Langston,
Cognitive Psychology, Notes 13  Reasoning and Decision Making
I. Goals.
A. Where we are/themes.
B. Logic.
C. Heuristics.
D. Probability.
II. Where we are/themes. In this unit we'll turn
our attention to some of the tasks that people think of when they think
cognitive psychology. How do you think and reason? My main
focus will be on problems in thinking (problems that arise due to the
unfortunate
interaction of normal cognitive activities). There are three
areas
we'll consider:
A. Logic: How people fail to use valid logic when thinking
(just a taste of this, but it fits nicely with the other areas where
we've
seen formal logic run into trouble as a model of cognition).
B. Heuristics: How little shortcut rules lead to problems
when applied to reasoning.
C. Probability: How a lack of appreciation for simple
concepts
from probability can lead people to make bad decisions.
By the end of the unit, you should have some idea of the way people
think, and how the way people think can lead to problems.
Top
III. Logic. We'll just consider one aspect of
logic:
Conditional reasoning.
A. The situation is this: You have a hypothesis (an ifthen
statement) and you want to test it. Here's an example from your
text:
If there's fog, then the plane will be diverted. How can we
determine if this statement is true? There are four tests we can
perform:
1. Present a situation where there's fog.
2. Present a situation where there's no fog.
3. Present a situation where the plane's been diverted.
4. Present a situation where the plane has not been diverted.
For each of these tests, we could get a particular outcome and then
determine whether or not the ifthen statement is true. Let's
have
some examples. For each of the four situations described below,
write
T or F to indicate whether this evidence leads you to conclude that the
hypothesis is true or false:
1. Present a situation where there's fog and find that the plane
is diverted.
2. Present a situation where there's no fog and find that the
plane is diverted.
3. Present a situation where the plane's been diverted and find
that there's no fog.
4. Present a situation where the plane has not been diverted
and find that there's no fog.
Here's the catch: Only two of these tests involve valid logic
(so only two of these tests can have any bearing on whether or not the
ifthen statement is true). That means that the correct answer to
two of the problems above is "I don't know." You probably didn't
write that. So, go back now and identify which two will have no
bearing
on the ifthen statement.
You probably had a hard time doing that. The correct answers
are:
1. T
2. I don't know
3. I don't know
4. T
Why do I say this? There are technical reasons based on logic,
and those are presented as clearly as I can present them in my research
methods notes. But, I think we can think our way through
it.
In order for statement 2 to be a valid test I would have to assume that
the only way a plane could be diverted is if there's fog. That is
obviously not true. Lots of reasons could cause a plane to be
diverted.
For statement 3, I would have to make the same assumption. In
reality,
neither of those tests has any bearing on the ifthen statement.
Contrast that with statement 1. Is fog a sufficient reason to
divert
a plane? Given the results of our test, the answer is yes.
In 4, we're also testing whether fog is sufficient to lead to a
diverted
plane.
To put it another way, in the ifthen statement I said fog will cause
the plane to be diverted, I didn't say the only way for the plane to be
diverted was for there to be fog.
B. Problems: People aren't very good at conditional logic
problems. Part of the trouble comes from the seductive nature of
the invalid logic. For example, imagine I've provided the
hypothesis
if you smoke, then you will get cancer
If someone says: "That can't be true, my uncle got cancer and
he never smoked" or that person says "That's not true, my uncle never
smoked
and he got cancer" those could both sound like good arguments if you're
not thinking carefully. But, again, I only said if you smoke,
then
you'll get cancer. I didn't say the only was to get
cancer
was to smoke. People who get cancer aren't really who I'm talking
about, I'm talking about people who smoke. One thing that
contributes
to making the invalid logic seductive is illicit conversion. That
happens when people reverse the if and then parts (so it would be
something
like "if you get cancer, then you smoked"). Obviously, once you
turn
the parts around, the "tests" presented above about our hypothetical
uncle
become valid. The important thing to remember is that the order
of
the parts in the if and then are not arbitrary, and that order has to
be
maintained.
Confirmation bias is a special problem for conditional reasoning.
People are much more likely to attempt to confirm their hypotheses than
they are to disconfirm them. That leads to a lot of errors in
conditional
reasoning. Try this problem: There are four cards
below.
If there's a letter on one side, there's a number on the other.
Which
two should you choose to test "If there's a vowel on the front, then
there's
an even number on the back?"
The correct two cards are "A" and "9." Some data from your book
(I'm guessing this is Wason & JohnsonLaird, 1972): 33% turn
over only "A." That shows a confirmation bias because A is a
vowel,
if there's an even number on the back, it confirms the rule. An
additional
46% turned over "A" and "2." This is an error because 2 has no
bearing
on the situation (it is a sort of illicit conversion, I never said even
numbers needed vowels on the other side). However, choosing 2
does
fit a confirmation bias. It's like people think something along
the
lines of "If there's a vowel on the other side of 2, that will prove it
true." The right combination is "A" and "9." Only 4% did
this.
Turning over 9 could serve to prove the hypothesis false, people rarely
seek negative evidence.
CogLab: We'll look at our
data from the Wason selection task.
There is a way to make people do this task correctly. In fact,
I can present you with a problem that 100% of you will get correct, and
I could guarantee that even without providing you with all of the
information
you've already seen. The rule is: If you're under 21 then
you
can't be drinking alcohol. Here are four people at a party:
Bob
18 yrs. old

Carol
drinking a Coke

Jerry
43 yrs. old

Emily
drinking beer

You're the vice squad. If you know an age, you can check the
beverage. If you know the beverage, you can check the age (the
beverages
are exactly as listed, with no secret ingredients). Who do you
need
to check to see if the rule is being followed at this party?
Everyone can tell immediately that it's Bob and Emily. Why is
this so easy when the other problems are so hard? This problem
has
a context. Additionally, this problem involves detecting
cheaters.
As we'll see in the last unit, there's a reason from evolutionary
psychology
for why we should be particularly good at problems that involve
detecting
cheaters (even if we stink at all of the rest of the problems).
That
might make a nice reaction paper discussion.
One last bit for this. Confirmation bias can lead to all sorts
of problems. Some examples of how it can lead research awry are
in
my methods
notes. In the real world, confirmation bias can lead to the
development
and maintenance of prejudices. In fact, the interaction between
confirmation
bias and the rules we discuss below can make it almost impossible to
overcome
prejudicial thinking. For example, a lot of the early research on
gender neutral pronouns demonstrated that when he was used as a
generic pronoun it actually led to thoughts of men. This was true
even when the person being described was in a stereotypically feminine
profession (for example, "if a schoolteacher wants to get ahead he
should
be friendly to parents") (MacKay & Fulkerson, 1979). One
problem
this causes is that it plays into people's confirmation biases in
situations
where a preexisting stereotype exists (engineer..he confirms people's
expectations). When you combine that with the fact that she
has often been used as the generic pronoun for stereotypically feminine
professions (like secretary) it can make it very hard to change
people's
stereotypes. If that translates into behavior ("we need to hire a
new girl for the office" biases against men and "let's get the best man
for the job" biases against women) it could be a problem. Add
this
bias for information that fits with the confirmation bias to the
heuristics
below, and there could be more trouble.
Top
IV. Heuristics. Outside of logic, what other
thinking
generalities can we uncover? There are two basic ways to work out
the solutions to problems. the algorithmic method is to use a set
of rules to methodically arrive at a conclusion. The best way to
see this is to multiply 365 by 48. You go step by step through
the
problem applying the rules for multiplication. You'll always
arrive
at the right answer (provided your math is correct).
Unfortunately,
this is impractical in a lot of realworld tasks. Instead, people
tend to rely on a set of roughandready rules that can apply to a
variety
of situations. These rules are called heuristics. Provided
that the information going into the application of a heuristic is
correct,
the shortcuts will produce relatively sound answers.
Unfortunately,
the information going into heuristics is frequently incorrect (often
due
to confirmation biases), making the results suspect as well.
Let's
consider some examples of heuristics (I'm also lumping in other
characteristic
modes of thinking).
A. Representativeness: The more something resembles your
prototype of its population, the more likely you are to assign it to
that
population. This can lead you to make some errors in
reasoning.
A simple example from the book: Which of these sequences is more
likely to have been produced by flipping a coin six times in a row,
HHHTTT
or HHTHTT? Most people choose the second one, but they're equally
likely. People choose one on the basis of which one looks more
random,
not on the basis of probability.
This example is related to a tip that will help you really appreciate
the odds of winning the lottery. Imagine playing 1, 2, 3, 4, 5,
6.
Does that seem like a really unlikely combination? If you think
to
yourself "there's no way that combination could win," you've got a
chance
to save yourself some money playing the lottery. All combinations
are equally likely. For example, in the UK lottery with 49
numbers
and you pick six, there are 13,983,816 combinations, each has a
1/13,983,816
chance of winning. If you think choosing a sequence that looks
more
random increases your chances, you're fooling yourself. Whenever
I play keno (which I do for the fun of tormenting my fellow players and
not from the expectation that I'll win), I like to choose "unlikely"
looking
sequences. It makes people crazy to see me throwing my money
away.
All the while they're trying to come up with a "random" sequence that
has
a better chance (or falling back on a belief in magic and trying to
read
the keno vibes in the air).
Here are some tips based on other people's faulty thinking that will
help you maximize your expected value in a lottery play (which is not
entirely
dependent on the odds). The idea is to pick numbers nobody else
would
pick so if you should be so fortunate as to win you won't share your
prize.
First, a lot of people think of 1, 2, 3, 4, 5, 6 as a good choice
because
"nobody else will think of it." It's representative of a choice
nobody
will play. Therefore, it's a bad choice to make. Another
strategy
that's representative of "numbers other people don't pick" is to choose
all numbers higher than 31 (numbers under 32 are possible birthdays,
which
a lot of people play). But, since a lot of people do this, and
there
are usually fewer numbers over 31, you're actually hurting
yourself.
One last thing (it's not really representativeness, but it's related to
the lottery): Avoid any strategy with "due" numbers (as in "42
hasn't
come up in 10 draws so it's due"). If there's any possible bias
in
the system it's that a slight physical defect in one of the balls or
the
mechanism helps or hurts a particular number. If 42 comes up 10
draws
in a row, there's a reasonable chance that the 42 ball is defective and
more likely to be picked, so go with it. If it never comes up,
the
chances are it's defective the other way, so you would be insane to
pick
it because it's "due." Your best case scenario when a ball never
comes up is that it's just a result of random chance, which is the way
it's supposed to work anyway. (Lottery information from Eastaway,
R., & Wyndham, J., 1998, Why do buses come in threes: The
hidden
mathematics of everyday life).
The representativeness heuristic can be a large factor in perpetuating
stereotypes. Combine it with confirmation biases and you will
notice
examples which are representative of the stereotype, store those away,
and use them for further processing. Think about astrology.
Cancers (like me) are supposed to be moody and crabby. If you
know
this, you might take note of my behavior when it seems representative
of
the cancer stereotype, and thereby reinforce your belief in the
accuracy
of astrology. Behavior in noncancers that is representative of
cancers
is less likely to be noted, and so unlikely to shake your belief in
astrology.
This is one of the problems with heuristics. Once a little bias
gets
into the system, the results aren't likely to be very successful.
B. Availability: If I ask you how likely something is,
you try to think of an example. The easier it is to think of an
example,
the more likely you say it is. For example, what's the
probability
of a batter reaching first base by getting a hit? By having the
catcher
drop a third strike? You should feel availability taking over by
trying to think of an example of each and using the ease of getting an
example to make your estimate.
Your book's example: Are there more words in English that start
with 'k' or that have 'k' as the third letter? You'll start
trying
to think of words, and conclude that starting with 'k' is more
common.
That's because you organize your mental lexicon around first letters
and
not third letters. So, it's easier to search that way and you get
more results. As you probably guessed, there are more with 'k' in
the third letter. Anything that affects the ease with which you
think
of something will affect availability (maybe as an exercise you should
try thinking of influences now):
1. Frequency: More frequent = more available. Again,
if you put in confirmation biases then what you encode more frequently
may not reflect the population, making your estimate inaccurate.
2. Familiarity: More familiar stuff is easier to recall
and so more available.
3. Vividness: More vivid stuff is easier to recall, so
more available. This is one reason why flying seems more
dangerous
than driving. Vivid plane crash stories are easy to retrieve, so
it seems like a crash is more likely (also plane crashes get more
coverage,
so frequency and familiarity come into play).
4. Recency: More recent stuff is easier to retrieve.
Demonstration: I have a powerful example of the way
availability
can make something really simple seem remarkable.
C. The simulation heuristic: Ease of simulation will affect
people's judgments. The example in your book describes two men
who
are on flights at the same time, are equally delayed getting to the
airport
(in the same car), and both arrive 1/2 hour after their planes were
supposed
to leave. However, when they arrive they find that Mr. Crane's
flight
left on time, but Mr. Tees' flight was delayed, and left just five
minutes
before they arrived. Who's more annoyed? Most people think
Mr. Tees is more annoyed. The reason is that it's easier to
simulate
how they could have been just five minutes earlier than a half hour
earlier.
Some influences:
1. Undoing: When people simulate undoing an event, it's
more common for them to file down an unusual detail to make it more
typical
(called a downhill change) than it is to add a new detail (an uphill
change).
It's easier to make an event more like the typical script than to make
it less like that script.
2. Hindsight: Once you know the outcome, it's easier to
simulate how that outcome happened. That makes it seem more
likely,
and can even make you change how you remember your predictions.
For
example, if someone on a game show decides to go for it and misses, you
might resimulate and decide that it was obvious they should have
stayed.
Demonstration: I have a few simulation examples.
D. And the rest: Here are some more influences on thinking.
1. Anchoring and adjustment. Do the multiplication problems
in the demonstration.
Demonstration: There will be a multiplication problem
to perform, but you will only have a short amount of time to do
it.
One half do the first problem. The other half do the second
problem.
Compare answers.
Another: You get one of two lotteries. The first is to
draw a red marble from a bag with 50% red and 50% white. The
second
is to draw seven reds in a row from a bag with 90% red and 10% white
(we'll
replace the marble drawn each time to keep the odds the same on each
draw).
Which gives you the best chance of winning?
Anchoring and adjustment is related to the fact that people start from
the first part of the problem (the anchor) and then make adjustments
from
that when heuristics take over. If the anchor is low, people tend
to guess low. If the anchor is high, people tend to guess high.
2. Set/fixedness: We have a lot of experience with the
world, and this usually influences our behavior, even when it's better
if it doesn't. Set: An example of this is the classic 9dot
problem. If you ask people to solve it, they usually get stuck
because
they don't think outside of their set, but that's what the solution
requires
Fixedness: We come up with a solution that works and keep
applying
it in the face of simpler solutions.
Functional fixedness: We can't stop thinking of an object in
its usual function, and that hinders finding the solution.
Demonstration: One for each above.
For set, connect the nine dots below by drawing four straight lines.
For fixedness your job is to do some jug problems. Basically,
you're given three jugs of various sizes and you're supposed to get a
particular
amount using those jugs. Solve each of the problems in the table
below (from Myers, 1995):
Problem 
Jug A 
Jug B 
Jug C 
Target Amount 
1 
21 
127 
3 
100 
2 
14 
46 
5 
22 
3 
18 
43 
10 
5 
4 
7 
42 
6 
23 
5 
20 
57 
4 
29 
6 
23 
49 
3 
20 
7 
15 
39 
3 
18 
For functional fixedness imagine this situation: You're in a
plane and it crashes in the desert. You're miles from help, and
you
have no food and water. All you have is a parachute, a pocket
mirror,
a compass, and a map. What's your most important asset?
3. Confidence: We usually have very poor calibration of
comprehension (knowledge about how well we did on a task). This
applies
to decisions as well. You can test that by answering this
question:
“Hirsute probably means ‘really hairy’ or ‘habitually late.’”
(Choose
one.) Generally, people are more confident of their answers to
these
questions than they are correct. The more confident, the more
they
overestimate their ability.
4. Belief: If I get you to state a belief first, it’s a
lot harder to get you to change your mind. So, if I say to you
“it’s
much safer to be in the back of a plane if there’s a crash, why do you
think that is?,” you can probably make something up to account for
it.
Then, if I give you opposite evidence, it will be really hard to
persuade
you to change your mind. Better yet, if I tell you that my
evidence
was just made up, you’ll still cling to your incorrect belief based on
that information.
5. Framing: How you ask the question will impact how people
feel about it. So, if I tell you that 10% of people who eat a
particular
kind of Sushi keel over and die, or I tell you 90% come through
unharmed,
you’ll think it’s more dangerous in the 10% die case (I’ve framed the
problem
negatively).
CogLab: We'll look at our
results from the decision making demonstration.
Top
V. Probability. One last thinking topic has to do
with people's generally poor comprehension of the laws of
probability.
This generally leads to a lot of thinking errors. (Most of this
came
from an excellent book called Using Statistical Reasoning in Everyday
Life.
The book will be published by Wadsworth this summer.
Unfortunately,
I don't currently know the author's name. If you've ever wondered
why you need to know anything about statistics, this book would be an
excellent
choice. What is below is just a taste.)
CogLab: We'll talk about
the Monty Hall problem as an interesting example of probability.
A. Conjunction. How do you combine the probabilities of
a bunch of independent events? Try the example in the
demonstration.
Demonstration: Estimate your likelihood of avoiding all
of the causes of death on the overhead.
Generally, people overestimate. Even though each number is high
(the odds of avoiding a car accident are 99%), their conjunction is not
so high. To compute correctly, multiply all together. Note
how anchoring and adjustment played into your estimate. Others
might
also have been involved. The lack of ability to correctly predict
the probability of conjunctions can have implications for real
life.
For example, there's a 90% chance I'll finish the paper on time, a 90%
chance I'll finish the takehome test, and a 90% chance I'll get my
chores
done, what's the chance of getting all three done? (It's not
90%.)
B. Conjunction fallacy. Read about Mr. F in the
demonstration
below.
Demonstration: Which fact about Mr. F seems more
likely?
Try Linda the bank teller.
Basically, the conjunction between two events has to be smaller than
the likelihood of either alone (or at the extreme the same size).
Most people use heuristics to estimate conjunctions (like
representativeness
for Mr. F) and overestimate the conjunction. Use a Venn diagram
to
illustrate this. We can also consider the story about
Linda.
You know the rule now, but 85% of the people reading about Linda went
for
the conjunction fallacy. Why?
CogLab: We'll look at the
results from our typical reasoning demonstration.
C. The power of chance. Now that you know the rule, try
the stockbroker example.
Demonstration: What are the odds of picking the direction
of change in a stock price 10 weeks in a row?
If you use the correct conjunction rule, you might say the odds aren't
too high. But, if you imagine that the stock pickers are just
flipping
a coin, the odds are that one of them will get all 10 right. In
other
words, it's very likely to happen just by chance. The odds of one
particular person getting it are low, the odds of someone
getting
it are not. It's sort of like the lottery. Your odds aren't
so great. But, the odds that someone will win are pretty
high.
In other words, just because something is very improbable doesn't mean
nobody will achieve it if enough people are in the game. I guess
the message is not to be too impressed with something that could have
happened
just by chance.
D. Amazing coincidences. The example above is related to
amazing coincidences (like dreaming about being in a car crash and then
crashing). Or, the eerie similarities between identical twins
raised
apart. Read the description in the demonstration.
Demonstration: Description of the similarities between
two women.
These women aren't twins. They were randomly paired in a study
by Wyatt, Posey, Welker, and Seamonds (1984). They found that
random
pairs also produced a bunch of similarities when they were compared on
a lot of dimensions. The point is that the odds of a particular
coincidence
(like political leanings) might be low, but the odds of some
coincidence
out of the millions of possibilities are actually quite high.
It's
not surprising if twins reared apart are similar in some way.
You could also relate this to fortune telling (segue back to Eastaway
and Wyndham, 1998). It would be impressive if a fortuneteller
made
a very specific prediction that came true ("you will meet an old friend
on the street this week"). If a general prediction came true
("something
interesting will happen this week"), that's not impressive. It's
especially not impressive given the heuristics and confirmation bias
discussed
above. Let's consider a prediction. In a room with 23
people,
I predict two will have the same birthday. If I'm proven correct,
is that impressive? Naive intuition might think it is (with 365
days
to choose from, the odds of two out of 23 having the same birthday seem
low). However, the odds are actually 51%. You can calculate
them by using the conjunction rule. Eastaway and Wyndham show
it's
easier to do this by calculating the odds of not having two birthdays
the
same. For 23, it's 365/365 X 364/365 X 363/365 X ... X
343/365.
That's 49%. So, there's a 51% chance of two birthdays being the
same.
What would be more impressive is if I picked two people and said they
would
have the same birthday. Then my odds are 1/365, which is a much
more
difficult prediction to get right by accident. So, even though
the
situation feels similar, one is actually a lot more likely.
I mentioned the heuristics above, how do they come into play?
They help you take note of the amazing things that do happen and
disregard
the amazing things that don't happen. They also help to determine
what counts as amazing. Eastaway and Wyndham (1998) point out
that
the odds of George Washington being born on February 22 and Queen
Victoria
being born on May 24 are 1 in 130,000. In other words, those two
birthdays happening are very unlikely. But, it's not an
impressive
coincidence because you attach no significance to it. A lot more
on coincidences can be found at Skeptical
Inquirer. I think the section on Lincoln/Kennedy coincidences
is particularly relevant for the discussion in this section.
E. Certainty. It's possible to know with relative certainty
what someone will do in a situation. This can be based on common
reasoning errors and the heuristics above. If people are relying
on intuition to interpret how remarkable events are, then they will be
easily tricked.
Demonstration: I have a math problem for you to try.
I think you will all get the same sum, which I will tell you once
you've
had a chance to do the problem.
There's a common mistake that leads to this result. This one's
not 100% certain, but it's very likely. You're probably not too
impressed,
however. Let me do some magic tricks.
Demonstration: I have a couple of magic tricks.
Were these impressive? I won't spoil the show by telling you
how they're done, I'll just let you know that they absolutely had to
work
out. My point is this: It shouldn't impress you when
someone
does something that had to come out the way it did. Not having an
appreciation of math (for my magic) or psychology (for most of the rest
of this unit) can lead you to be overly impressed. If there's
time,
I'll wrap up with a very impressive magic trick relying entirely on
psychology.
Let's see if you can figure it out.
Top
Cognitive Psychology Notes 13
Will Langston
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