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John Miyamoto
Email: [email protected]
http://faculty.washington.edu/jmiyamot/p355/p355-set.htm
Psych 355: Introduction to Cognitive Psychology
Spring 2016
Study Questions for Goldstein, E. B. (2014). Cognitive psychology: Connecting mind, research
and everyday experience (4th ed.).
Chapter 12: Problem solving
Chapter 13: Reasoning and Decision Making
Ch 12: Problem Solving
1.
The Gestalt approach to problem solving emphasizes the ideas of problem representation and the
restructuring of the problem representation as a means toward solving a problem.
* How can restructuring the problem help to solve the circle problem?
* How can a false constraint make it difficult to solve the cheap necklace problem (this problem is called the chain
problem in your textbook, p. 338)?
* State in general terms what are the main differences between the Gestalt approach to problem solving and the
information processing approach to problem solving.
2.
Functional fixedness and mental set are two potential obstacles to problem solving.
* What is a mental set in problem solving? Can you give an example of a mental set that has been shown to occur in
problem solving?
* What is functional fixedness in problem solving? Can you give an example of functional fixedness in problem solving.
* Is it more accurate to say that functional fixedness and mental set are (a) always an obstacle to probem solving, or (b)
sometimes they are an obstacle and sometime they help at solving problems?
3.
Metcalfe and Wiebe (1987) found that people could anticipate when they were close to solving an
algebra problem, but they had less awareness of when they were close to solving an insight problem
(the cheap necklace problem/chain problem).
* What was their evidence?
* What does this suggest about the difference between the process by which an algorithmic problem is solved and the
process by which an insight problem is solved?
4.
The information processing approach to problem solving tries to analyze problem solving as a series
of small steps within a problem space. I won't expect you to know the details of this approach, i.e.,
you don't need to know the details of the information processing approach (pp. 341 - 345), but it is
worth understanding the basic ideas:
* The problem solver has a representation of the problem. Different stages in solving a problem are represented by
different configurations of the problem representation.
* Every problem has an initial state and a goal state. In other words, there is a representation of the initial state and a
representation of the goal state.
* There is a definition of the legitimate moves or transformations that can be used to change one state of the problem
representation to another state of the problem representation. For example, in the Tower of Hanoi problem, moving the
top ring from one pin to another pin that has a bigger ring on it is a legitimate move; moving the top ring from one pin to
another pin that has a smaller rink on it is an illegal move. See the Tower of Hanoi diagrams on p. 342 and 345.
* Newell and Simon proposed a number of strategies for solving problems, like working backwards, working forwards
and means-end analysis, but you don't need to know the details of these strategies.
* For Newell and Simon, problem solving consists in discovering a series of legal moves that transform the initial state to
the goal state by traveling through a series of intermediate states.
5.
The concept of problem isomorphs is important in the psychology of problem solving because they
reveal how different versions of the same problem can produce different psychological responses.
Differences in psychological responses are inferred from problem solving behavior and
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neuropsychlogical processes, to the extent that they are known, that carry out the problem solving
behavior.
* Why are some versions of a problem easier to solve and other versions are harder to solve even though all version of the
problem are isomorphic? Of course, you can't give a full answer to this question, nobody knows a complete answer, but
you have seen some examples.
* E.g., what makes some versions of the mutilated checkerboard problem easier or harder? (See lecture 09-1 and
Goldstein, 346 - 348) discuss various problems that are isomorphic to the mutilated checkerboard problem. What is the
main difference between the versions of the problem that are easier and those that are harder? What do these differences
suggest about what makes this problem easy or hard?
6.
What are incubation effects? What are some psychological reasons why a period of incubation
(being away from a problem) can help a person discover a solution to a problem?
* In Psych 355 we did not discuss any experiments that directly investigated the factors that produce incubation effects in
problem solving, but we did discuss many aspects of memory and concepts like schemas and set that are relevant to why
incubation effects occur. So I want you to identify some of the psychological factors that are likely to cause incubation
effects, whether or not any studies have directly tested whether these factors play a role in producing incubation effects.
7.
According to the cognitive analysis of analogy, solving a problem by analogical reasoning involves:
(i) a representation of a source problem; (ii) a representation of a target problem; (iii) noticing the
possibility of an analogy; (iv) constructing a mapping between source and target problems; and (v)
applying the mapping. Briefly explain the role that each of these elements play in the construction of
an analogy.
* When people have difficulty making use of a potential analogy, which stage listed above is often the locus of their
difficulty? What is the evidence for claiming that difficulties in analogical reasoning are associated with this particular
stage?
* What is the role of problem schemas in solving analogical reasoning problems? (See lecture 9-3 & 9-4; the discussion
of analogical encoding on pp. 353 - 354 makes a similar point to the one made in lecture.)
8.
Dunbar proposed that there is an "analogical paradox," a discrepancy between subjects' performance
in cognition experiments on analogical reasoning and the use of analogical reasoning by real-world
problem solvers (research biologists, engineers, etc.).
* What is the analogical paradox?
* Give a few reasons why this discrepancy exists. (There is no known definitive answer to this question, but there are
some reasonable guesses.)
9.
What are some important differences between the way that experts solve problems and the way that
novices solve problems? E.g., what are differences between physics experts and physics novices
when working on physics problems?
Ch 13: Reasoning and Decision Making
1.
What is the difference between deductive inference and inductive inference?
* Why are psychologists interested in people's inductive reasoning?
* Why are psychologists interested in people's ability to judge probabilities?
2.
Describe how people use the availability heuristic to judge the probability of an event. For example,
if I ask what percentage of UW undergrads have a job while they are in school, how would you use
the availability heuristic to answer this question?
* The availability heuristic probably leads to reasonably accurate probability judgments in many situation; there are also
situations where use of the availability heuristic will lead to systematic errors in judged probability.
* Give an example of a situation where use the availability heuristic leads to reasonably accurate probability judgment,
and an example where the judgments are likely to be biased. What is the difference between situations?
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* What is egocentric bias? What experimental evidence shows that people are affected by an egocentric bias?
What does egocentric bias have to do with the availability heuristic?
3.
What is the representativeness heuristic? E.g., suppose you meet a middle-aged man at a party; he
seems to know a lot about modern American poetry. You wonder whether he writes poetry as well
as appreciating poetry. How would you use the representativeness heuristic to judge the likelihood
that this man writes poetry?
4.
What is base rate neglect? Describe some evidence that suggests that people tend to ignore base
rates1.
3
∘⋅
* If people use a representativeness heuristic to judge event probabilities, they will tend to ignore base rates.
Explain why this is so.
5.
What is a conjunction error in probabilistic reasoning? (The conjunction error is referred to as a
violation of the conjunction rule in Goldstein, pp. 374-375).
* The Linda problem is a famous example of a problem on which people produce conjunction errors (Goldstein, 374).
Can you explain the conjunction error in terms of the Linda problem? Can you propose a different problem on which
people are likely to produce a conjunction error?
* If people use a representativeness heuristic to judge event probabilities, they will tend to make conjunction errors.
Explain why this is so.
6.
Why do psychologists (actually, scholars from many fields) regard it as important that humans make
conjunction errors on probabilistic reasoning problems? Suggested answeri.
7.
Table 13.2 (p. 377) lists common types of errors in probability judgment. Unfortunately, I think
some of the information in Table 13.2 is misleading. The following is a revised version of
Table 13.2, where I have entered my "improvements" on the information in the table.
Miyamoto's revised version of Goldstein's Table 13.2 (p. 377).
SOURCE
DESCRIPTION
ERROR OCCURS WHEN
Availability heuristic
Events that are more easily remembered are
judged to be more likely than they are.
Less likely events come readily to mind, e.g., because they are
dramatic; conversely, errors occur when more likely events do not
come easily to mind, e.g., because they are less salient.
Illusory correlation
Strong correlation between two events
appears to exist but doesn’t.
There is no correlation or only a weak correlation but people have
an intuitive theory that predicts a strong correlation, e.g., many
arthritis patients believe that there is a substantial correlation
between pain of arthritis and weather; studies have found that
the correlation is close to 0.
Representativeness
heuristic
Probability that A is a member of class B is
determined by how well properties of A
resemble properties usually associated with
B.
People overlook that aspects of Class B that are unrelated to
similarity are also relevant to the likelihood that A is a B, e.g., the
base rate of Class B is relevant to the likelihood but it is unrelated
to similarity of A to Class B; e.g., set inclusion relations are
unrelated to the similarity of A to Class B (overlooked in
conjunction errors).
Base rate neglect
Relative proportions of different classes in
the population should influence the judged
likelihood that A is a member of each of
these classes.
People use the similarity of A to the stereotype of various classes,
Class B, Class C, etc., to judge the likelihood that A is a member
of Class B or Class C or .....
Conjunction error
Probability of conjunction of two events (A
and B) cannot be higher than the probability
of single constituents.
An individual seems more similar to a conjunction of A and B than
B alone, e.g., Linda is more similar to "feminist bank teller" than
to "bank teller" alone.
1
I should add that people do not invariable ignore base rates; they ignore base rates in some problems but not in others. There
is much debate about which types of problems do or do not produce base rate neglect.
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SOURCE
DESCRIPTION
ERROR OCCURS WHEN
Law of large numbers
The larger the number of individuals drawn
from a population, the more representative
the group will be of the entire population.
It is assumed that a small number of individuals accurately
represents the entire population.
Myside bias
Tendency for people to generate and
evaluate evidence and test their hypotheses
in a way that is biased toward their own
opinions and attitudes; the myside bias is a
type of confirmation bias.
People let their own opinions and attitudes influence how they
evaluate evidence needed to make decisions.
Confirmation bias
Selectively looking for information that
conforms to a hypothesis and overlooking
information that argues against it.
There is a narrow focus only on confirming information.
8.
What is a framing effect?
* What does it mean to say that people are typically risk averse for gains and risk seeking for losses?
* In lecture, I defined a framing effect to be a case where people's preferences change when (i) the description of the
choice problem is changed AND (ii) the content of the choice problem is not changed. Goldstein (p. 384) defined a
framing effect only in terms of condition (i); he omitted any mention of condition (ii). In my opinion, this omission is a
mistake, i.e., my definition is better on theoretical grounds and it is closer to how the idea of a "framing effect" is used in
the literature of judgment and decision making.
* Changing the wording of the Asian disease problem (pp. 384 - 385) from "lives saved" to "lives lost" causes people to
switch their preference from a sure saving of 200 people to a gamble where nobody will die (1/3 chance) or 600 people
will die (2/3 chance). Explain why this fits the pattern of a framing effect. Explain what this has to do with risk
aversion or risk seeking.
* Do you think that a framing effect is the same as or different from the effects of problem isomorphs on problem solving?
9.
What is the focusing illusion? How does the focusing illusion affect people's evaluations of different
possibilities? (The focusing illusion was not discussed in Goldstein, but it will be discussed in
lecture.)
10. Explain what is a confirmation bias.
*
*
*
*
What is the relationship between myside bias and confirmation bias?
Explain why typical errors on the 2-4-6 task seem to indicate that people are prone to a confirmation bias.
Explain why the typical errors on the four card problem seem to show a tendency towards a confirmation bias.
Suppose that Mr. X is prone to confirmation bias and suppose that Mr. X believes that young people don't know very
much about politics. When Mr. X meets a young person, how would Mr. X behave, given his confirmation bias and his
belief about young people's knowledge of politics.
11. Affective Forecasting
• What is affective forecasting? Give an example of an affective forecasting error; briefly explain why
it should be regarded as an error.
• Kermer et al. (2006) argued that people anticipated a much stronger negative emotional impact of a
future loss than they report when the actually experience the loss (see Figure 13.4 and related text).
They attribute this effect to people's tendency to overlook their own mechanisms for coping
psychologically. This tendency has been dubbed immune neglect by social psychologists, Dan
Gilbert and colleagues.
• The focusing illusion is a tendency to exaggerate the importance of an aspect of a situation or
outcome if attention is focused on this aspect. Describe the basic structure of the Kahneman et al.
(2006) study of working women's self report and predictions of "percentage of a random day spent in
a bad mood" (described in lecture). They showed that the predicted impact of a series of variables
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was greatert han the actual impact. What was their evidence? How is this related to the focusing
illusion?
12. Lerner et al. (2004) argued for two points: (i) emotions affect economic transactions (willingness to
sell or willingness to buy); and (ii) different emotions have different effects on these transactions
(see Figure 13.5). Is it intuitively credible that disgust makes people want to expel material objects,
hence the low selling price and low buying price for subjects who are disgusted2? This is claimed in
the discussion of Figure 13.5. Is it intuitively credible that sadness makes people desire change;
setting low selling prices and high buying prices both promote change, i.e., make transactions more
likely.
13. What is the ultimatum game?
* Comment: The ultimatum game is an important problem is economic psychology, and Sanfey's study is very interesting,
but I don't think that Goldstein's discussion of this problem gets at the most interesting aspects of this study, i.e., this
topic will probably not be on the final exam.
* What are the neurophysiological differences between people who accept or reject an offer from a human?
* Is the pattern different for offers from a computer?
14. [For the Spring 2016 Psych 355 final, you can skip the discussion of categorical syllogisms on
pp. 387 (bottom) - 391 (top). You will have to read the discussion of the conditional syllogism on
pp. 391 - 395 because this background is needed to understand the discussion of the Four Card
Problem] Note that a valid syllogism is one for which the conclusion follows logically from the
premises. It is not required that the premises or the conclusion be true; it is only required that if the
premises were true, then the conclusion would necessarily be true.
∘⋅
15. Table 13.4 (p. 391) lists four syllogisms for conditional reasoning. Two of these syllogisms are valid
and two are invalid. What does it mean to be a valid syllogism? Give a counterexample for each of
the two invalid syllogisms, i.e., for each of the two invalid syllogisms, given an example where the
premises of the syllogism are true and the conclusion is false.
16. The Four Card Problem (pp. 393 - 396)
• What is the correct answer and what is the typical answer to the Four Card Problem as shown in the
Demonstration Box on p. 393?
• Fact: Subjects often do better on a concrete version of the Four Card Problem, especially ones that
concern who does or does not have permission to behave a certain way. What is a permission
schema? What evidence suggests that people can use a permission schema to help them perform on
the four card problem? Why does the permission schema help subjects to perform better on the four
card problem?
17. A number of cognitive psychologists have proposed that there are two systems that interact during
reasoning (the dual systems approach). System I is fast and associative; System II is slower and
more reflective.
• Page 397 lists four ways that System I and System II differ (see list in the middle of the page).
Without looking it up, can you list these properties? Later, check your answer.
• Both systems are active when we reason about issues in everyday life. For example, if you are trying
to decide what vacation you should take this summer (assuming that you can choose between several
options including "don't take a vacation"), what are the roles of System I and System II in your
approach to this decision?
2
A low selling price for the pens will make it easy to sell them (get rid of them); a low buying price for the pens makes it less
likely that the subject will acquire them (find a willing seller).
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The occurrence of conjunction errors is important because it is one of the main pieces of evidence that people's evaluation of
uncertainties is inconsistent with probability theory.