Base-Rate Respect (Barbey & Sloman, 2007)

1. Barbey & Sloman

2. 

3. Category instances (outside view, expect
better performance ): “Here is a new sample of
patients who have obtained a positive test result
in routine screening. How many of these patients
do you expect to actually have the disease? __
out of __.”
Category properties (inside view): “Pierre has a
positive reaction to the test.” [then compute
probability estimate]

5.  Single-event:
 “A 40-year-old woman who participates in routine
screening has 10 out of 1,000 chances to have
breast cancer.”
 Frequencies:
 “A proportion of 0.01 of women at age 40 who
participate in routine screening have breast
cancer.”

6. Swiss Army Natural Natural Non-evo. Nested sets and
Knife frequency frequency natural freq. dual processes
algorithm heuristic heuristic
Impenetrable NOT impenetr. NOT impenetr. NOT impenetr. NOT impenetr.
Encapsulated Encapsulated Not encapsulat. Not encapsulat. Not encapsulat.
One module Simplified form Heuristic to Simplified Bayes’ General purpose
represents of Bayes’ compute Bayes’ calculation, no reasoning
natural theorem: rule from natural need for natural processes (Sys. I
frequencies calculate number frequencies, sampling and II) -
of cases where “fast and frugal” “associative and
#1: natural hypothesis and Sampling rule-based”
frequency info observations method that
easy to store occur (“the “one way or Bayesian
#2: preserves Ratio”) another” people inference from
sample size can use rule-based
(10/1,000) system
Inaccessible to No explicit No explicit High degree of
conscious control consideration of consideration of cog control
base rates base rates
Evo Evo Evo Non-evo Non-evo
“The mind is a frequency monitoring device”

7.  Bayesian inference comes from rule-based
system
 Errors from cognitive heuristics come from
associative processes
 Base-rate neglect comes from “associative
responding” and facilitation comes when
people use rules to make inferences

8. 

9. 10 out of 10,000 women have breast cancer
Structure: representation of category instances
demonstrates set structure (10 have, 9,990 don’t, but
also everyone either has or does not have)
Nested sets theory

11.  First and second frameworks
can really be collapsed into
one, identical to #3 (Brase)
 Non-evolutionary natural
frequency heuristic is non-
evolutionary….

12. Swiss Army Natural Natural Non-evo. Nested sets and
Knife frequency frequency natural freq. dual processes
algorithm heuristic heuristic
Impenetrable NOT impenetr. NOT impenetr. NOT impenetr. NOT impenetr.
Encapsulated Encapsulated Not encapsulat. Not encapsulat. Not encapsulat.
One module Simplified form Heuristic to Simplified Bayes’ General purpose
represents of Bayes’ compute Bayes’ calculation, no reasoning
natural theorem: rule from natural need for natural processes (Sys. I
frequencies calculate number frequencies, sampling and II) -
of cases where “fast and frugal” “associative and
#1: natural hypothesis and Sampling rule-based”
frequency info observations method that
easy to store “one way or
#2: preserves
Really,(“the same
occur the Nonsense
another” people
Bayesian
Ratio”) inference from
sample size can use rule-based
(10/1,000) system
Inaccessible to No explicit No explicit High degree of
conscious control consideration of consideration of cog control
base rates base rates
Evo Evo Evo Non-evo Non-evo

13. Predictive factors:
 Degree of cognitive control in probability
judgment
 More control = Bayesian inference in more contexts
 Cognitive operations that underlie estimates of
probability (only *more control* theories)
 Evolutionary & non-evolutionary frequency heuristics
depend on structural features of question
 Nested set does not depend on natural frequencies,
and instead predicts Bayesian inference when
problem structure is transparent (because it triggers
these elementary set operations)

14.  Academic selectivity of university
 Monetary incentive
“The former observation is consistent with the
view that Bayesian inference depends on domain
general cognitive processes to the degree that
intelligence is domain general. The latter
suggests that Bayesian inference is strategic, and
not supported by automatic (e.g., modularized)
reasoning processes.”
BUT: Money decreases performance on cog tasks…

15. Diagrammatic Representations!
48% got it

16. Idea: Bayesian inference with natural frequency
estimates depends on accurate encoding of
autobiographical events.
Really: If people are bad at remembering events
(e.g., # beers had past week), then we can’t be
Bayesian with natural frequency estimates.
Result: Our autobiographical memories are really,
really, really, really bad, so we “don’t have that
capacity.”

17.  What about hypotheses that are not
mutually exclusive and exhaustive (MECE)?
(“I eat cookies AND I eat them with milk”)
 What about non-independent events?
(“sweaty palms is symptomatic in 640 out of
800 patients have a disease, and 160 out of
200 patients without the disease”  80%
have symptom in both cases)

18. Partitioned data + prompt to use sample
category = best chance of proper calculation
 Understand question
 See underlying nested set structure by
partitioning data into subsets (to do
elementary set operations)
 Select pieces of evidence needed for solution

19. 1) Effects of intelligence and motivation support
the idea of domain general (vs. automatic,
modular) processes, supporting the nested sets
hypothesis

20. 2) Use of category instances and divide solution
into two parts of ratio facilitate proper
judgment, facilitation depends on cues to the set
structure (vs. natural frequencies)

21. 3) Frequency judgments come from fragmented
and incomplete inferential strategies

22. 4) People don’t accurately weigh and combine
priors, and use irrelevant info in calculations

23. 5) Nested set representations improve correct
calculation rates

24. 1. Effects of intelligence and motivation support the
idea of domain general (vs. automatic, modular)
processes, supporting the nested sets hypothesis
2. Since use of category instances and divide solution
into two parts of ratio facilitate proper
judgment, facilitation depends on cues to the set
structure (vs. natural frequencies)
3. Frequency judgments come from fragmented and
incomplete inferential strategies
4. People don’t accurately weigh and combine
priors, and use irrelevant info in calculations
5. Nested set representations improve correct
calculation rates

25.  “Cognitive algorithms, Bayesian or otherwise,
cannot be divorced from the information on which
they operate and how that information is
represented.” (Gaissmaier, et al.)
 Mind is prepared to interpret “ecologically
structured information” (Gigerenzer & Hoffrage)
 Perceptual system uses info through capacities for
pattern recognition (G & H)
 Require computational models of cognitive
processes to evaluate ecological rationality (G & H)

26.  Do people need to be able to explicitly solve
Bayesian problems to do them automatically?
 “Without formal training they will have no
access to the rules of Bayesian inference and
can therefore only attempt to use general-
purpose analytic reasoning procedures which
involve constructing and manipulating mental
models to represent the problem information”
(Evans & Elqayam)  does this explain the
education effect?

27. Frequencies (whole numbers) is better than rates
(percentages)
due to configuration of human brain in the
representation of sets and numbers
(Butterworth)
Automatic neural process of extracting numbers
from visible objects (Butter.)

28.  “We can find no evidence in the target article
for the authors’ assertion that base-rate
neglect is due to associative processing”
(Evans & Elqayam)
 Problem is really the failure to integrate base rate
and diagnostic info and weigh them equally
 B&S say: use System 2 = perfect!
 Response: basically, breast cancer is
associated with a mammogram (?)

29.  What about people revising their judgment in
light of new information? (Girotto &
Gonzales)
 Confusion of whether observed frequencies
are actually statements of expected or
observed probabilistic (“8 out of 10 women
with breast cancer will get a positive
mammography”) (Girotto & Gonzales)
 Heuristics can be good
(Gaissmaier, Straubinger, Funder)