Meet Linda
Linda is 31, single, outspoken, and very bright. She majored in philosophy.
As a student, she was deeply concerned with issues of discrimination and
social justice, and participated in anti-nuclear and anti-war demonstrations.
What happened to Linda?
Rank order the following possible outcomes:
Linda failed to graduate from college
Linda works as a bank teller
Linda works for Green Peace
Linda works as a bank teller and is active in the feminist movement
The probability that Linda is a bank teller must be at least as large as
the probability that Linda is a bank teller and active in the feminist movement
What is Rational?
Two inadequate definitions:
The absence of emotional involvement
Thinking is that is objective, not subjective
One cannot divorce rational thinking from feelings and emotions: The desirability
or undesirability of outcomes is an emotional issue
Rational thinking is all about beliefs and values. These are inherently
subjective
Better definitions:
Avoiding self-contradictory conclusions
Behavior based only on current information and future consequences
Behavior consistent with formal theories of logic and probability
Behavior that best enables one to achieve one’s goals
These four definitions are just different ways of looking at the same thing
- Consistency (coherence) of beliefs and values
Another View of Rationality
For some authors, any thoughtful response is by definition rational, consistent
or not
Consider some explanations for “wrong” answers to the Linda problem:
“Just a slip - I got it wrong because I was not thinking carefully”
“For me, ‘likely’ is not the same thing as ‘probable’.
It’s a matter of what words mean”
“I assumed (b) meant ‘bank teller and not feminist’–so
my answer would be correct”
The Great Rationality Debate
Fifty years of bitter debate over the rationality of human thought
How might we resolve it?
Rationality: Another Example
Breast cancer screening is carried out using mammography. The probability
that a woman in the region has breast cancer is 1%.
If a woman has breast cancer, the probability she tests positive is 90%
(sensitivity).
If she does not have breast cancer, the probability she tests positive is
9% (false positive rate).
A woman tests positive. What is the probability that she has breast cancer?
Prior probability of cancer = 1%. Odds of 1 / 99
The data: 90% hit rate versus 9% false alarms. Ratio of 10 / 1
To find the new odds, multiply priors by data: (1/99) * (10/1) = 10 / 99
Roughly 10 / 100: Odds are 10 to 1 against cancer
Probability roughly 1 / 11 = 9%
Another View of Bayes Theorem
Assume 1,000 women from this population. How many are likely to have breast
cancer?
10 (990 do not)
Of the 10 cases, how many will be detected? 9
Of the 990, how many false alarms? 990 * 9% = 89
We have 98 positive tests. How many of these really have cancer? 9 / 98
= 9%
What are the two systems of reasoning that Evans describes? How do they differ
from each other?
System 1: Rapid, parallel, automatic, carried out without conscious awareness.
Old in evolutionary terms
System 2: Slow, sequential, deliberate.
System 2 may serve as an inhibitory process, suppressing the effects of
System 1.
What evidence exists to support the idea of two separate systems in human
reasoning?
The belief-bias effect: Arguments with believable conclusions are more
likely to be judged valid
These problems place logic and belief in conflict
System 2 (logical reasoning) must override the System 1 response that is
triggered by beliefs
Two Systems and the Wason Four-Card Task
People have great difficulty solving the non-deontic version (“If
B then N > 20”)
There is no ready System 1 solution
System 1 may offer a “matching heuristic”: Select the cards that
match elements in the hypothesis (“B” and “22”)
For deontic versions, the cheat-detector module provides a System 1 response
that is (usually) valid
Two Systems and Linda
(b) Linda works as a bank teller
(d) Linda works as a bank teller and is active in the feminist movement
System 1: The stereotype of bank teller is inconsistent with what we know
about Linda
But if she is active in the feminist movement in her spare time, that makes
it plausible
System 2: An analytic approach
Stephen Gould: ‘I know the conjunction is less probable, yet a little
homunculus in my head continues to jump up and down, shouting at me, “but
she can’t be a bank teller - read the description!”’
I.e., System 1 and System 2 in conflict
System 1: driven by problem specific details
System 2: driven by a context-free analysis
How are individual differences treated in the dual process model of reasoning?
System 2 demands cognitive resources
Some people have greater cognitive capacity, and more ability to use System
2
Stanovich: Independent of resources is a “thinking dispositions”
variable”: Willingness to engage in analytical thinking
Intelligence and Reasoning
Stanovich: Correlations between SAT scores and reasoning tasks:
Logical syllogisms .47
Wason 4-card problem .39
Statistical reasoning .35
Argument evaluation .36
Composite of 7 tasks .55
The relationships presumably represent enhanced working memory capacity,
as indicated by measures of general intelligence
Intelligence or Motivation?
What is needed for rational responding is not only cognitive capacity,
but the willingness to use it.
Thinking Dispositions: a measure of active cognitive style - willingness
to switch perspectives, consider alternative opinions, etc.
Partial correlations with performance:
SAT score .48
Thinking Dispositions .33
How is the dual process model related to evolutionary theories?
System 1 is another problem-specific evolutionary solution
System 2 seems to be a general purpose reasoning system
But how did System2 evolve?
It is the “long leash” solution that was invented for the human
species
Short Leash versus Long Leash Genetic Programming
The organism is a vehicle by means of which the genes reproduce themselves
Short Leash Goals vs Long Leash Goals
How did De Neys test the dual process model? Why did he choose the experimental
methods that he used?
The task: syllogistic reasoning
Independent variables:
Ease of the reasoning task (belief bias)
Additional load on working memory
Individual differences in capacity
The dual process theory predicts a triple interaction
How do De Neys's results bear on the theoretical points made by Evans?
Results: Triple (three-way) interaction