Every action a person takes is the result of having thought about what it is they think they should do and then doing it. Life is riddled with problems that require solving. Should you buy name brand clothing or off brand? Should you trust the person you just met at the bar? Decisions are a complex matter, and cognitive psychologists are interested in figuring out the various ways people reach the conclusions they do, and subsequently do the things they do.
At any given time in life you have a myriad of choices. If you’re sitting in class and not feeling well you could decide to tough it out and keep taking notes, ignore what the teacher is saying, get up and leave, or go and tell the teacher that you’re not feeling well and figure out some way to get the notes you missed at a later time. Choosing what to do relies heavily on the person’s personality and current situation. The process includes generating a list of possibilities, evaluating their pros and cons, and selecting a course of action. Though some decisions seem more logical or rational than others, there are external forces that can influence a person’s judgment. Going back to our example, if the student thinks that the teacher will grade him harshly for interrupting class to tell him he feels sick, then he will be less likely to make that choice even though it might be the best thing to do. Psychologist Herbert Simon proposed that decision making follows a rule called bounded rationality, in which a person does not make perfect or optimal decisions all of the time, but does make pretty good decisions most of the time . Cognitive psychology tries to observe what and how external influences can affect a person’s problem solving abilities, and infers what is going on inside someone’s head when they make a decision.
The act of reasoning can be divided into to different theories. Normative reasoning is the way a person should reason, and descriptive reasoning is the way a person actually does reason. In other words, normative reasoning encompasses rules of logic and descriptive reasoning involves biases and heuristics, both of which will be explained in greater detail later on.
An easy way to observe the difference between these two theories is to look at an example involving statistics. Let’s say you just visited an oncologist and learned that your breast cancer mammogram result was positive. Does this mean that it is a for sure thing that you have breast cancer? Probably not. To analyze this information you would want to know statistics. The doctor tells you that 80% of all women with breast cancer have a positive mammogram result. Your first thought would probably be that there is an 80% chance you have cancer, which seems logical considering the information you’ve just been given. The problem here, though, is that you have only been told the hit rate (80%).
To make an accurate judgment you should also learn the false alarm rate and base rate. The false alarm rate in this case is the percentage of people who test positive for breast cancer even though they do not have cancer, and you are told it is 10%. The last bit of useful information is the base rate, which in this case is the number of people in the world who actually have breast cancer. You’re told that for every 1000 people, only 10 will have breast cancer. This means that only 1% of the entire population has what you’ve tested positive for.
When the hit rate, false alarm rate, and base rate are all taken into account and the probability is recalculated, normative theory is being implemented . Using something called Bayes’ Theorem, we find that the actual probability you have breast cancer is no longer 80%, but rather 7%. That is quite a big difference, and a good example of why it is important to consider all statistical factors before drawing a conclusion. However, people don’t usually use normative reasoning. By ignoring current evidence and/or base rate, which are the most common errors, people are using descriptive reasoning.
It is important to remember that descriptive
reasoning does not always have to be something bad. Sometimes making
quick conclusions is helpful, especially when one does not have the
time to collect all of the information required for normative reasoning.
When making judgments and decisions, people can make mistakes that prevent them from arriving at the correct answer, like we saw in the case of descriptive reasoning. Some common thought processes that can lead to flawed judgment are heuristics and biases. Heuristics are mental shortcuts that humans use to reach conclusions quickly, and are especially helpful when there is not much time to problem solve or when there is a large amount of uncertainty .
An example of the representativeness heuristic can be seen when we ask participants to decide the likelihood of statistical probabilities. If a fair coin is flipped five times, which of these two outcomes is more likely:
After comparing the two options, the participant will usually choose ‘a’ after analyzing the similarity of the results. The problem is that both ‘a’ and ‘b’ are equally likely since each coin flip offers a 50% chance for either side, which means that the participant chose the wrong answer by using the representativeness heuristic rather than taking the base rate calculation into consideration.
Another example of this heuristic is an experiment where participants were asked whether a man named Jack was an Engineer or a lawyer. One group was told that Jack comes from a group of 70 lawyers and 30 engineers, and the other group was told that Jack comes from a group of 30 lawyers and 70 engineers. Using these base rates, the participants labeled Jack as whatever profession had higher numbers. In other words the first group rated the probability that Jack was an engineer as 30% and the second group said the probability he was an engineer is 70%.
Then the same experimenters told different participants to read the following:
“Jack is a 45-year-old man. He is married and has four children. He is generally conservative, careful, and ambitious. He shows no interest in political and social issues and spends most of his free time on his many hobbies, which include home carpentry, sailing, and mathematical puzzles.”
Participants were given the same exact base rate information. Interestingly enough, the addition of a description caused the participants to ignore the base rates, and most everyone labeled Jack as an engineer. They used the representativeness heuristic when they compared the description of Jack to the typical engineer or lawyer. Since they found the description to be more similar to their representation of an engineer, they overwhelmingly said he was an engineer despite base rates that did not always support their decision.
The availability heuristic occurs when a person calculates a decision by estimating frequency or probability by the ease with which instances or associations are brought to mind . In other words, a conclusion drawn using the availability heuristic is usually based on the information a person has stored in their head. If you ask a person whether death by plane crashes or floods is more likely, they will probably think about all of the plane crashes they have read about or seen in the news and movies, and decide that plane crashes result in more deaths. Sometimes this is fine, and the person reaches a good conclusion, but other times they will be wrong (floods actually kill more people than plane crashes do). Unless a person is very knowledgeable about a specific topic, this heuristic is not going to be a reliable way to solve problems, especially since it involves a person’s biases. Here is a list of words that were paired and presented to participants in a study. The bold words are the ones that subjects believed were a more frequent cause of death in the United States. All of them were wrong on each answer, and the non-bold words are actually a more frequent cause of death .
Breast Cancer vs. Diabetes
Flood vs. Homicide
Lung Cancer vs. Stomach Cancer
Strokes vs. All Types of Accidents
Tornadoes vs. Asthma
Let’s say you are given two weather related conditions: sunny or hot. You are then asked to rate the probability that it is just hot, just sunny, or both sunny and hot. People will often say there is a higher probability of it being sunny and hot rather than just one or the other. This is an example of the conjunction fallacy, where people mistakenly believe the probability of a conjunction of two events is greater than the probability of one of the events . Another study highlighting the conjunction fallacy told participants that a health survey was conducted on adult males, and that Mr. F was one of those who took the survey. They then asked the participants which of the following choices was more probable:
That Mr. F has had one or more heart attacks.
That Mr. F has had one or more heart attacks and is over 55.
55% of the participants chose the second sentence as being more probable, even though it was much less probable than the first sentence since it involved the multiplication of two different probabilities. The conjunction fallacy is a very common logic flaw and is committed by everyone at least sometime in their lives.
One very interesting aspect of judgment and decision making has to do with a phenomenon called the framing effect. The same exact information can be presented in different forms, influencing people’s decisions in response to that information. For example, people are more likely to choose a medical treatment that has a 50% success rate than one with a 50% failure rate, even though these two statistics are saying the same thing. The same goes for a gas pump that says ‘cash discount’ rather than ‘credit surcharge’, and condoms with a 98% success rate rather than a 2% failure rate. This effect is applicable to many fields, especially that of advertising or journalism. In summary, the way in which information about a subject is presented will determine just how appealing that subject is.
When there is a clear goal in sight
but no clear set of directions or means to attain that goal, then it is
called a problem. Problems can be broken down into four aspects; goal,
givens, means of transforming conditions, and obstacles.
- The goal is the desired end state which the problem solving is being
directed toward. The hope is to reach that end state and be able to
assess whether or not you achieved what you wanted.
Givens - These are the objects, conditions, and constraints that accompany a problem, and can be either explicit or implicit.
Means of Transforming Conditions
- There should be a way of changing the initial state of the problem.
This is most usually a person’s knowledge or skill level. For instance,
a computer programmer presented with a problem would utilize his or her
knowledge of programming languages to transform the state of the
Obstacles – The problem should present a challenge.
If there are no challenges involved and the situation can be easily
solved then it is not so a problem so much as a routine task.
Every problem has a problem space, which is the whole range of possible states and operators. Only some of these states and operators will bring the person closer to the goal state. The problem starts at the initial state and operators are applied to change the state, creating a series of intermediate states that should hopefully lead to the final goal state .
Types of Problems
possible way to categorize problems was first proposed by Reitman in
1965, stating that there are two kinds of problems: well defined and
Well defined problems – These are
problems that have specific initial conditions, goals, and means of
transforming conditions. They can be solved using a series of
instructions, tools, or methods, and the answer will usually be exact.
Examples of well defined problems include games, puzzles, and geometry
Ill defined problems
- These problems have aspects that are not completely specified. Ill
defined problems are mostly abstract and have no simple answers.
Examples include finding the perfect mate, deciding what kind of career
you should pursue, and bringing peace to the middle east .
has been argued that the key to problem solving is being able to take
an ill defined problem, which seems almost impossible to solve, and
breaking it down into a set of easier, well defined problems. For
instance, rather than focusing on finding the perfect mate the person
could decide to spend more time getting to know a couple of different
girls they’re interested in.
Problem Solving Stages
Problem solving follows a fairly simple series of stages:
- Form a representation
- Construct a plan
- Execute plan
- Reformulate representation if necessary and repeat stages
Arguably the most important stage is the first, where a representation of the problem and everything it involves must be formulated in the person’s brain. What kind of representation a person forms largely decides how difficult the problem will be to solve. There are a number of examples which show the importance of representation. One of these has to do with paper folding, where the following question is asked:
“Picture a normal piece of A4 paper (300 mm long, 0.05 mm thick). In your imagination, fold it once (now having two layers). Fold it once more (now having four layers), and continue folding it over on itself 50 times. It is true that it is impossible to fold any actual piece of paper 50 times. But for the sake of the problem imagine that you can. About how thick would the 50-times-folded paper be?“
Most people will think of the original, unfolded paper’s thickness as something extremely tiny (which it is) and then figure that the thickness of that paper folded fifty times over would not be very much. The answer, however, is 50,000,000 miles thick, or over half the distance from the earth to the sun .
Another example showing the importance of representation is the nine dot problem. Participants are given the following picture, and asked to draw four straight, connected lines that will go through all nine dots, but through each dot only once:
Most people will have trouble completing the task. The answer involves drawing outside of the area most people are willing to stay inside of:
In other words, a person must change their representation of the problem by zooming out and allowing themselves to draw well outside the imaginary boundary lines that are often imposed by the nine dots.
One technique people can employ while trying to solve a problem is the use of analogies. An analogy is a representation of a problem in one’s memory that is similar to the problem they are currently trying to solve. The similarity can either be obvious, in which case there is surface similarity, or non obvious, in which case there is deep similarity.
A famous study that shows how analogies help solve problems is called ‘Duncker’s Ray Problem’ . Participants were given the following paragraph to read, and were then asked to solve the problem posed in the paragraph:
“Suppose you are a doctor faced with a patient who has a malignant tumor in his stomach. It is impossible to operate on the patient, but unless the tumor is destroyed the patient will die. There is a kind of ray that can be used to destroy the tumor. If the rays reach the tumor all at once at a sufficiently high intensity, the tumor will
be destroyed. Unfortunately, at this intensity the healthy tissue that the rays pass through on the way to the tumor will also be destroyed. At lower intensities the rays are harmless to healthy tissue, but they will not affect the tumor either. What type of procedure might be used to destroy the tumor with the rays, and the same time avoid destroying the healthy tissue?”
Most people were not able to give a correct solution to the problem. In fact, only 10% of participants were able to solve it. Participants were then shown this military problem :
“A small country was ruled from a strong fortress by a dictator. Many roads led to the fortress through the countryside. A rebel general vowed to capture the fortress, which he knew he could do with an attack by his entire army. However, the general learned that the dictator had planted mines on each of the roads. The mines were set so that small bodies of men could pass over them safely. However, any large force would detonate the mines. The general devised a simple plan. He divided his army into small groups and dispatched each group to the head of a different road. When all was ready he gave the signal and each group marched down a different road. Each group continued down its road to the fortress so that the entire army arrived together at the fortress at the same time. In this way, the general captured the fortress and overthrew the dictator.“
Participants who read both the x-ray and military problem were able to more easily solve the x-ray problem. This is because the military problem serves as an analogy, where the general’s plan to win can act as a hint on how to destroy the tumor. The actual answer to the x-ray problem is to use many low intensity rays from different angles, on different areas of skin so that they all meet at the tumor and eventually kill it. With the help of the military problem, 30% of participants solved the x-ray problem.
To help participants even more, certain lines in the military problem that were especially analogous to the x-ray problem were highlighted. With this ‘hint’, 80% of the participants were able to solve the x-ray problem.
A common hindrance when problem solving is something called functional fixedness, which is a top-down preconception to see an object as having only one fixed and familiar function . A study by Duncker had participants try to solve a problem with only a few accessories at their disposal. The problem was trying to make a candlestick stay attached to a wall. They could use matches, the candle, and thumbtacks that were in a box. The thumbtacks were too small to go through the entire candlestick. Only 43% of participants were able to solve the problem. The answer involves dumping the thumbtacks out of the box, placing the candle in the box, and then tacking the box to the wall. When participants were given the same problem, except this time with the tacks already out of the box, 100% of them were able to solve it.
The point of functional fixedness is that, in order to form correct representations of problems, we must sometimes rethink preconceptions about people, objects, or ideas that work to hinder our problem solving abilities.
Plans and Strategies
We have looked at a couple of important aspects in representation forming, but what do we do after an appropriate representation has been formed? Once we have a representation we construct a plan, execute that plan, and then check and evaluate to see if that plan worked. If it did not, then we reformulate our representation and/or plan and re-execute.
There are two main types of plans that can be created: algorithms and heuristics. Algorithms are used for problems with which there is a guaranteed solution. After considering all the possible moves within a problem space, the person chooses the best one and carries out their algorithm. Heuristics are short cuts or rules of thumb that are used to quickly reach a conclusion.
Difference reduction is the practice of selecting an operator that moves a person closer to their intended goal state. After each operation, the person analyzes whether their new state is closer to the goal. The point is that a person should never do something that moves them further away from their intended goal state.
One strategy to solve problems is called means-end analysis. This involves finding the largest difference between the current state and the goal state, setting a subgoal to reduce that difference, and finding and applying an operator to reduce the difference . If the operator cannot be applied, then a new subgoal should be set to remove the obstacles prevent the use of the operator.
Sometimes the most efficient way to solve a problem is to look at the solution or goal state, if possible, and work backwards from there. This is helpful when dealing with problems that have many different possible paths branching from the initial state, such as mazes. If you know what it is you’re trying to obtain, you can piece together your operators backwards until you’re ready to move forward in a logical and progressive way.
Studies have found that the best way to become an expert at something is to practice. Problem solving requires rich, organized schemas that incorporate declarative and procedural knowledge. The way to build and perfect one’s skills is to constantly practice their problem solving abilities. Experts take less time to complete problems than novices, but spend more time building a representation of the problem before they begin to solve it. This is because they immediately recognize subcomponents and use less means-end analysis than beginners. Practice offers experience and makes a person better at whatever it is they enjoy doing.
Nobody is a perfect problem solver. Everyone makes mistakes during life, but it is important to learn from them and approach future problems and situations in a new way, so that failure may be avoided. Judgment and approach are key to successfully solving life’s dilemmas.