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Summary 2.1 Problem 7: When Logics Die
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Notes (summary + class notes) of problem 7 from course 2.1: Thinking & Remembering.
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2.1 Problem 7: When Logics DieEysenck: Ch.13:
Judgment = involves deciding on the likelihood of various events using incomplete info,
e.g., using info about your previous examination performance to judge probability you will
succeed in your next examination. What matters in judgment is accuracy
Decision-making = involves selecting one option from several possibilities, e.g., deciding
which university to attend. Factors involved in decision-making depend on importance of
decision (processes involved in deciding on career path are more complex than deciding what
to drink).
- We assess decision quality in terms of consequences – a decision can be good given
in the info available at the time, even if its consequences are poor
- Judgment forms important initial part of decision-making process, e.g., when deciding
what car to buy, judging how often you’re going to use it, etc.
Judgment Research
Bayesian inference: focused on situations where there are 2 possible subjective
beliefs/hypotheses (e.g., X is lying vs. X is not lying), and showed how new data/info
changes the subjective probabilities of each hypothesis being correct
Initial beliefs get modified by incoming info – strength of info increases/decreases based on
info you get
According to Bayes’ theorem, we need to evaluate beliefs concerning the relative
probabilities of these 2 hypotheses before the data are obtained (prior odds/beliefs). We also
need to calculate the relative probabilities of obtaining the observed data under each
hypothesis (likelihood ratio). Bayesian methods evaluate probability of observing data, D, if
hypothesis A is correct, written p(D/HA), and if hypothesis B is correct, p(D/HB).
On the right side, there’s the prior odds of each hypothesis being correct before data was
collected, multiplied by likelihood ratio based on probability of data given each hypothesis
Kahneman & Tversky’s taxi-cab problem (base rate)
- Cab was involved in accident one night
- Of the city’s cabs, 85% belonged to Green company, 15% belonged to Blue company
- Eyewitness identified cab as Blue cab. But when her ability to identify cabs under
similar visibility conditions was tested, she was wrong 20% of the time. What is the
probability that the cab was Blue?
, - Hypothesis for cab was blue is HA, hypothesis it was green is HB. Probability for HA
is .15, probability for HB was .85
- Probability of eyewitness identifying cab as Blue when it was Blue = p(D/HA) is .80
Probability of eyewitness identifying cab as Blue when it was Green = p(D/HB)
is .20.
- According to formula:
So, odds ratio is 12:17, and there is 41% chance the taxi cab was Blue.
Neglecting Base Rates
- Bayes: when making judgments, we should take base-rate info into account ( =
relative frequency of an event within a given population)
However, this info is often ignored, e.g., taxi-cab problem; most people ignore base-
rate info about relative numbers of Green & Blue cabs
- Kahneman & Tvesky: lawyer-engineer problem
One group of participants told that 70 descriptions were of engineers, 30 of lawyers,
other group was told that 70 descriptions were of lawyers, 30 of engineers.
Participants decided there was a .90 probability Jack was engineer, regardless of
condition – they ignored base-rate info
Heuristics
- Heuristics = rules of thumb, ‘strategies that ignore part of the info, with the goal of
making decisions more quickly than complex methods’
- Heuristics often reduce effort associated w/cognitive tasks
Representativeness heuristic = involves deciding something belongs to a category
because it appears typical/representative of that category. E.g., Jack’s description seems
more typical/representative of engineer
Heeding Base Rates
- Sometimes people use base-rate info, e.g., engineer-lawyer problem: when majority of
sample were engineers, guess that statement was from engineer was higher
- Participants often use based-rate info irrelevant to judgment task
Krynski & Tenenbaum: false-positive scenario
Women at age 60 who participate in routine mammogram screening:
2% of women have breast cancer at time of screening, most of them will receive
positive result on mammogram
, There is a 6% chance that a woman without breast cancer will receive a positive result
on the mammogram
If a woman age 60 gets positive result during mammogram, what are the chances she has
breast cancer?
- Base rate of cancer in population often ignored by participants given this task. This
may have happened bc breast cancer is the only cause of positive mammograms
explicitly mentioned
- If problem was reworded slightly to indicate alternative cause of positive
mammograms, e.g.: ‘there is a 6% chance that a woman without breast cancer will
have a dense but harmless cyst that looks like a cancerous tumour, and causes a
positive result on the mammogram
Participants given this scenario were more likely to take base-rate info into account
rather than those given false-positive scenario
- People also use base-rate info when strongly motivated to do so
Availability Heuristic
- Frequencies of events can be estimated by how easy/hard it is to retrieve them from
LTM
- Lichtenstein: asked people to judge relative likelihood of different causes of death.
Those attracting much publicity (e.g., murder) were judged more likely than those that
do not (e.g., suicide) even when the opposite was the case
- Pachur: we can explain people’s judged frequencies of various causes of death in 3
ways:
1) They may use an availability heuristic based on their own direct experience
2) They may use an availability heuristic based on media coverage of causes of death
+ their own experience
3) They may use affect heuristic: feeling of dread of one is higher than other
Pachur: availability based on recall of direct experiences was best predictor of judged
frequencies of different causes of death. Judged risks (dread) also predicted by
availability heuristic. Availability based on media coverage was least successful
predictor
From left to right:
1) Affect heuristic
(overall dread
score)
2) Affect heuristic
(single dread
item)
3) Availability-by-
recall (direct
experience)
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