Reasoning

1
Reasoning Decision Making
Monty Python The Search for the The Holy Grail
Witch Scene http//www.youtube.com/watch?vyp_l5nt
ikaU
2

• 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

3
Reasoning Decision MakingBackbone of Problem
Solving Creativity

• Logic
• Decision making

4
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

5
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....

6
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.

7
Second  Questiondon'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?

8
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?

9
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!

10
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  

11
(No Transcript)
12
(No Transcript)
13
(No Transcript)
14
(No Transcript)
15
(No Transcript)
16
(No Transcript)
17
(No Transcript)
18
(No Transcript)
19
(No Transcript)
20
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
• If it rains the street gets wet
• It rained
• The street gets wet
• Is this a valid or invalid conclusion?
• -valid!

1
21
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
22
If, then statements
If it rains, then the streets get wet. It
doesnt rain. Therefore, I conclude that the
streets dont get wet. This argument is valid
This argument is invalid
2
23
If, then statements
If it rains, then the streets get wet. The
streets are not wet. Therefore, I conclude that
it has not rained. This argument is valid
This argument is invalid
3
24
If, then statements
If it rains, then the streets get wet. The
streets are wet. Therefore, I conclude that it
must have rained. This argument is valid
This argument is invalid
4
25
If, then statements
If p, then q. I observe p. Therefore, I
conclude that q must be the case. This
argument is valid This argument is invalid
5
26
If, then statements
If p, then q. I dont observe p. Therefore, I
conclude that q is not the case. This
argument is valid This argument is invalid
6
27
If, then statements
If p, then q. I dont observe q. Therefore, I
conclude that p must not be the case. This
argument is valid This argument is invalid
7
28
If, then statements
If p, then q. I observe q. Therefore, I
conclude that p must be the case. This
argument is valid This argument is invalid
8
29
If, then statements
If it rains, then the streets get wet. It
rains. Therefore, the streets gets wet.
p
q
30
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

31
If, then statements
p
q
it rains
the streets get wet
if
the streets dont get wet
p
it doesnt rain
q
the streets get wet
If it rains, then the streets get wet It
rains Therefore the streets get wet AFFIRMING THE
ANTECEDANT VALID
q
32
If, then statements

If it rains, then the streets get wet. It
rains. Therefore, the streets gets wet.
p
q
Valid!
Consequent
Antecedent
Affirming the antecedent
If p, then q.
33
If, then statements
If it rains, then the streets get wet. It
doesnt rain. Therefore, I conclude that the
streets dont get wet. This argument is valid
This argument is invalid
2
Denying the antecedent
34
If, then statements
p
q
it rains
the streets get wet
if
the streets dont get wet
p
it doesnt rain
q
the streets get wet
If it rains, then the streets get wet It doesnt
rain Therefore I conclude that the streets dont
get wet DENYING THE ANTECEDENT INVALID
q
35
If, then statements
If it rains, then the streets get wet. The
streets are not wet. Therefore, I conclude that
it has not rained. This argument is valid
This argument is invalid
3
Denying the consequent
36
If, then statements
p
q
it rains
the streets get wet
if
the streets dont get wet
p
it doesnt rain
q
the streets get wet
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
q
37
If, then statements
If it rains, then the streets get wet. The
streets are wet. Therefore, I conclude that it
must have rained. This argument is valid
This argument is invalid
4
Affirming the consequent
38
If, then statements
p
q
it rains
the streets get wet
if
the streets dont get wet
p
it doesnt rain
q
the streets get wet
If it rains, then the streets get wet The streets
are wet Therefore I conclude that it must have
rained AFFIRMING THE CONSEQUENT INVALID
q
39
(No Transcript)
40
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?

41
Wason (1966) Selection Task
E
K
4
7
p
p
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
• p
• p
• q
• q

Affirming the antecedent Denying the
antecedent Affirming the consequent Denying the
consequent
E
K
4
7
42
If, then statements
p
q
vowel
even number
if
odd number
p
consonant
q
even number
q
43
Griggs Cox (1982)

• If a person is drinking beer, then the person
  must be over 21

Drinking beer
Drinking Coke
16 years of age
22 years of age
p
q
p
q
44
If, then statements
p
q
drinks beer
older than 21
if
younger than 21
p
drinks coke
q
older than 21
q
45
Griggs Cox (1982)

• If a person is drinking beer, then the person
  must be over 21

Drinking beer
Drinking Coke
16 years of age
22 years of age
p
q
p
q
46
If, then statements
p
q
drinks beer
older than 21
if
younger than 21
p
drinks coke
q
older than 21
q
47
Griggs Cox (1982)

• If a person is drinking beer, then the person
  must be over 21

Drinking beer
Drinking Coke
16 years of age
22 years of age
p
q
p
q
48
If, then statements
p
q
drinks beer
older than 21
if
younger than 21
p
drinks coke
q
older than 21
q
49
Griggs Cox (1982)

• If a person is drinking beer, then the person
  must be over 21

Drinking beer
Drinking Coke
16 years of age
22 years of age
p
q
p
q
50
If, then statements
p
q
drinks beer
older than 21
if
younger than 21
p
drinks coke
q
older than 21
q
51
Griggs Cox (1982)

• If a person is drinking beer, then the person
  must be over 21

Drinking beer
Drinking Coke
16 years of age
22 years of age
p
q
p
q
52
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 Ill transfer
  the house to you.

53
(No Transcript)
54
(No Transcript)
55
(No Transcript)
56
(No Transcript)
57
(No Transcript)
58
(No Transcript)
59
(No Transcript)
60
(No Transcript)
61
(No Transcript)
62

• Daniel Ariely Why We Think Its Ok To Lie
  (sometimes) http//www.youtube.com/watch?vnUdsTiz
  SxSI

63
(No Transcript)
64
Probability in the Real WorldFrequentists and
Bayesians
65
Probability in the Real WorldBayesian Probability
66
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 dont do itat least
  not consistently, thoroughly, or very well.

67
Probability in the Real World
68
Probability in the Real World
69
Probability in the Real World
70
Probability in the Real World
71
Probability in the Real World
72
Probability in the Real World
73
Probability in the Real World
74
Probability in the Real World
75
Probability in the Real World
76
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

77
Three Major Human Probability-Assessment
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

78
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?

79
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

80
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 persons
  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

81
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

82
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 Gamblers 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)

83
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

84
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 Bs seems more predictive of a final
  grade-point average than a set of As and Cs
• Redundant, correlated data increases confidence

85
Representative Bias (6)Misconceptions of
Regression

• People tend to ignore the phenomenon of
  regression towards the mean
• E.g., correlation between parents and childrens
  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)

86
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

87
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

88
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?

89
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

90
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

91
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

92
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)

93
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

94
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

95
Strategies for Comprehension

1. Questioning and Explaining (SQ3R)
2. Concept Maps
3. Hierarchies
4. Networks
5. Matrices

96
Collins and Quillians Semantic Network Model
97
I once shot an elephant in my pajamas.
How he got in my pajamas, Ill never know
Who was wearing the pajamas?
98
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.

99
Language and Memory Tricks with Retrieval

How many animals of each kind did Moses take on
the ark? ________ How confident are you? (1not
at all, 7 very confident) ____ In the biblical
story, what was Joshua swallowed by? ________ How
confident are you? (1not at all, 7 very
confident) _____
100
Aspects of memory Retrieval

• Moses didnt have an arkNoah did!
• Joshua wasnt swallowed by a whale Jonah was!

101
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?
102
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?
103

• 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.

104

• Famous study by Tversky Kahneman (1981)
• A 72
• B 28
• C 22
• D 78

105

• 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

106
Problem planning and representation

• Lets try some! ?
• People in the community have a fear of crime!
• Redefine it!
• Fear of crime - - - - - - gt reducing crime
• Solutions
• 1. Make capital punishment the law
• 2. Incarcerate criminals for life if they are
  convicted of three major crimes

107
Problem planning and representation

• People in the community have a fear of crime!
• Redefine it again!
• Fear of crime - - - - - - gt 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

108
Problem planning and representation

• People in the community have a fear of crime!
• Redefine it again!
• Fear of crime - - - - - - gt 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

109
Problem planning and representation

• People in the community have a fear of crime!
• Redefine it again!
• Fear of crime - - - - - - gt 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!)

110
Problem planning and representation

• People in the community have a fear of crime!
• Redefine it again!
• Fear of crime - - - - - - gt Reducing violent
  crime
• Solutions
• 1. Make guns illegal to own
• 2. Legalize drug use