about predicting the future as we think we are. So, we confidently make bad predictions.
  10. We are vulnerable to framing effects (the way the problem is worded affects the decision that we will make) because we are loss adverse: we hate to think that we might lose something. We like to gain, but we HATE to lose. Insurance companies and bankers love us for this.
  11. We have an optimism bias, so we overestimate the chances that our solution will work. Examples of optimism bias:
    • Businesses think that mergers will be successful, even though 84% of merger deals did not boost shareholder return.
    • President Trump said that the COVID-19 would go away by April, 2020.
    • People dying by taking unproven cancer "cures" when they could have been saved by traditional medicine.
    • The planning fallacy: Things take much longer than we think that they will.
  12. Groupthink: People don't raise objections because they want to get along.
     

Step 4: Making a Decision

    Besides inertia, you may have trouble making a decision and acting on it because (a) you  may make the wrong decision and (b) the decision may have consequences that you did not anticipate. To help you make decisions with less stress,

Step 5: Evaluate the "Solution"

Why we fail to answer the question: Is our "solution working?

We can't answer this question "Is it working" because

We ask the question "Is it working" but get the wrong answers because
  1. Confirmation bias: We pay attention to evidence that appears to support our beliefs while ignoring or downplaying evidence that appears to refute our beliefs. We think we are being rational, but we are really rationalizing. By looking only at signs indicating that our "solution" is working, we may think our solution is working when it is failing. Remember, even though it doesn't work and may have killed George Washington, people and doctors believed in blood-letting for thousands of years.
  2. Cognitive dissonance: We can't admit to ourselves that we made the wrong decision so we rationalize the decision.  Cult members who have given up everything to join a cult are resistant to changing their mind about the cult leader's predictions have been disproven.
  3. Sunken cost fallacy: We know we have made a mistake, but we have invested so much (time, money, emotional energy) in the "solution" that we feel we can't stop now. Sadly, as the saying goes, we "throw good money after bad."  See a 6 minute video illustrating a trap caused by the sunken cost fallacy.
  4. The short term outcomes of our decision may be different from the long term outcomes (e.g., increasing the national debt often has the short-term effect of improving the economy but may have a negative long-term effect; allowing companies to pollute may not immediately increase death rates; a change to a business may at first hurt productivity until workers get used to the new procedures; eating that cake may make the dieter feel good in the short-term but bad in the long-term).
  5. The outcome is affected by factors beyond our control, so we can (a) make the wrong decision but get a good outcome as well as  (b) make the  right decision but get a bad outcome.

We don't ask the question "Is it working" because


By now, you should be able to:

  1. List the 5 steps of the problem solving model.

  2. Explain why defining the problem is the most important step in problem solving.

  3. Give at least one example of a "problem" that our society may have incorrectly defined.

  4. Explain three errors that people commonly make in defining a problem.

  5. Describe how expert problem solvers differ from non-expert problem solvers.

  6. Describe the difference between algorithms and heuristics.

  7. Give two reasons why people tend to use heuristics rather than algorithms.

  8. Describe the advantages and disadvantages of using the representativeness heuristic.

  9. Describe the phenomenon of "set."

  10. Explain how functional fixedness is a particular type of set .

  11. Explain why STM's limitations interfere with our ability to generate solutions to problems.

  12. Explain why people "satisfice" rather than optimize.

  13. Tell someone a strategy they could use so that they could optimize.

  14. Explain why knowing the probability of different outcomes is essential to being able to make the best choice among alternatives.

  15. Explain how the availability heuristic may cause us to make poor decisions.

  16. Explain how people can persuade us to do things by taking advantage of framing effects.
  17. See how we can use computers to get around our limited ability to realize how much we should weight information.
  18. Consult a decision-making site (like this one) to get some tips on how to make better decisions.
  19. Use this decision making program to get around some of STM problems that limit decision making.

 


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