Reasoning &
Decision making
Tobias.Johansson@hkr.se
Reasoning
Information
Conclusion
Reasoning - deductive
Information
Premise 1
Premise 2
…….
Premise n
Conclusion
Conclusion
Valid deductions = if premises true, then conclusion true
A deduction can be valid even if premises are false
Only form matters, not content
Reasoning - inductive
Information
Conclusion
Inductive reasoning goes beyond the data
Conclusions never follow definitely from observations
Deduction - Syllogisms
Categorical syllogisms
- Deductions involving All, No, Some
All A are B
All B are C
Therefore, all A are C
All students are smart people
All smart people are rich
Therefore, all students are rich
Conditional syllogisms
- Deductions involving If…Then
If p then q
p
Therefore q
If you talk at the movies you go to prison
You talk at the movies
You go to prison
Categorical Syllogisms
Valid and invalid categorical syllogisms
Valid
Invalid
1
Some A are B
2
All B are C
Con Therefore some A are C
1
All A are B
2
Some B are C
Con Therefore, some A are C
Some cats are lazy
All who are lazy are dogs
Therefore some cats are dogs
All cats are lazy
Some who are lazy are dogs
Therefore some cats are dogs
Valid, despite false premise
Categorical Syllogisms
What kind of errors do people make?
- Belief bias
- If conclusion true, then syllogism valid
No A are B
Some C are B
Therefore some A are not C
Invalid
A
No babies are evil
Some dogs are evil
Therefore some babies are not dogs
B
No heroin is healthy
Some chemicals are healthy
Therefore some heroin is not chemicals
People judge A as valid more often than B, more believable conclusion
Categorical Syllogisms
Conditional Syllogisms
Premises
Conclusion
Valid
Performance
If p then q
p
q
Yes
97 %
If p then q
Not q
Not p
Yes
60%
If p then q
q
p
No
40%
If p then q
Not p
Not q
No
40%
Conditional Syllogisms
Why do people make errors in conditional reasoning?
- One reason is lack of falsification strategies
- which is affected by the format of the problem
To see this, we will look at the Wason four-card problem
Wason four-card problem
Potential falsifiers
Indicate the minimum number of cards you have to
turn to test the rule:
If there is a vowel on one side,
then there is an even number on the other side.
Wason four-card problem
If there is a vowel on one side,
then there is an even number on the other side.
Beer problem
If a person is drinking beer,
then he/she must be at least 19 years old.
Results – beer vs. abstract
(Griggs & Cox, 1982)
Theories
Why is the beer task easier?
Pragmatic reasoning schema (permissions)
- people are familiar with checking permissions
Cheating detection - Social exchange theory
- In order to monitor social exchange, people have
developed cheating detection mechanisms that do not
presuppose familarity
Permissions
(Cheng & Holyoak, 1985)
If one side says ”Enter”,
then the other says ”Cholera”
A
- Tropical diseases
B
- Inoculations to ensure protection against disease
Results
Checking for inoculations indirectly emphasizes to check
for permission to enter the country.
This ”permission” group performs much better.
Cheating
(Cosmides & Tooby, 1992)
Found high performance in conditions that were
unfamiliar to the participants and involved cheating.
Non-cheating situations reduced performance.
Permission schema or cheating detection?
- support for both accounts
Induction
Observation:
Everytime I have met John he is rude. And
Steve says the same thing about John.
Conclusion:
John is a rude person.
Observation:
Only humans seem to use language.
Conclusion:
Humans have specially developed language
mechanisms that other species do not have.
Strength of induction
Representativeness
Studying aeroplanes does not tell you much about eagles.
Frequency
A replicated experiment is better than an unreplicated.
Quality
An astronomical story is more coherent than an astrological.
Heuristics
Some errors in inductive reasoning may be due to heuristics
(even though the heuristics themselves may often be useful)
Heuristics
- ”Rules of thumb”, ”shortcuts”
- Can be adaptive, can lead to error
- Computationally attractive
- Availability heuristic
- Representativeness heuristic
- Commitment heuristic
Availability heuristic
Which is a more likely cause of death?
or
Tornado
Asthma
Asthma is 20 times more likely to kill. About 40% chose tornado.
Tornados make the news.
Representativeness heuristic
How likely is it that X belongs to the class Y.
How similar is X to the prototype of Y.
People tend to neglect base rates and focus on characteristics.
Representativeness heuristic
Conjunction fallacy
Linda
- 31 years, single, outspoken, bright
- philosophy, concerned with justice
- antinuclear demonstrations
Which is more probable?
A - Linda is a bank teller
B - Linda is bank teller and active in feminist movement
Many people chose B, because that fits with the feminist stereotype (or did?).
But, the probability of two events together cannot be higher than the
probability of either.
Commitment heuristic
(Lagnado & Shanks, 2003)
- More people read tabloids than broadsheets.
- The Reporter is the most popular newspaper.
- More progressives than liberals read the Reporter.
- More Liberals than Progressives read the others.
- Overall, 50% of readers are Liberals and 50% progressives.
Commitment heuristic
- More people read tabloids than broadsheets.
- The Reporters is the most popular newspaper.
- More progressives than liberals read the Reporter.
- More Liberals than Progressives read the others.
- Overall, 50% of readers are Liberals and 50% progressives.
A reader is drawn randomly from the population.
How likely is it that the person is a Liberal?
People answer 50% (correct).
Commitment heuristic
- More people read tabloids than broadsheets.
- The Reporters is the most popular newspaper.
- More progressives than liberals read the Reporter.
- More Liberals than Progressives read the others.
- Overall, 50% of readers are Liberals and 50% progressives.
A reader is drawn randomly from the population.
What newspaper would you guess the person reads?
Many people guess the Reporter (reasonable).
Now, what party does the person vote for?
People now judge the person with 80% certainty (instead of 50)
to be a progressive!
Commitment heuristic
- More people read tabloids than broadsheets.
- The Reporters is the most popular newspaper.
- More progressives than liberals read the Reporter.
- More Liberals than Progressives read the others.
- Overall, 50% of readers are Liberals and 50% progressives.
A reader is drawn randomly from the population.
What type of newspaper would you guess the person reads?
Many people guess Tabloid (reasonable).
Now, what party does the person vote for?
People now judge the person with 38% certainty (instead of 50)
to be a progressive!
Commitment heuristic
So what?
- The amazing thing is that people change their estimates purely on the
basis of no information.
- They just guess what type of paper, or what specific paper, the person
reads. The person is drawn randomly.
- They then commit to the truth of this category and assign estimates of
political voting thereafter.
- The estimates change (up or down) depending on category specificity
(specific paper or type of paper) because the category structure is nonaligned.
Non-aligned categories
Brazil is the most likely country to win the World Cup.
At the same time, it is more likely that a European country will win than a
South American country.
Commitment heuristic
Lagnado and Shanks (2003) study demonstrates that
simply asking about a category makes people use the information
associated with that category, at that level.
It is an extreme form of base rate neglect, because the subjects
are not given any misleading information. They are just asked a
question without feedback.
Confirmation bias
An additional source of induction errors is confirmation bias
- tendency to notice information that supports one´s beliefs.
Testing rules (Wason, 1960)
What rule do I have in mind with these 3 numbers?
2
4
6
Write down three numbers and I will say whether they follow the rule. Tell me when
your are certain you have discovered the rule.
Most subjects tried numbers that followed their own hypothesis.
They key to discovering the rule is to generate numbers that would falsify one´s
hypothesis.
Judgment and decision making
Utility approach
- people are rational
- maximize expected utility
Problems
- people do not always act rationally
- people have limited computational resources
- utility is ambiguous
- people focus on different aspects dependning on context
Focusing illusion
A -How happy are you?
B -How many dates did
you have last month?
Correlation between answers
0,7
0,6
0,5
0,4
0,3
0,2
0,1
0
A then B
B then A
Framing
(Tversky & Kahneman, 1981)
A disease is about to burst out. If nothing is done, 600 people will
die. There are two programs for dealing with the situation. The
estimates of the outcomes are as follows:
Program A
- 200 people will be saved.
Program B
- 1/3 probability that 600 people are saved, 2/3 probability that
noboby will be saved.
72% chose A
Framing
A disease is about to burst out. If nothing is done, 600 people will
die. There are two programs for dealing with the situation. The
estimates of the outcomes are as follows:
Program C
- 400 people will be killed.
Program D
- 1/3 probability that nobody will die, 2/3 probability that 600
people will die.
78% chose D
Framing
The results are remarkable, since
Program A = Program C
(same expected utility)
Program B = Program D
(same expected utility)
Decision justification
Offer to buy a vacation package at low price.
Options:
- buy
- don´t buy
- pay 5 dollar fee to postpone decision 2 days
Pass group
- You just passed an exam
Fail group
- You just failed an exam
Indeterminate group
- You will find out about exam results in 2 days
Percentage of participants
70
60
50
40
Buy
Don´t buy
Wait
30
20
10
0
Pass
Fail
Indeterminate
- Many chose ”wait” in the indeterminate group.
- But the pass and fail groups indicate that outcome doesn´t matter.
- People want some justification, before they make the decision that they will
make anyway, no matter what the outcome is.
Reasoning, deciding, & the brain
Prefrontal cortex (PFC)
- sensory information
- memory retrieval
- working memory
- planning
- coordination
- anticipation
- inhibition
- relational integration
- emotion/response integration
Reasoning, deciding, & the brain
Prefrontal cortex (PFC)
Perseveration
- task switching difficulty
PFC damage reduces performance in
- card sorting tasks, which require switching strategies
- tasks that require connecting different parts
- problem solving tasks generally
- Problem solving activates PFC in normal participants
- More complex problems activate larger areas of PFC.
Reasoning, deciding, & the brain
Prefrontal cortex (PFC)
Relational integration (Waltz et al., 1999)
Task 1
Easy: A is smaller than B, B is smaller than C
Hard: A is smaller than B, C is smaller than A
Easy
Task 2
Medium
Hard
Reasoning, deciding, & the brain
Prefrontal cortex (PFC)
Relational integration (Waltz et al., 1999)
Emotional decisions and the brain
Prefrontal cortex (PFC)
IOWA gambling task and somatic markers
- four decks of cards
- associated with different outcomes and probabilities
- participants chose cards from any deck for 100 trials
- for each choice they win money, or win and lose money
A
Win every trial:
100
Net result every 10 trials: -250
Status:
BAD
B
C
D
100
-250
BAD
50
+250
GOOD
50
+250
GOOD
VMPFC patients go for the bad decks
(high consistent wins, but higher variable losses also).
Control patients show higher SCR
response to the bad decks (A B)
Control patients learn to go for the good decks
(lower consistent wins, but lower variable losses also).
VMPFC patients do not.
Emotional decisions and the brain
Prefrontal cortex (PFC)
IOWA gambling task and somatic markers
- PFC is thought to integrate somatic markers, emotion-based
bodily signals generated from the body, with different
response options
- PFC damage reduces task performance and somatic markers associated
with different choices
Win every trial:
Net result every 10 trials:
Status:
A
B
C
D
100
-250
BAD
100
-250
BAD
50
+250
GOOD
50
+250
GOOD
Emotional decisions and the brain
Ultimatum game
Partner: sometimes human, sometimes computer
Offers: 5/5, 7/3, 8/2, 9/1
Turn the offer down, and you get nothing
Emotional decisions and the brain
Ultimatum game (Sanfey et al., 2003)
People sometimes reject the offer, when the offers are ”unfair”.
They do this to a larger extent if the partner is human.
Emotional decisions and the brain
Ultimatum game (Sanfey et al., 2003)
Activation difference: [Human unfair] – [Human fair]
Emotional decisions and the brain
Ultimatum game (Sanfey et al., 2003)
Anterior Insula
- Negative emotion, pain, distress, hunger, etc
Anterior Cingulate Cortex
- Cognitive conflict, error detection
Dorsolateral Prefrontal Cortex
- Goal maintenance, executive control
Emotional decisions and the brain
Ultimatum game (Sanfey et al., 2003)
Activation for
unfair offers
Emotional decisions and the brain
Ultimatum game (Wout et al., 2006)
Skin conductance
Synthetic Happiness
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