Decision making, reasoning and deduction

1
Decision making, reasoning and deduction

• Simon J. Davies

daviess_at_hope.ac.uk
2
Thinking and cognitive psychology

• Three areas within cognitive psychology can be
  categorized as high level cognition
• Problem solving where we have a goal that were
  not too sure how to achieve.
• Decision making where we decide to select
  between two or more options rationally.
• Reasoning and deduction logic applied to
  arriving at an objectively correct decision.

3
Decision making

• Simply, selection from a limited set of choices.
• Decision making answers questions such as
• Do people consistently make optimal decisions?
• What shortcuts do people use to make decisions?
• Do people reason logically?
• As with reasoning, decision making involves
  objectively correct answers.

4
Decision making - rationality

• Involve rationality this means that the choices
  we make are internally consistent.
• Rationality displays transitivity relationships
  that are consistent are predictable.
• The fact that something is rational does not
  however dictate what choice someone will make.

5
Normative theories

• Normative theories are what you should do that
  is, one choice usually appears better than
  others, or is optimal in a given situation.
  Theories differ as to what is optimal
• Expected value here choices are made because
  they offer the maximal payoff.
• Expected utility here choices are made that
  appear to be the most useful given current
  circumstances.

6
Descriptive Prescriptive theories

• Descriptive theories tell us what people actually
  do when they make decisions what influences
  their decisions, and so why they made them.
• Prescriptive approach how can we make people
  make better decisions? Approaches such as
  decision analysis allow us to make probabilities
  of outcomes alongside the utility (usefulness) of
  the outcome.

7
You are given the following choice, which do you
choose?

• 0.5 chance of winning 50.
• 0.25 chance of winning 110.

• 0.5 x 50 25
• 0.25 x 110 27.50

8
Percentage returns from casino games not good
to use expected value!
Game Bet
Average return Roulette
Single number
94.7 Roulette Red
or Black
97.2 Blackjack
Varies
99 Craps Pass or
dont pass 98.6 Slot
machine Ten pence
84.8 Slot machine
Twenty pence
89.9 Baccarat
Banker
98.6 Baccarat
Player
98.2
9
You are hungry and broke. Given the following
choices which would you choose?

• 0.85 chance of winning 8.
• 0.25 chance of winning 28.

• 0.85 x 8 6.80
• 0.25 x 28 7.00

10
Irrationality and decisions

• Rational decisions require us to fulfill two
  principles
• Description invariance we will make the same
  choices no matter how the problem is described as
  long as the structure is the same.
• Procedure invariance we will make consistent
  choices irrespective of our personal preferences.
• Kahneman and Tversky (1986) demonstrate how our
  problem frame makes us irrational.

11
Suppose I give you 300, but you must select One
of the following two options

• 1 chance of gaining 100.
• 0.5 chance of gaining 200 and
• a 0.5 chance of gaining nothing.

• 72 chose A.
• 28 chose B.

12
Suppose I give you 500, but you must select One
of the following two options

• 1 chance of losing 100.
• 0.5 chance of losing nothing and
• a 0.5 chance of losing 200.

• 36 chose A.
• 64 chose B.

13
A disease is expected to kill 600 people you must
decide which intervention to take.

• 200 people will be saved. (72)
• Theres a 1/3 chance that 600 people will
• be saved and a 2/3 chance that no one will
• be saved. (28)

• 400 people will die (22)
• Theres a 1/3 chance that no one will die
• and a 2/3 chance 600 will die. (78)

14
Other irrationalities

• Psychic budgets (Thaler, 1980) how do we
  mentally categorize money.
• Sunk cost spent money (or time, etc.) that
  cannot be redeemed but we persist in the activity
  to get our moneys worth.
• Loss aversion (Kahneman, Knetsch, Thaler, 1990)
  the unpleasantness of a loss is larger than the
  pleasure of a similar gain.

15
(No Transcript)
16
Reasoning and deduction
Reasoning refers to the processes by which
people evaluate and generate logical arguments.
Logic is a sub-discipline of philosophy and
mathematics that tries to formally specify what
it means for an argument to be correct. Anderson
17
Induction and deduction

• Deductive reasoning
• Problems to which one can apply formal logic and
  derive an objectively correct solution.

• Inductive reasoning
• Reasoning that allows one to say that a
  conclusion is more or less likely to be true but
  does not allow one to say that a conclusion must
  be true.

Quotes from Willingham, 2004
18
Conditional reasoning

• A form of reasoning that is conditional upon
  something else (i.e. a premise or proposition)
  being true. Operators direct the logic
• e.g.
• If I steer to the right, the car goes right.
• I steer to the right.
• Therefore, the car goes right.
• Other operators are not, ifthen, and, if and
  only if.

19
Rules of inference (RoI)

• In logic we have something called rules of
  inference.
• These specify when it is possible to infer a
  conclusion from a set of premises.
• A premise is simply a statement that is assumed
  to be true (for the purpose of drawing a
  conclusion).

20
Premises and Consequents

• We make a conditional premise or statement of
  truth (e.g. if P then Q).
• If Sue is happy, she has money (if P then
  Q).
• Sue is happy. (P)
• Therefore, Sue has money (Q)

21
Modus Ponens (RoI)

• This is simply stated as If P then Q (P stands
  for our premise, and Q for our conclusion).
• e.g. We can reformulate this into plain English
• A implies B, and given we know A we can infer
  B.
• If Bob drinks on Sunday night, hell be late
  for work Monday morning (if P then Q)
• Bob drank Sunday night (P)
• Therefore, Bob will be late Monday morning. (Q)

22
Modus Tollens (RoI)

• This is similar to Modus Ponens. It simply
  states If P then Q given not-Q (i.e. Q is
  untrue).
• If Bob drinks on Sunday night, hell be
  late
• for work on Monday morning (if P then Q)
• Bob is not late for work on Monday (not Q) -
• Therefore, Bob did not drink on Sunday night.
  (P)

23
(No Transcript)
24
Truth tables
T True F False, P premise, Q consequent
Truth tables let us lay out the possible truth
values for any set of conditionals and
propositions
25
Invalid inferences

• Denial of the antecedent
• If P then Q,
• Q,
• therefore P.

• Affirmation of the consequent
• If P then Q,
• not Q,
• therefore not P.

People frequently draw incorrect or invalid
inferences from these two types of propositional
relationship.
26
If P, then Q (If I eat too much desert, then I
am uncomfortably full.)
1st premise
P (I ate too much Dessert.)
Q (I am uncomfort- ably full.)
Not P (I didnt eat too much dessert)
Not Q (I am not uncom- fortably full.)
2nd premise
(I am uncomfort- ably full.)
(I ate too much Dessert.)
(I am not uncom- fortably full.)
(I didnt eat too much dessert)
Conclusion
Valid
Not valid
Not valid
Valid
Modus Ponens
Confirming the consequent
Denying the antecedent
Modus Tollens
Adapted from Willingham, 2004
27
Marcus and Rips (1979)
28
Performance with reasoning

• Overall people are not very good at reasoning
  with conditionals.
• Performance can be further affected by the
  addition of extra premises or information.
• When alternative antecedents are given people
  avoid making invalid inferences (Markovits, 1985)
• Byrne (1989) also found that additional
  information can prevent valid inferences also.

29
(No Transcript)
30
Wasons card selection task

• Wasons (1966) task requires the use of deductive
  reasoning to solve an apparently simple task.
• If there is a vowel on one side of a card, then
  there is an even number on the other side of the
  card.
• Findings suggest that people tend to try and
  confirm hypotheses when reasoning, rather than
  disprove them.

31
E
K
4
7
P Not-P Q Not-Q
? ? ? ?
32
Why is Wason so difficult? 1

• In Johnson-Laird and Wasons (1970) card task
  only 5 out of 128 gave valid inferences.
• Evans (1984) suggests that subjects select cards
  that are mentioned in the rule matching bias.
• Concrete tasks do not suffer the same difficulty.
  Typically, subjects can solve a concrete task 70
  of the time (Griggs Cox, 1982).
• Some of the difficulty therefore seems to derive
  from the abstract nature of the original task.

33
Beer
22
Coke
17
If a person is drinking beer, then the person
must be over 18 years of age. Select the card or
cards that you definitely need to turn over to
determine whether they are violating the rule.
Griggs Cox, 1982
34
Why is Wason so difficult? 2

• Manktelow and Over (1991) argue that concrete or
  thematic versions of the task permit a different
  type of reasoning, called deontic reasoning
  rather than the usual indicative form.
• Indicative form If there is a P then there is a
  Q
• Deontic form If you do P then you must do Q
• Cheng and Holyoak (1985) supported this view, but
  also showed support for a memory-cueing
  hypothesis (specific experience facilitates
  reasoning).

35
(No Transcript)
36
Syllogisms 1

• A syllogism is similar to the process of
  deductive reasoning. It has two premises and a
  conclusion
• e.g. All students study
• Some study leads to exam success
• Therefore, some students have exam
  success
• True or false?

False
37
Syllogisms 2

• For any syllogism to be considered true it must
  be true under all conditions.
• One way to check this is to use a Venn diagram to
  express the relations between statements
  concerning syllogistic components (i.e. A, B, C).
• So, some things can be true but necessarily false
  using syllogistic reasoning.

38
All A are B All B are C ?All A are C
Some A are B Some B are C ?Some A are C
Some A are B No B are C ?No A are C
All A are B Some B are C ?Some A are C
False
False
False
True
C
B
A
A
B
B
A
C
B
C
A
C
Adapted from Willingham, 2004
39
Test
All of the Frenchmen in the room are wine
drinkers. Some of the wine drinkers are
gourmets. Some of the Frenchmen are gourmets.
True or false?
False
All of the Frenchmen in the room are wine
drinkers. Some of the wine drinkers in the room
are Italians. Some of the Frenchmen in the room
are Italians.
Oakhill, Johnson-Laird, Garnham, 1989
40
(No Transcript)
41
Abstract rule theory (natural logic theory)

• Braine and OBriens theory suggests that humans
  have a natural form of logic.
• ART is a syntactic model we apply rules to
  premises to prove a conclusion is true.
• We develop a mental representation of the
  premises in WM.
• Invalid inferences come from misunderstanding and
  misrepresenting the premises.

42
Abstract rule theory 1

• Direct reasoning
• Core schemas these encode reasoning rules from
  premises such as Modus ponens.
• Feeder schemas provide intermediate conclusions
• Incompatibility rules examines WM for invalid
  inferences such as contradictions.
• ART sees these schema being controlled via a
  reasoning production system (e.g. ACT).

43
Abstract rule theory 2

• Indirect reasoning high error rates, but in
  non-normal situations (i.e. Modus tollens) people
  can also learn domain-specific schemas.
• Direct reasoning can also lead to errors
• Comprehension errors
• Heuristic inadequacy errors
• Processing errors

44
Abstract rule theory pros cons

• ART synthesizes problem solving with reasoning.
  It achieves its flexibility through appealing to
  a small set of abstract operators.
• ART lacks detailed specification for how it deals
  with comprehension.

45
Mental models Johnson-Laird

• Mental models is a semantic model a deductive
  form of reasoning where the conclusion is true
  under all conditions where the premises are true.
• Therefore the meaning (i.e. comprehension) of the
  problem is critical to its solution.
• Models are created that represent the stated
  problem premises.

46
Mental Models - processes

• In mental models there are three processes
• Comprehension models are constructed to
  meaningfully represent the premises.
• Combination and description premise models are
  integrated, then their relations simply
  described.
• Validation counterexamples are sought where all
  the premises are still true but the conclusion is
  false.

47
Wilma is on the right of Barney Fred is on the
left of Barney Bam-Bam is in front of Fred Dino
is in front of Wilma.
Premises
Fred
Wilma
Barney
Mental model
Bam-Bam
Dino
To disprove this model we need to find another
counterexample where the premises are true but
the mental model is different.
48
Wilma is on the right of Barney Fred is on the
left of Wilma Bam-Bam is in front of Fred Dino is
in front of Barney.
Bam-Bam is to the left of Dino?
Fred
Wilma
Barney
Bam-Bam
Dino
Barney
Wilma
Fred
Dino
Bam-Bam
49
MM with conditionals

• MM works with Modus ponens because the
  antecedent need not be represented. Only then Q
  need to be kept in mind.
• Modus tollens is difficult because not Q as well
  as P need to be represented.
• MM argues that reasoning becomes difficult due to
  processing limitations inherent to our cognitive
  systems.

50
MM pros and cons

• MM is well-specified and deals with a range of
  additional reasoning tasks (e.g. the card
  selection task).
• MM specifies that models will only be constructed
  that are required to solve the problem. Bonatti
  (1994) points out that there are numerous models
  for most problems.
• MM is under-specified with respect to the
  comprehension component (especially previous
  knowledge).

51
Probabilistic theory (information gain model)

• Oaksford and Chater (1994) argue that humans
  dont explicitly reason but rather think in terms
  of information gain.
• When confronted with a problem humans therefore
  make decisions that maximize gain.
• Putting these in order determines the likelihood
  of one option being chosen above others.

52
Eaten tripe
Not eaten tripe
Sick
Not sick
P Not-P Q Not-Q
If you eat tripe then you feel sick (if P then Q)
Information gain order P, Q, not-Q, not-P
53
PT pros and cons

• Provides a bridge between judgement and decision
  making with reasoning. It seems to provide a
  better match for human performance on abstract
  reasoning tasks.
• Lacks any performance mechanism to describe
  processes of conclusion selection or top-down
  influences of prior experience.

54
(No Transcript)
55
End of decision making, reasoning and deduction
lecture