A Descriptively Adequate Model of Conditional Reasoning Henrik Singmann Christoph Klauer Sieghard Beller Overview Singmann H amp Klauer K C 2011 Deductive and inductive conditional inferences Two modes of reasoning ID: 582061
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Slide1
Beyond Bayesian Updating: A Descriptively Adequate Model of Conditional Reasoning
Henrik SingmannChristoph KlauerSieghard BellerSlide2
OverviewSingmann, H., & Klauer, K. C. (2011). Deductive and inductive conditional inferences: Two modes of reasoning.
Thinking & Reasoning, 17(3), 247–281. http://doi.org/10.1080/13546783.2011.572718Singmann, H., Klauer, K. C. &
Beller, S. (under review). Probabilistic Conditional Reasoning: Disentangling Form and Content with the Dual-Source Model. Revised manuscript submitted for publication.Slide3
What is Reasoning
Reasoning is a "transition in thought, where some beliefs (or thoughts) provide the ground or reason for coming to another" (Adler
, 2008).Deductive Reasoning:The current prince will be the next king.Prince Charles is the current prince.
Therefore, Prince Charles will be the next king.Inductive Reasoning:The beer I have tasted in the UK so far was rather bland.Therefore, all British beer is bland.Irrational Reasoning:Too many immigrants coming to the UK.
Most of these immigrants are coming from outside the EU.
Therefore, the UK should leave the EU.Slide4
mortal
beings
Reasoning and Logic Syllogisms (Aristotle)
All men are mortal.
Socrates is a man.
Therefore, Socrates is mortal.
All men are mortal.
Socrates is
mortal.
Therefore, Socrates is
a man.
Set Interpretation
of
Syllogisms
men
SocratesSlide5
mortal
beings
Reasoning and Logic Syllogisms (Aristotle)
All men are mortal.
Socrates is a man.
Therefore, Socrates is mortal.
All men are mortal.
Socrates is
mortal.
Therefore, Socrates is
a man.
Set Interpretation
of
Syllogisms
men
SocratesSlide6
Reasoning and Logic
Syllogisms (Aristotle)All men are mortal.
Socrates is a man.Therefore, Socrates is mortal.All men are mortal.Socrates is mortal.
Therefore, Socrates is a man.Conditional Inferences
If
someone
is
human
then
she
is mortal.
Socrates is human.Therfore, Socrates is
mortal.If someone is human then she
is mortal
.Socrates is mortal.Therfore, Socrates
is human.Slide7
4 Conditional Inferences
Modus Ponens (MP):If p then
qpTherefore,
q
Modus Tollens (MT):
If
p
then
q
Not
q
Therefore
, not
p
Denial
of
the
antecedent
(DA):
If
p
then
q
Not
p
Therefore
, not
q
Affirmation
of
the
consequent
(AC):
If
p
then qqTherefore, pSlide8
4 Conditional Inferences
Modus Ponens (MP):If p then
qpTherefore, not
q
Modus Tollens (MT):
If
p
then
q
Not
q
Therefore
, not
p
Denial
of
the
antecedent
(DA):
If
p
then
q
Not
p
Therefore
, not
q
Affirmation
of
the
consequent
(AC):
If
p
then qqTherefore, not p
Logic
tells
us
how
people
should
reason
.
But
how
do
they
reason
?Slide9
Theories of Human Reasoning
Mental Rules/Logic (Inhelder & Piaget, 1958; Rips, 1994;
Stenning & van Lambalgen, 2008)Mental Model Theory (Johnson-Laird, 1983; Johnson-Laird & Byrne,
1991)Bayesian/Probabilistic Approach (Oaksford & Chater, 2007)
Suppositional
Theory
(Evans & Over, 2004)Slide10
Effect of Inference
MP (valid):
If a person fell into a swimming pool, then the person is wet.A person fell into a swimming pool.
How valid is the following conclusion from a logical perspective?The person is wet.
AC (invalid
)
:
If a person fell into a swimming pool, then the person is wet.
A person
is wet.
How valid is the following conclusion
from a logical
perspective?
The person
fell into a swimming pool.
Singmann &
Klauer
(2011,
Exp
. 2)Slide11
Effect of ContentMP (valid)
If a person fell into a swimming pool, then the person is wet.A person fell into a swimming pool.
Therefore, the person is wet.If a girl had sexual intercourse, then she is
pregnant.A girl had sexual intercourse.Therefore, the girl is pregnant.
AC (invalid)
If a person fell into a swimming pool, then the person is wet.
A person is wet
.
Therefore, the
person fell into a swimming
pool.
If
a girl had sexual intercourse, then she is pregnant.
A girl
is pregnant.
Therefore, the girl had sexual intercourse.
prological
counterlogicalSlide12
Effect of ContentMP (valid)
If a person fell into a swimming pool, then the person is wet.A person fell into a swimming pool.
Therefore, the person is wet.If a girl had sexual intercourse, then she is
pregnant.A girl had sexual intercourse.Therefore, the girl is pregnant.
AC (invalid)
If a person fell into a swimming pool, then the person is wet.
A person is wet
.
Therefore, the
person fell into a swimming
pool.
If
a girl had sexual intercourse, then she is pregnant.
A girl
is pregnant.
Therefore, the girl had sexual intercourse.
prological
counterlogicalSlide13
Effect of InstructionMP (valid)
If a person fell into a swimming pool, then the person is wet.
A person fell into a swimming pool.How valid is it that the person is wet?
If a person fell into a swimming pool, then the person is wet.A person fell into a swimming pool.How likely is it that the person is wet?
AC (invalid)
If a person fell into a swimming pool, then the person is wet.
A person is wet.
How
valid
is it that the person fell into a swimming pool?
If a person fell into a swimming pool, then the person is wet.
A person is wet.
How
likely
is it that the person fell into a swimming pool?
deductive
probabilisticSlide14
Effect of InstructionMP (valid)
If a person fell into a swimming pool, then the person is wet.
A person fell into a swimming pool.How valid is it that the person is wet?
If a person fell into a swimming pool, then the person is wet.A person fell into a swimming pool.How likely is it that the person is wet?
AC (invalid)
If a person fell into a swimming pool, then the person is wet.
A person is wet.
How
valid
is it that the person fell into a swimming pool?
If a person fell into a swimming pool, then the person is wet.
A person is wet.
How
likely
is it that the person fell into a swimming pool?
deductive
probabilisticSlide15
Mental Rules/
Logic (
Inhelder & Piaget, 1958; Rips, 1994 ; Stenning & van Lambalgen
, 2008)Mental Model Theory (Johnson-Laird, 1983; Johnson-Laird & Byrne, 1991)Bayesian
/
Probabilistic
Approach (
Oaksford
&
Chater
, 2007)
Suppositional
Theory
(Evans & Over, 2004)Theories of Human
Reasoning
Klauer & Singmann (2011):At least two
processes contribute
to reasoning.Single
process theories (e.g., Mental Models; Bayesian
approaches
)
cannot
explain
both
,
deductive
and
probabilistic
reasoning
. Slide16
4 Conditional Inferences
Modus Ponens (MP):If p then
qpTherefore,
q
Modus Tollens (MT):
If
p
then
q
Not
q
Therefore, not
p
Denial of the
antecedent (DA):
If p then q
Not pTherefore, not q
Affirmation
of
the
consequent
(AC):
If
p
then
q
q
Therefore
,
pSlide17
Probabilistic Model
3 free parameters
Provides conditional probabilities/predictions:P(MP) = P(q|
p) = P(p q) / P(p)P(MT)
= P
(
¬
p
|
¬
q
)
= P
(
¬p ¬q) / P
(¬q)P(AC) = P(p
|q) = P(p q) / P(q)
P(DA) = P(¬
q|¬p) = P(¬p
¬q) / P(
¬
p
)
Inference
MP
MT
AC
DA
p
→
q
p
q
p
→
q
¬
q
¬
p
p
→
q
q
p
p → q¬p
¬qResponse reflectsP(q
|p)P(¬p|
¬
q
)
P(
p
|
q
)
P(¬
q|
¬
p
)
Oaksford
,
Chater
, & Larkin (2000)
Oaksford
&
Chater
(2007)
Joint
probability
distribution
q
¬
q
p
P(
p
q
)
P(
p
¬
q
)
¬p
P(
¬
p
q
)
P(
¬
p
¬
q
)Slide18
Probabilistic Model
3 free parameters
Provides conditional probabilities/predictions:P(MP) = P(q|
p) = P(p q) / P(p)P(MT)
= P
(
¬
p
|
¬
q
)
= P
(
¬p ¬q) / P
(¬q)P(AC) = P(p
|q) = P(p q) / P(q)
P(DA) = P(¬
q|¬p) = P(¬p
¬q) / P(
¬
p
)
Inference
MP
MT
AC
DA
p
→
q
p
q
p
→
q
¬
q
¬
p
p
→
q
q
p
p →
q¬p ¬
q
Response
reflects
P(
q
|
p
)
P(¬
p|
¬
q
)
P(
p
|
q
)
P(¬
q|
¬
p
)
Oaksford
,
Chater
, & Larkin (2000)
Oaksford
&
Chater
(2007)
Joint
probability
distribution
q
¬
q
p
P(
p
q
)
P(
p
¬
q
)
¬p
P(
¬
p
q
)
P(
¬
p
¬
q
)Slide19
Effect of Conditional
If a girl had sexual intercourse, then she is pregnant.A girl had sexual intercourse.
How likely is it that the girl is pregnant?
Full Inferences (Week 2)If a girl had sexual intercourse, then she is pregnant.A girl had sexual intercourse.
How likely is it that the girl is pregnant?
Reduced Inferences (Week 1)
Klauer
, Beller, & Hütter (
2010,
Exp
. 1) Slide20
Effect of Conditional
Data:Conditional increases endorsement.Validity effect: Stronger increase for valid (MP & MT) than invalid (AC & DA)
inferences.Bayesian Model (Oaksford & Chater, 2007):
Conditional changes background knowledge.Probability distribution updates given conditional.Dual-Source Model (Klauer et al., 2010):Background knowledge determines responses for reduced inferences: Bayesian ReasoningConditional provides form-based information.Responses to full inferences reflect mixture of knowledge and form information.Slide21
Dual-Source Model (DSM)
knowledge-based
form-
based
C
=
content
(
one
for
each
p and q
)x = inference (MP, MT, AC, & DA)
Exp. 1: validate
Exp. 2: validate
Singmann, Klauer, & Beller (under review)Slide22
Reduced Inferences (Week 1)
If a girl had sexual intercourse, then she is pregnant.
A girl had sexual intercourse.
How likely is it that the girl is pregnant?
Exp. 1: Manipulating Form
Conditional Inferences (Week 2/3)
If a girl had sexual intercourse, then she is pregnant.
A girl had sexual intercourse.
How likely is it that the girl is pregnant?
Biconditional Inferences (Week 2/3)
If a girl had sexual intercourse, then and only then she is pregnant.
A girl had sexual intercourse.
How likely is it that the girl is pregnant?
4 different conditionals
4 inferences (MP, MT, AC, DA) per conditional
N = 31Slide23
Reduced Inferences (Week 1)
If a girl had sexual intercourse, then she is pregnant.
A girl had sexual intercourse.
How likely is it that the girl is pregnant?
Exp. 1: Manipulating Form
Conditional Inferences (Week 2/3)
If a girl had sexual intercourse, then she is pregnant.
A girl had sexual intercourse.
How likely is it that the girl is pregnant?
Biconditional Inferences (Week 2/3)
If a girl had sexual intercourse, then and only then she is pregnant.
A girl had sexual intercourse.
How likely is it that the girl is pregnant?
4 different conditionals
4 inferences (MP, MT, AC, DA) per conditional
N = 31Slide24
Reduced Inferences (Week 1)
If a girl had sexual intercourse, then she is pregnant.
A girl had sexual intercourse.
How likely is it that the girl is pregnant?
Exp. 1: Manipulating Form
Conditional Inferences (Week 2/3)
If a girl had sexual intercourse, then she is pregnant.
A girl had sexual intercourse.
How likely is it that the girl is pregnant?
Biconditional Inferences (Week 2/3)
If a girl had sexual intercourse, then and only then she is pregnant.
A girl had sexual intercourse.
How likely is it that the girl is pregnant?
4 different conditionals
4 inferences (MP, MT, AC, DA) per conditional
N = 31
ns
.
***Slide25
Reduced Inferences (Week 1)
If a girl had sexual intercourse, then she is pregnant.
Anne eats a lot of parsley
.
How likely is it that
the level of iron in her blood will increase
?
Exp.
2: Manipulating Expertise
Full Inferences,
Expert
(Week 2)
A
nutrition scientist
says: If Anne eats a lot of parsley then the level of iron in her blood
will increase
.
Anne eats a lot of parsley.
How likely is it that the level of iron in her blood will increase?
Full Inferences, N
on-Expert
(Week 2)
A
drugstore clerk
says
: If Anne eats a lot of parsley then the level of iron in her blood will increase.
Anne eats a lot of parsley.
How likely is it that the level of iron in her blood will increase?
6 different conditionals
3 expert
3 non-
exprt
4 inferences (MP, MT, AC, DA) per conditional
N = 47
orSlide26
Reduced Inferences (Week 1)
If a girl had sexual intercourse, then she is pregnant.
Anne eats a lot of parsley
.
How likely is it that
the level of iron in her blood will increase
?
Exp.
2: Manipulating Expertise
Full Inferences,
Expert
(Week 2)
A
nutrition scientist
says: If Anne eats a lot of parsley then the level of iron in her blood
will increase
.
Anne eats a lot of parsley.
How likely is it that the level of iron in her blood will increase?
Full Inferences, N
on-Expert
(Week 2)
A
drugstore clerk
says
: If Anne eats a lot of parsley then the level of iron in her blood will increase.
Anne eats a lot of parsley.
How likely is it that the level of iron in her blood will increase?
6 different conditionals
3 expert
3 non-
exprt
4 inferences (MP, MT, AC, DA) per conditional
N = 47
orSlide27
Reduced Inferences (Week 1)
If a girl had sexual intercourse, then she is pregnant.
Anne eats a lot of parsley
.
How likely is it that
the level of iron in her blood will increase
?
Exp.
2: Manipulating Expertise
Full Inferences,
Expert
(Week 2)
A
nutrition scientist
says: If Anne eats a lot of parsley then the level of iron in her blood
will increase
.
Anne eats a lot of parsley.
How likely is it that the level of iron in her blood will increase?
Full Inferences, N
on-Expert
(Week 2)
A
drugstore clerk
says
: If Anne eats a lot of parsley then the level of iron in her blood will increase.
Anne eats a lot of parsley.
How likely is it that the level of iron in her blood will increase?
6 different conditionals
3 expert
3 non-
exprt
4 inferences (MP, MT, AC, DA) per conditional
N = 47
or
ns
.
*Slide28
Dual-Source Model (DSM)
knowledge-based
form-
based
C
=
content
(
one
for
each
p and q
)x = inference (MP, MT, AC, & DA)
Exp. 1: validate
Exp. 2: validate
Singmann, Klauer, & Beller (under review)
Oaksford
&
Chater
, …Slide29
Reduced Inferences (Week 1)
If a girl had sexual intercourse, then she is pregnant.
A girl had sexual intercourse.
How likely is it that the girl is pregnant?
Bayesian Updating
Full Inferences (Week 2)
If a girl had sexual intercourse, then she is pregnant.
A girl had sexual intercourse.
How likely is it that the girl is pregnant?
Joint
probability
distribution
:
g
q
¬
q
p
P(
p
q
)
P(
p
¬
q
)
¬p
P(
¬
p
q
)
P(
¬
p
¬
q
)
Updated
joint
probability
distribution
:
g'
q'
¬
q'
p'
P(
p'
q'
)
P(
p'
¬
q'
)
¬p'
P(
¬
p'
q'
)
P(
¬
p'
¬
q'
)
?
Role of conditional in Bayesian models:
PROB
: increases probability of conditional, P(
q
|
p
) (
Oaksford
et al., 2000)
EX-PROB
: increases probability of conditional P
MP
(
q
|
p
) > P
other
(
q
|
p
) (
Oaksford
&
Chater
, 2007)
KL
: increases P(
q
|
p
) &
Kullback-Leibler
distance between
g
and
g
'
is minimal (Hartmann &
Rafiee
Rad, 2012)Slide30
Meta-ANalysis7
data sets (Klauer et al., 2010; Singmann et al., under
review)total N = 179reduced and
full conditional inferences onlyno additional
manipulations
each
model
fitted
to
data
of each individual participant
.
17.3
17.7
17.7
22.1
mean
free
parameters
:Slide31
Effect of InstructionMP (valid)
If a person fell into a swimming pool, then the person is wet.
A person fell into a swimming pool.How valid is it that the person is wet?
If a person fell into a swimming pool, then the person is wet.A person fell into a swimming pool.How likely is it that the person is wet?
AC (invalid)
If a person fell into a swimming pool, then the person is wet.
A person is wet.
How
valid
is it that the person fell into a swimming pool?
If a person fell into a swimming pool, then the person is wet.
A person is wet.
How
likely
is it that the person fell into a swimming pool?
deductive
probabilistic
Singmann & Klauer (2010, Exp. 2)Slide32
Dual-Source Model (DSM)
knowledge-based
form-
based
C
=
content
(
one
for
each
p
and q)
x = inference (MP, MT, AC, & DA)probabilistic
knowledge-based
form-
based
deductiveSlide33
Effect of InstructionMP (valid)
If a person fell into a swimming pool, then the person is wet.
A person fell into a swimming pool.How valid is it that the person is wet?
If a person fell into a swimming pool, then the person is wet.A person fell into a swimming pool.How likely is it that the person is wet?
AC (invalid)
If a person fell into a swimming pool, then the person is wet.
A person is wet.
How
valid
is it that the person fell into a swimming pool?
If a person fell into a swimming pool, then the person is wet.
A person is wet.
How
likely
is it that the person fell into a swimming pool?
deductive
probabilistic
R
2
=.95
24 data points
15 free parameters (9
ξ
, 4
τ
, 2
λ
)
τ
(MP) = 1.00,
τ
(AC) = .46
λ
p
= .45,
λ
d
= .64Slide34
SummarySingle process theories not able to account for full pattern of conditional inferences.
Bayesian updating does not seem to explain effect of conditional.Probability theory cannot function as wholesale replacement for logic as
computational-level theory of what inferences people should draw (cf. Chater & Oaksford, 2001
).DSM adequately describes probabilistic conditional reasoning:When formal structure absent, reasoning purely Bayesian (i.e., based on background knowledge only).Formal structure provides reasoners with additional information about quality of inference (i.e., degree to which inference is seen as logically warranted).Responses to full inferences reflect weighted mixture of Bayesian knowledge-based component and form-based component.
DSM useful and parsimonious measurement model.Slide35
That was allSlide36
Baseline Condition
If
a balloon is pricked with a needle then it will quickly lose air
.
A balloon is pricked with a needle.
How likely is it that
the
balloon quickly looses air?
Suppression Effects: MP
Disablers Condition
If a balloon is pricked with a needle then it will quickly lose
air.
If
a balloon is inflated to begin with then it will quickly lose air.
A balloon is pricked with a needle.
How likely is it that the balloon quickly looses air?
Alternatives Condition
If a balloon is pricked with a needle then it will quickly lose air.
If a balloon is
pricked with a knife then
it will quickly lose air.
A balloon is pricked with a needle.
How likely is it that the balloon quickly looses air?
Additional disablers reduce endorsement to MP and MT.
Additional
alternatives do not affect endorsement to MP and MT.
Byrne (1989)Slide37
Baseline Condition
If
a balloon is pricked with a needle then it will quickly lose air
.
A balloon quickly looses air.
How likely is it that
the
balloon was pricked with a needle?
Suppression Effects: AC
Disablers Condition
If a balloon is pricked with a needle then it will quickly lose
air.
If
a balloon is inflated to begin with then it will quickly lose air.
A balloon quickly looses air.
How likely is it that the balloon was pricked with a needle?
Alternatives Condition
If a balloon is pricked with a needle then it will quickly lose air.
If a balloon is
pricked with a knife then
it will quickly lose air.
A balloon quickly looses air.
How likely is it that the balloon was pricked with a needle
?
Additional disablers do not affect endorsement to AC and DA.
Additional
alternatives reduce endorsement to AC and DA.
Byrne (1989)Slide38
Full Baseline Condition
If
a balloon is pricked with a needle then it will quickly lose air
.
A balloon is pricked with a needle.
How likely is it that
the
balloon quickly looses air?
Reduced Baseline Condition
If a balloon is pricked with a needle then it will quickly lose air.
A balloon is pricked with a needle.
How likely is it that
the
balloon quickly looses air?
Exp. 3: Procedure
Full Disablers Condition
If a balloon is pricked with a needle then it will quickly lose
air.
If
a balloon is inflated to begin with then it will quickly lose air.
A balloon is pricked with a needle.
How likely is it that the balloon quickly looses air?
Full Alternatives Condition
If a balloon is pricked with a needle then it will quickly lose air.
If a balloon is
pricked with a knife then
it will quickly lose air.
A balloon is pricked with a needle.
How likely is it that the balloon quickly looses air?
Reduced Disablers Condition
If a balloon is pricked with a needle then it will quickly lose
air.
If
a balloon is inflated to begin with then it will quickly lose air.
A balloon is pricked with a needle.
How likely is it that the balloon quickly looses air?
Reduced Alternatives Condition
If a balloon is pricked with a needle then it will quickly lose air.
If a balloon is
pricked with a knife then
it will quickly lose air.
A balloon is pricked with a needle.
How likely is it that the balloon quickly looses air?Slide39
Exp. 3: Disabling Condition
If a person drinks a lot of coke then the person will gain weight.A person drinks a lot of coke.
How likely is it that the person will gain weight?Please note:A
person only gains weight ifthe metabolism of the person permits it,the person does not exercise as a compensation,the person does not only drink diet coke.
Full Inferences (Week 2)
If a person drinks a lot of coke then the person will gain weight.
A person drinks a lot of coke.
How likely is it that the person will gain weight?
Please note:
A person only gains weight if
the metabolism of the person permits it,
the person does not exercise as a compensation,
the person does not only drink diet coke.
Reduced Inferences (Week 1)
Total N: 167Slide40
Exp. 3: Disabling Condition
If a person drinks a lot of coke then the person will gain weight.A person drinks a lot of coke.
How likely is it that the person will gain weight?Please note:A
person only gains weight ifthe metabolism of the person permits it,the person does not exercise as a compensation,the person does not only drink diet coke.
Full Inferences (Week 2)
If a person drinks a lot of coke then the person will gain weight.
A person drinks a lot of coke.
How likely is it that the person will gain weight?
Please note:
A person only gains weight if
the metabolism of the person permits it,
the person does not exercise as a compensation,
the person does not only drink diet coke.
Reduced Inferences (Week 1)
Total N: 167Slide41
Exp. 3: Disabling Condition
If a person drinks a lot of coke then the person will gain weight.A person drinks a lot of coke.
How likely is it that the person will gain weight?Please note:A
person only gains weight ifthe metabolism of the person permits it,the person does not exercise as a compensation,the person does not only drink diet coke.
Full Inferences (Week 2)
If a person drinks a lot of coke then the person will gain weight.
A person drinks a lot of coke.
How likely is it that the person will gain weight?
Please note:
A person only gains weight if
the metabolism of the person permits it,
the person does not exercise as a compensation,
the person does not only drink diet coke.
Reduced Inferences (Week 1)
Total N: 167
***
**
*
***
***
***Slide42
Suppression Effects in Reasoning
In line with formal accounts: Disablers and alternatives suppress form-based evidence for „attacked“ inferences.In line with probabilistic accounts: Alternatives (and to lesser degree disablers)
decreased the knowledge-based support of the attacked inferences.Difference suggests that disablers are automatically considered, but not alternatives: neglect of alternatives in causal Bayesian reasoning (e.g., Fernbach &
Erb, 2013).Only disablers discredit conditional (in line with pragmatic accounts, e.g., Bonnefon & Politzer, 2010)Slide43
That was allSlide44
Formal Account of Uncertain Reasoning
Pfeifer and Kleiter’s (2005; 2010)
mental probability logicInferences should be probabilistically coherent: estimated probabilities agree with known/fixed probabilities according to elementary probability theory
.Missing/unkown probabilities in [0, 1]
→
responses
should
lie
in
predicted
intervalE.g., MP: P(q) = [
P(q|p)P(
p) , P(q|p)P(p) + (1 - P(p
)) ]Example:
If car ownership increases then traffic congestion will get worse. (P = 0.8)Car ownership increases. (P = 0.95)
Under these premises, how probable is that traffic congestion will get worse?
[
.
80 × .
95 , .
80 × .95 + (1 - .95
) ] = [ .76 , .81 ]Slide45
Formal Account of Probabilistic Reasoning
Probabilized
conditional reasoning task: all premises
uncertainOnly highly believable conditionals (Evans et al., 2010
), e.g.,
If car ownership increases then traffic congestion will get worse.
If jungle deforestation continues then Gorillas will become extinct
.
Two
phase
experiment
:
Participants
provide estimates of premises
directly and independently.Participants estimate
probably of
conclusion, while estimates (
1.) are presented.Slide46
Example ItemIf car ownership increases then traffic congestion will get worse.
(Probability 80%)Car ownership increases.(Probability 95%)
Under these premises, how probable is that traffic congestion will get worse?
XSlide47
Replicating
main finding
from research on deductive reasoning:
Individuals
do not
reason
according
to
probabilistic
norms.