Dr. Mark L. Mitchell

The Five Ordered Steps of Problem-Solving

I. Define problem

A. Why this step is the most important step: Defining the problem defines the solution (The treatment depends on the diagnosis).

    Quotes illustrating the importance of this step:

    Examples of insights due to re-defining the problem

       

B. Three pitfalls in defining the problem.

1. Defining the problem too narrowly. For example, 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?"

He has also been accused of asking

"How can we have a good economy by wrecking the environment?" when 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?"

 

            Ways to avoid defining the problem too narrowly

             A longer look at reframing the problem

2.  Finding the source of the problem

Two reasons we have difficulty with this step:

  1. Not taking responsibility for our role (Examples: "It's not my fault," "Look at what you made me do!", "You are making me mad", "That's a nasty question," )
  2. . One way to deal with this trap 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."

  3. In our chaotic, complex world, Isolating the cause of an effect is difficult. Consequently, 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.

3. We may misdiagnose the problem because we think we have one type of problem when we really have another.

              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.

                   


II. Generate solutions

A. 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, but not for problems with human relationships.

2. Heuristics: a general rule that guides problem-solving, but does not guarantee a perfect solution. (Click here for a weather-related heuristic.)  Examples of useful heuristics:

 

 

 

One type of heuristic: The representativeness heuristic:

a general rule used when people decide whether something is a typical case. If the target matches their memory of a typical instance, they will decide that the target is a typical case. We use the representativeness heuristic to classify people and things.

Examples of the representativeness heuristic: Determining whether someone is a child or an adult based on their appearance matching your memorized examples of children and adults.

Advantages: We can take advantage of our experience. For example, a doctor can quickly diagnose a patient who has a disease that the doctor has seen hundreds of times before.

Disadvantages:

  1. Problems may look similar, but be different. So, the representativeness heuristic may lead to stereotyping and overlooking key differences. Remember,  "History doesn't repeat, but it may rhyme." (quote often attributed to Mark Twain, but probably best attributed to John Robert Columbo)
  2. We may stick with an old solution when we could come up with a better solution.

B. 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. Set: a rigidity in problem-solving due to wanting to continue to do things the old way.

    Examples: Continuing to try to open a car door with a remote when it could be opened with the key;
    waiting to add 4 5-pound weights to a barbell when 2 10-pound weights are available.

    Functional fixedness: a type of set where we consider only the usual function of an object and overlook other possible uses. Ex: Thinking that the only possible use for a brick is to build a wall. (Here, you can see Duncker's Candle Problem--a way of showing the power of functional fixedness).

    2. STM's limits-- Because STM is limited, we can't think of many options at once and we can't think of all the pros and cons of a decision at once. One way to deal with this problem is to make a pro-cons table of the options. Another alternative is to have a computer program help you make a decision.


III. Evaluate alternatives

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.  Correctly weight all those pros and cons

4. 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 (there are too many to fit in STM)

    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.

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

  3. Because we rely on the availability heuristic

    (which should have been called the accessibility heuristic), we are bad at estimating the frequency of events. That is, we estimate how often something happens based on how easy it is to remember examples of that event occurring. The problem is that some events, even if they don't occur very often, are easy to recall (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.).
    • 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 offier job), loggers (more than 6X as dangerous), pilots(more than 3X as dangerous), roofers, steel workers, truck drivers, and garbage collectors.
     

  4. We are not nearly as accurate about predicting the future as we think we are. So, we confidently make bad predictions.
  5. (If you came here from reading about the survey, click here to return )

  6. 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.
  7. We have an optimism bias, so we think things will turn out well, and we forget that decisions often have unintended consequences (heroin was once considered a solution to opium addiction). In other words, a "solution" may not work and will probably have side effects. 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.
    • 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.
    • People dying by taking unproven cancer "cures" when they could have been saved by traditional medicine.
  8. Decision making can be stressful. Possible solutions:
    • Don't rush to a decision. Sleep on it.
    • Ask "What would I advise a friend to do?"
    • Ask "What would happen if I did nothing?"
    • Ask "How would I feel about this decision 5 years from now?"
    • Have a Plan B.
    • Change your options from "should I do x OR y?"  to "Could I do X AND Y?"

IV. Act

V. Evaluate: Is it working?
Why we fail to find out whether our solution is effective.

We can't answer this question because

We ask the question 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. We feel we have invested so much time, money, or effort in our "solution," that we must stick with it.
  3. 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 has 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).
  4. The outcome may be affected by factors beyond our control.
We don't answer this question 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 llmited 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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