Reasoning & Decision Making
Monty Python The Search for the The Holy Grail: Witch Scene
http://www.youtube.com/watch?v=yp_l5ntikaU
• The folly of mistaking a paradox for a
discovery, a metaphor for a proof, a torrent of
verbiage for a spring of capital truths, and
oneself for an oracle, is inborn in us.
-- Paul Valery
Reasoning & Decision Making
Backbone of Problem Solving & Creativity
–Logic
–Decision making
Reasoning, Decision Making and
Problem solving
– Logic
• As you have noticed by now, there is very little
that is logical about how the brain processes
information. So, it will not surprise you that we
have problems with doing logic.
– Decision making
Test for Reasoning
Four ( 4 ) questions and a bonus question.
You have to answer them instantly.
You can't take your time, answer all of them
immediately .
Let's find out just how clever you really are....
First Question
You are participating in a race. You
overtake the second person. What position
are you in?
Answer: If you answered that you are first,
then you are absolutely wrong! If you
overtake the second person and you take
his place, you are second!
Try not to screw up next time.
Second Question
don't take as much time as you took for the first question, OK ?
If you overtake the last person, then you
are...?
Answer: If you answered that you are second to last,
then you are wrong again. Tell me, how can
you overtake the LAST Person?
You're not very good at this, are you?
Third Question
Very tricky arithmetic! Note: This must be done in
your head only . Do NOT use paper and pencil or a
calculator. Try it…
Take 1000 and add 40 to it. Now add
another 1000. Now add 30. Add another 1000.
Now add 20. Now add another 1000. Now add 10.
What is the total?
Did you get 5000?
The correct answer is actually 4100.
If you don't believe it, check it with a calculator!
Today is definitely not your day, is it?
Fourth Question
Mary's father has FIVE daughters:
Nana, Nene, Nini, Nono.
What is the name of the fifth daughter?
Did you Answer Nunu?
NO! Of course it isn't.
Her name is Mary.
Read the question again!
Bonus Question
A mute person goes into a shop and wants to buy a
toothbrush. By imitating the action of brushing
his teeth he successfully expresses himself to the
shopkeeper and the purchase is done.
Next, a blind man comes into the shop who wants to
buy a pair of sunglasses; how does HE indicate
what he wants?
He just has to open his mouth and ask....
It's really very simple…
If, then statements
• If, then statements = conditional logic
– If the first part of a statement is true then the
second part must also be true
1
If it rains the street gets wet
It rained
The street gets wet
Is this a valid or invalid conclusion?
-valid!
If, then statements
p
q
If it rains then the street gets wet
It rained
The streets get wet
Antecedent Consequent
If p,
Then q
If, then statements
If it rains, then the streets get wet.
It doesn’t rain.
Therefore, I conclude that the streets don’t
get wet.
2
This argument is valid
This argument is invalid
If, then statements
If it rains, then the streets get wet.
The streets are not wet.
Therefore, I conclude that it has not
rained.
3
This argument is valid
This argument is invalid
If, then statements
If it rains, then the streets get wet.
The streets are wet.
Therefore, I conclude that it must have
rained.
4
This argument is valid
This argument is invalid
If, then statements
If p, then q.
I observe p.
Therefore, I conclude that q must be the
case.
5
This argument is valid
This argument is invalid
If, then statements
If p, then q.
I don’t observe p.
Therefore, I conclude that q is not the
case.
6
This argument is valid
This argument is invalid
If, then statements
If p, then q.
I don’t observe q.
Therefore, I conclude that p must not be
the case.
7
This argument is valid
This argument is invalid
If, then statements
If p, then q.
I observe q.
Therefore, I conclude that p must be the
case.
8
This argument is valid
This argument is invalid
If, then statements
p
q
If it rains, then the streets get wet.
It rains.
p
Therefore, the streets gets wet.
q
If, then statements
• Tree Diagrams
– Critical information represented along “branches”.
– Help to determine validity of a statement
If it rains, then the streets get wet
It rains
Therefore the streets get wet
If, then statements
p
it rains
q
the streets get wet
if
~p
it doesn’t rain
If it rains, then the streets get wet
It rains
Therefore the streets get wet
AFFIRMING THE ANTECEDANT: VALID
the streets don’t get
wet
~q
the streets get wet
q
If, then statements
p
q
If it rains, then the streets get wet.
It rains.
p
Therefore, the streets gets wet.
q
Valid!
Consequent
Antecedent
Affirming the
If p, then q.
antecedent
If, then statements
If it rains, then the streets get wet.
It doesn’t rain.
Therefore, I conclude that the streets don’t
get wet.
2
This argument is valid
This argument is invalid
If p, then q.
I don’t observe p.
6
Denying the
antecedent
Therefore, I conclude that q is not the case.
If, then statements
p
it rains
q
the streets get wet
if
~p
it doesn’t rain
the streets don’t get
wet
~q
the streets get wet
If it rains, then the streets get wet
It doesn’t rain
q
Therefore I conclude that the streets don’t get wet
DENYING THE ANTECEDENT: INVALID
If, then statements
If it rains, then the streets get wet.
The streets are not wet.
Therefore, I conclude that it has not
rained.
3
This argument is valid
This argument is invalid
If p, then q.
I don’t observe q.
7
Denying the
consequent
Therefore, I conclude that p must not be the case.
If, then statements
p
it rains
q
the streets get wet
if
~p
it doesn’t rain
If it rains, then the streets get wet
The streets are not wet
Therefore I conclude that it has not rained
DENYING THE CONSEQUENT: VALID
the streets don’t get
wet
~q
the streets get wet
q
If, then statements
If it rains, then the streets get wet.
The streets are wet.
Therefore, I conclude that it must have
rained.
4
This argument is valid
This argument is invalid
If p, then q.
I observe q.
8
Affirming the
consequent
Therefore, I conclude that p must be the case.
If, then statements
p
it rains
q
the streets get wet
if
~p
it doesn’t rain
If it rains, then the streets get wet
The streets are wet
Therefore I conclude that it must have rained
AFFIRMING THE CONSEQUENT: INVALID
the streets don’t get
wet
~q
the streets get wet
q
E
K
4
7
“If a card has a vowel on one side, then it has an
even number on the other side”
Which cards do you need to turn over to test the
validity of the rule?
Wason (1966) Selection Task
E
K
p
4
~p
7
q
~q
“If a card has a vowel on one side, then it has an even
number on the other side”  If p, then q
Answer:
Affirming the antecedent
E p
K ~p
Denying the antecedent
4 q
Affirming the consequent
7 ~q
Denying the consequent
If, then statements
p
vowel
q
even number
if
~p
consonant
odd number
~q
even number
q
Griggs & Cox (1982)
• If a person is drinking beer, then the person
must be over 21
Drinking
beer
p
Drinking
Coke
~p
16 years
of age
~q
22 years
of age
q
If, then statements
if
p
drinks
beer
~p
drinks coke
q
older than 21
younger than 21
~q
older than 21
q
Griggs & Cox (1982)
• If a person is drinking beer, then the person
must be over 21
Drinking
beer
p
Drinking
Coke
~p
16 years
of age
~q
22 years
of age
q
If, then statements
if
p
drinks
beer
~p
drinks coke
q
older than 21
younger than 21
~q
older than 21
q
Griggs & Cox (1982)
• If a person is drinking beer, then the person
must be over 21
Drinking
beer
p
Drinking
Coke
~p
16 years
of age
~q
22 years
of age
q
If, then statements
if
p
drinks
beer
~p
drinks coke
q
older than 21
younger than 21
~q
older than 21
q
Griggs & Cox (1982)
• If a person is drinking beer, then the person
must be over 21
Drinking
beer
p
Drinking
Coke
~p
16 years
of age
~q
22 years
of age
q
If, then statements
if
p
drinks
beer
~p
drinks coke
q
older than 21
younger than 21
~q
older than 21
q
Griggs & Cox (1982)
• If a person is drinking beer, then the person
must be over 21
Drinking
beer
p
Drinking
Coke
~p
16 years
of age
~q
22 years
of age
q
If, then statements
• Why difficulty with 4-card task, not the
drinking task?
– Permission schema: If true then we have
permission to do it!
• Ex: If a passenger has been immunized against cholera,
then he may enter the country.
– Obligation schema: If true then obligated to do
something else
• Ex: If you pay me $100,000, then I’ll transfer the house
to you.
• Daniel Ariely Why We Think It’s Ok To Lie
(sometimes) http://www.youtube.com/watch?v=nUdsTizSxSI
Probability in the Real World
Frequentists and Bayesians
Probability in the Real World
Bayesian Probability
Probability in the Real World
• Bayes Theorem is “normative”
– It takes into account more information
– It includes all the information into its formulas
– The formulas produce the most moderate outcomes; as
close to a normal distribution as you can get for any given
problem
– Even simple sea-slugs exhibit habituation and many
invertebrates show classical conditioning, all of which are
forms of Bayesian inferences
• Not surprisingly, we humans don’t do it…at least not
consistently, thoroughly, or very well.
Probability in the Real World
Probability in the Real World
Probability in the Real World
Probability in the Real World
Probability in the Real World
Probability in the Real World
Probability in the Real World
Probability in the Real World
Probability in the Real World
The Need to Assess Probabilities
• People need to make decisions constantly, such as
during diagnosis and therapy
• Thus, people need to assess probabilities to classify
objects or predict various values, such as the
probability of a disease given a set of symptoms
• People employ several types of heuristics to assess
probabilities
• However, these heuristics often lead to significant
biases in a consistent fashion
• This observation leads to a descriptive, rather than a
normative, theory of human probability assessment
Three Major Human ProbabilityAssessment Heuristics/Biases
(Tversky and Kahneman, 1974)
• Representativeness
– The more object X is similar to class Y, the
more likely we think X belongs to Y
• Availability
– The easier it is to consider instances of class Y,
the more frequent we think it is
• Anchoring
– Initial estimated values affect the final
estimates, even after considerable adjustments
A Representativeness Example
• Consider the following description:
“Steve is very shy and withdrawn, invariably
helpful, but with little interest in people, or in
the world of reality. A meek and tidy soul, he
has a need for order and structure, and a
passion for detail.”
• Is Steve a farmer, a librarian, a physician, an
airline pilot, or a salesman?
The Representativeness Heuristic
• We often judge whether object X belongs to class
Y by how representative X is of class Y
• For example, people order the potential
occupations by probability and by similarity in
exactly the same way
• The problem is that similarity ignores multiple
biases
Representative Bias (1):
Insensitivity to Prior Probabilities
• The base rate of outcomes should be a major factor in
estimating their frequency
• However, people often ignore it (e.g., there are more
farmers than librarians)
– E.g., the lawyers vs. engineers experiment:
• Reversing the proportions (0.7, 0.3) in the group had no effect on
estimating a person’s profession, given a description
• Giving worthless evidence caused the subjects to ignore the odds
and estimate the probability as 0.5
– Thus, prior probabilities of diseases are often ignored when
the patient seems to fit a rare-disease description
Representative Bias (2):
Insensitivity to Sample Size
• The size of a sample withdrawn from a
population should greatly affect the
likelihood of obtaining certain results in it
• People, however, ignore sample size and
only use the superficial similarity measures
• For example, people ignore the fact that
larger samples are less likely to deviate
from the mean than smaller samples
Representative Bias (3):
Misconception of Chance
• People expect random sequences to be “representatively
random” even locally
– E.g., they consider a coin-toss run of HTHTTH to be more
likely than HHHTTT or HHHHTH
• The Gambler’s Fallacy
– After a run of reds in a roulette, black will make the overall run
more representative (chance as a self-correcting process??)
• Even experienced research psychologists believe in a law
of small numbers (small samples are representative of
the population they are drawn from)
Representative Bias (4):
Insensitivity to Predictability
• People predict future performance mainly by
similarity of description to future results
• For example, predicting future performance
as a teacher based on a single practice lesson
– Evaluation percentiles (of the quality of the
lesson) were identical to predicted percentiles of
5-year future standings as teachers
Representative Bias (5):
The Illusion of Validity
• A good match between input information and output
classification or outcome often leads to unwarranted
confidence in the prediction
• Example: Use of clinical interviews for selection
• Internal consistency of input pattern increases
confidence
– a series of B’s seems more predictive of a final grade-point
average than a set of A’s and C’s
– Redundant, correlated data increases confidence
Representative Bias (6):
Misconceptions of Regression
• People tend to ignore the phenomenon of
regression towards the mean
– E.g., correlation between parents’ and children’s heights
or IQ; performance on successive tests
• People expect predicted outcomes to be as
representative of the input as possible
• Failure to understand regression may lead to
overestimate the effects of punishments and
underestimate the effects of reward on future
performance (since a good performance is likely to
be followed by a worse one and vice versa)
The Availability Heuristic
• The frequency of a class or event is often
assessed by the ease with which instances of it
can be brought to mind
• The problem is that this mental availability
might be affected by factors other than the
frequency of the class
Availability Biases (1):
Ease of Retrievability
• Classes whose instances are more easily
retrievable will seem larger
– For example, judging if a list of names had more
men or women depends on the relative frequency
of famous names
• Salience affects retrievability
– E.g., watching a car accident increases subjective
assessment of traffic accidents
Availability Biases (2):
Effectiveness of a Search Set
• We often form mental “search sets” to estimate
how frequent are members of some class; the
effectiveness of the search might not relate
directly to the class frequency
– Who is more prevalent: Words that start with r or
words where r is the 3rd letter?
– Are abstract words such as love more frequent than
concrete words such as door?
Availability Biases (3):
Ease of Imaginability
• Instances often need to be constructed on the
fly using some rule; the difficulty of
imagining instances is used as an estimate of
their frequency
– E.g. number of combinations of 8 out of 10
people, versus 2 out of 10 people
– Imaginability might cause overestimation of
likelihood of vivid scenarios, and underestimation
of the likelihood of difficult-to-imagine ones
Availability Biases (4):
Illusory Correlation
• People tended to overestimate co-occurrence of
diagnoses such as paranoia or suspiciousness
with features in persons drawn by hypothetical
mental patients, such as peculiar eyes
• Subjects might overestimate the correlation due
to easier association of suspicion with the eyes
than other body parts
The Anchoring and Adjustment
Heuristic
• People often estimate by adjusting an initial
value until a final value is reached
• Initial values might be due to the problem
presentation or due to partial computations
• Adjustments are typically insufficient and are
biased towards initial values, the anchor
Anchoring and Adjustment Biases (1):
Insufficient Adjustment
• Anchoring occurs even when initial estimates (e.g.,
percentage of African nations in the UN) were explicitly
made at random by spinning a wheel!
• Anchoring may occur due to incomplete calculation, such
as estimating by two high-school student groups
– the expression 8x7x6x5x4x3x2x1 (median answer: 512)
– with the expression 1x2x3x4x5x6x7x8 (median answer: 2250)
• Anchoring occurs even with outrageously extreme anchors
(Quattrone et al., 1984)
• Anchoring occurs even when experts (real-estate agents)
estimate real-estate prices (Northcraft and Neale, 1987)
Anchoring and Adjustment Biases (2):
Evaluation of Conjunctive and Disjunctive Events
• People tend to overestimate the probability of
conjunctive events (e.g., success of a plan that
requires success of multiple steps)
• People underestimate the probability of
disjunctive events (e.g. the Birthday Paradox)
• In both cases there is insufficient adjustment
from the probability of an individual event
Anchoring and Adjustment Biases (3):
Assessing Subjective Probability Distributions
• Estimating the 1st and 99th percentiles often leads to
too-narrow confidence intervals
– Estimates often start from median (50th percentile) values,
and adjustment is insufficient
• The degree of calibration depends on the elicitation
procedure
– state values given percentile: leads to extreme estimates
– state percentile given a value: leads to conservativeness
Strategies for Comprehension
1.
2.
3.
4.
5.
Questioning and Explaining (SQ3R)
Concept Maps
Hierarchies
Networks
Matrices
Collins and Quillian’s Semantic
Network Model
“I once shot an elephant in my pajamas.
How he got in my pajamas, I’ll never
know…”
Who was wearing the
pajamas?
More…
• Used Cars: Why go elsewhere to be cheated? Come
here first!
• Spotted in a safari park: Elephants please stay in
your car.
• Panda mating fails; veterinarian takes over.
Language and Memory: Tricks with Retrieval
How many animals of each kind did Moses take on the ark?
________
How confident are you? (1=not at all, 7= very confident) ____
In the biblical story, what was Joshua swallowed by?
________
How confident are you? (1=not at all, 7= very confident)
_____
Aspects of memory: Retrieval
• Moses didn’t have an ark—Noah did!
• Joshua wasn’t swallowed by a whale: Jonah
was!
Imagine that Santa Cruz is preparing for the outbreak
of an unusual disease, which is expected to kill 600
people. Two alternative programs to combat the
disease have been proposed. Assume that the exact
scientific estimate of the consequences of the
programs are as follows:
• If Program A is adopted, 200 people will be saved.
• If Program B is adopted, there is a 1/3 probability that
600 people will be saved, and 2/3 probability that no
people will be saved.
Which of the two programs would you
favor?
Imagine that Santa Cruz is preparing for the outbreak
of an unusual disease, which is expected to kill 600
people. Two alternative programs to combat the
disease have been proposed. Assume that the exact
scientific estimate of the consequences of the
programs are as follows:
• If Program C is adopted, 400 people will die.
• If Program D is adopted, there is a 1/3 probability
that nobody will die, and 2/3 probability that 600
people will die.
Which of the two programs would you
favor?
• If Program A is adopted, 200 people will be saved.
• If Program B is adopted, there is a 1/3 probability
that 600 people will be saved, and 2/3 probability
that no people will be saved.
• If Program C is adopted, 400 people will be
die.
• If Program D is adopted, there is a 1/3
probability that nobody will die, and 2/3
probability that 600 people will die.
• Famous study by Tversky & Kahneman (1981)
– A: 72%
– B: 28%
– C: 22%
– D: 78%
• Anchoring
– Related to framing
– Unconscious use of an easily accessible “starting point” for
making a judgment about a quantity or cost
– How much to spend or donate
• $25
$50 $75
$100
• Buy one get one free! -why not just adjust the price?
– What do we anchor?
• We make jusdgments and evaluations relative to some frame of
reference
Problem planning and representation
• Lets’ try some! 
People in the community have a fear of crime!
Redefine it!
“Fear of crime” - - - - - - > “reducing crime”
Solutions:
1. Make capital punishment the law
2. Incarcerate criminals for life if they are convicted
of three major crimes
Problem planning and representation
People in the community have a fear of crime!
Redefine it again!
“Fear of crime” - - - - - - > “Make life safer for citizens”
Solutions:
1. Provide better security
2. Offer self-defense course
3. Organize anti-crime groups in the neighborhoods
4. “Neighborhood watch”
Problem planning and representation
People in the community have a fear of crime!
Redefine it again!
“Fear of crime” - - - - - - > “Reduce the # of criminals”
Solutions:
1. Send criminals to Siberia
2. Return to using gallows, public humiliation, beheading, etc..
.
3. Increase afterschool activities
4. Improve educational program
Problem planning and representation
People in the community have a fear of crime!
Redefine it again!
“Fear of crime” - - - - - - > “Change public perspective of
crime”
Solutions:
1. Give people anti-anxiety drugs
2. Provide public info that crime is down (may be true or false)
- It is changing perception of crime not the crime rates
themselves! (not necessarily ethical!)
Problem planning and representation
People in the community have a fear of crime!
Redefine it again!
“Fear of crime” - - - - - - > “Reducing violent crime”
Solutions:
1. Make guns illegal to own
2. Legalize drug use