Download Psychology 100.18

Psychology
100
Chapter 8
Part II
Thinking
&
Intelligence
Outline
o Cognition, C’ont
o Problem solving
o Decision Making
Study Question:
• What is the availability
heuristic? Give an example
of a reasoning error that
might be attributed to
availability.
Math Phobic’s Nightmare
Cognition
Valid Arguments
If P -> Q
P
therefore, Q
If it is an apple, it a fruit
It is an apple
It is a fruit
Modus Ponens
If P -> Q
~Q
therefore, ~P
If it is an apple, it a fruit
It is not a fruit
It is not an apple
Modus Tollens
Invalid Arguments
If P -> Q
~P
therefore, ~ Q
If P -> Q
If it is an apple, it a fruit
Q
It is not an apple
therefore, P
It is not a fruit
Denying the antecedent
If it is an apple, it a fruit
It is a fruit
It is an apple
Confirming the consequence
Cognition
• The Wason selection task
– Each card has a letter on one side and a number on
the other
– What are the fewest cards you need to turn over to
confirm or deny the following hypothesis:
If it has a vowel on one side, there is an even number on
the other side
A
B
1
2
Cognition
• The Wason selection task
– Within a familiar content
> You are working at a bar
> There is a table of 4, each person is drinking something, you can see
that one person is drinking beer, another is drinking Coke.
> You know the other two people,one is 18, one is 19 yrs old.
If one is drinking beer, they must be nineteen
18
19
Coke
Beer
Cognition
• Why do we confirm the consequence?
– Conditional vs. biconditional syllogism
>If and only if.
>E.g.
If you don’t eat your supper, you get no ice cream
– We say or hear a conditional statement, but
we think or mean a biconditional.
Problem
Cognition
Solving
Two flagpoles are standing, each 20 meters
tall. A 30 meter rope is strung from the top of
one of the flagpoles to the top of the other
and hangs freely between them. The lowest
point of the rope is 5 meters above the
ground. How far apart are the two flagpoles?
20 m
5m
?
Cognition
• Problem Solving
– The Gestaltist tradition
>The goal of problem solving is the achievement
of a Gestalt.
 A form, configuration or whole pattern.
 Parallels between perception and problem solving
Problem
Cognition
Solving
• Problem Solving
– The Gestaltist tradition
Wolfgang Kohler
>Wolfgang Kohler (Circa WW I)
 Studied visual discrimination in animals
 Applied gestalt principles to animal perception
 Coined the term ‘insight’ to describe the sudden
perception of proper relations.
 Observed insightful behaviour in chimps
solving problems
Problem
Cognition
Solving
• Problem Solving
– The Gestaltist tradition
>Wallas’ (1926) stages of thinking
 Preparation
• Recognize a problem exists
• Find a representation for the problem
• Preliminary attempts at solution
Problem
Cognition
Solving
• Problem Solving
– The Gestaltist tradition
>Wallas’ (1926) stages of thinking
 Incubation
• After failing to solve the problem it is set aside
• No longer work on the problem at a conscious
level
• Work proceeds at an unconscious level
Problem
Cognition
Solving
• Problem Solving
– The Gestaltist tradition
>Wallas’ (1926) stages of thinking
 Illumination
• Flash of insight
• Answer suddenly appears in consciousness
 Verification
• Confirm the insight
• Usually involves simple checking.
Problem
Cognition
Solving
• Problem Solving
– The Gestaltist tradition
>Preparation: The role of representation
 The Buddhist monk problem
Top
Base
6 AM
6 PM
Cognition
• Problem Solving
– The Gestaltist tradition
>Incubation
 Fulgosi & Guilford (1968)
Imagine that all power stations shut down, then list
all possible consequences.
• Waiting 20 min before listing improved retrieval of obvious
(but not remote) consequences
• No effect for 10 min waiting interval
Problem
Cognition
Solving
• Problem Solving
– The Gestaltist tradition
>Incubation
Cognition
• Problem Solving
– The Gestaltist tradition
>Incubation
 Silveira (1971)
• The chain necklace problem
• Control Group: Works on problem for 30 min
• Four Experimental Groups
> Brief or long preparation
> 30 min or 4 hr interuption
> Everyone worked for a total of 30 min
Cognition
• Problem Solving
– The Gestaltist tradition
>Incubation
 Silveira (1971)
Cognition
• Problem Solving
– The Gestaltist tradition
>Incubation
 Is it unconscious problem solving?
• Silveria’s verbal protocol
• Subjects tended to pick up the problem where they
left off
 Another explanation
• Incubation allows us to change inappropriate sets
• Improves performance
 Incubation can impair performance as well
• If the initial set had been appropriate
Cognition
• Problem Solving
– The Gestaltist tradition
>Illumination and insight
OTTFFSSEN…
 Archimedes
 Insight problems
 The fourth tree
 Metcalfe & Wiebe (1987)
• Had subjects complete either algebra or insight
problems
• Recorded “warmth” ratings
Problem
Cognition
Solving
• Problem Solving
– The Gestaltist tradition
>Difficulties in problem solving
 Functional Fixedness
• Duncker’s candle problem
Cognition
• Problem Solving Basics
– Characteristics of problem solving
>Three parts to a problem (Newell & Simon)
 Initial state
 Goal state
 Operations to move through intermediate
states
• Rules to get you from the initial state to the goal
state
>E.g., The Tower of Hanoi
Cognition
• Problem Solving Basics
– E.g., The Tower of Hanoi
Initial State
Cognition
• Problem Solving Basics
– E.g., The Tower of Hanoi
Goal State
Problem
Cognition
Solving
• Problem Solving Basics
– E.g., The Tower of Hanoi
>Operations through intermediate states
 Disks may be moved one at a time to any post
 A larger disk may NOT rest on top of a smaller disk
>The problem space
 The initial state, the goal state, and the intermediate
steps to reach the goal. Also includes the problemsolver’s knowledge at each step
• E.g., Problem graphs
Problem graph for the
Tower of Hanoi Puzzle
Cognition
• Problem Solving Basics
– Well-defined and ill-defined problems
> Well defined problems
 Clearly defined start state and goal state
 Operations for moving from one state to the next are clearly
defined
 E.g.s.
• The Tower of Hanoi
• Hobbits and Orcs
> Ill-defined problems
 One or more of the above three are not clearly defined
 E.g.s.
• Making a purse from a sows ear
• Many of the day to day problems that we attempt to solve
Cognition
• Problem Solving Basics
– Strategies for solving problems
>Subgoals
HHH
OOO
Boat
HHH
OOO
Boat
1H 1O
HH
OO
1H 1O
2O
H
O
Boat
HHH
O
1H
OO
Boat
HH
OO
OOO
Boat
OOO
Boat
1O
HHH
O
Boat
HHH
1O
OO
OO
2H
H
O
HHH
OO
Boat
2O
2O
HH
OO
Boat
HHH
O
Boat
2H
1H1O
HH
OO
Boat
HHH
O
1O
O
O
HHH
OO
Boat
1H
1O
HHH
OO
Boat
H
O
Boat
2O
H
O
Cognition
• Problem Solving Basics
– Strategies for solving problems
>Subgoals
 The Hobbits and Orcs problem
graph
>Hayes (1966)
 Presented a 5/5 boat
transformation task
 Gave subjects a subgoal
Three orcs on one side without
the boat
 Control group: 30 moves
 Experimental group: 20 moves
Problem
Cognition
Solving
• Problem Solving Basics
– Strategies for solving problems
> Brute Force
 Go through all possible states until solution is found
> Hill Climbing
 Always move towards goal
> Analogy
 The jealous husbands problem
 People tended not make use of the analogy
 Attack - dispersion, Radiation, & Oil fire problem
• Students who read two stories and could describe the
covergence schema were more likely to solve the third.
Problem
Cognition
Solving
• Problem Solving Basics
– Strategies for solving problems
> Working backwards
 The card game problem
A
Round 3
(8)
Round 2
16
Round 1
8
Ante
4
B
8
(4)
14
7
C
8
4
(2)
13
Cognition
• Inductive Reasoning
– Algorithms and Heuristics
>Reasoning under uncertainty: Inductive
reasoning
 Algorithms versus heuristics
>Kahneman and Tversky’s work
 Behavioural decision work
 Ups and downs of heuristics
 Cf. Visual illusions
Cognition
• Inductive Reasoning
– Algorithms and Heuristics
>The representiveness heuristic
 E.g., Flip a coin 6 times, which is more likely
HHHHHH or HHTHTT
 Which lottery ticket is most likely to win the next 6-49?
04-11-19-29-33-39 or 01-02-03-04-05-06
 The representativeness heuristic - samples are like the
populations that they are pulled from.
• The representativeness heuristic leads to a
number of decision biases
Cognition
• Inductive Reasoning
– The representiveness heuristic
>The law of small numbers
 Who is more likely to have days where more than 60%
of the births are male? St. Martha’s or the IWK?
>Ignoring base rates
 Cancer Screening example
• 1% of women at age forty who participate in routine screening have
breast cancer. 80% of women with breast cancer will get positive
results. 9.6% of women without breast cancer will also get positive
results. A woman in this age group had a positive mammography in
a routine screening. What is the probability that she actually has
breast cancer?
>The Gambler’s fallacy
>The hot hand in basketball
Cognition
• Inductive Reasoning
– The Availability Heuristic
> Our estimates of how often things occurs or are
influenced by the ease with which relevant examples can
be remembered
> This leads to a number of biases
1) Which is a more likely cause of death in the United States: being
killed by falling airplane parts or being killed by a shark?
• Airplane parts! 30 X more likely than shark attacks.
2) Do more Americans die from a) homicide and car accidents, or
b) diabetes and stomach cancer?
• Diabetes and stomach cancer by a ratio of nearly 2:1.
3) Which claims more lives in the US: lightning or tornadoes?
• Lightning
Cognition
• Inductive reasoning
– The Availability Heuristic
>Important factors
 Vividness and Saliency
• E.g., the full moon
 Repetition effects
 Anything that makes recollection easier
• Role of the media
Cognition
A large city is on the verge of a rare asian bird flu
outbreak and it is expected that 600 people will be
infected. Two alternative programs have been
proposed to fight the disease. Assume that these
are the exact scientific estimates of the two
programs:
If Program A is adopted, 200 people will be saved.
If Program B is adopted, there is a one-third possibility that
600 people will be saved, and a two-thirds probability that
no people will be saved.
Which program would you favour?
Cognition
• Inductive Reasoning
– The framing effect (Kahneman & Tversky)
> The wording of question in conjunction with the
background context can influence the decision.
> Both of the previous plans were rejected, consider the
following:
 If Plan C is adopted, 400 people will die.
 If Plan D is adopted, there is one-third probability that nobody will
die, and a two-thirds probability that 600 people die.
> Kahneman & Tversky’s results
Plan A
1/3 Saved
Plan B
P=1/3 Saved
Plan C
2/3 Die
Plan D
P=2/3 Die
72%
28 %
22%
78 %
Cognition
• Inductive reasoning
– The framing effect (Kahneman & Tversky)
>Risk seeking and avoidance
 When questions are framed in terms of gains we avoid risk
(Prefer A over B)
 When framed in terms of losses we are risk-seekers
(Prefer D over C)
>Other findings relating to the Framing Effect
 It is unrelated to statistical sophistication
 It is not eliminated when the contradiction is pointed ou