causal cognition 2: reasoning david lagnado university college london

Causal Cognition 2: Causal Cognition 2: reasoningreasoning

David LagnadoDavid LagnadoUniversity College London

Causal models in reasoningCausal models in reasoning

How are causal models used?How are causal models used?– Probability judgments Probability judgments – Inductive and counterfactual reasoning Inductive and counterfactual reasoning – Categorization Categorization – Evidential and legal reasoning Evidential and legal reasoning – Decision making Decision making – Attributions of responsibility Attributions of responsibility

Probability judgment

People better at causal than probabilistic reasoning

Use prior causal models to generate probability judgments (via mental simulation)

Neat fit between causal model and probability judgments facilitates probabilistic reasoning

Medical diagnosis problem

The probability of breast cancer is 1% for a woman at age forty who participates in routine screening. If a woman has breast cancer, the probability is 80% that she will get a positive mammography. If a woman does not have breast cancer, the probability is 9.6% that she will also get a positive mammography. A woman in this age group had a positive mammography in a routine screening.

What is the probability that she actually has breast cancer? __ %7.8

Empirical Results

Eddy (1982)– 95% of doctors gave answers around 75%!– Only 5% gave correct answer

Casscells et al. (1978) – Only 18% gave correct answer

Most responses close to 80% = P(+ve test|cancer)

Replicated numerous times

Correct Bayesian solution

– P(D) = .01; P(¬D) = .99– P(T+|D) = .8– P(T+|¬D) = .096

)().|()().|(

)().()(

DPDTPDPDTP

DP|DTP =D|TP

99.*096.01.*8.

01.*8.)(

=D|TP

078.0)( =D|TP

Standard account: Attribute substitution

Computation of P(cancer|+ve test) is hard Substitute with a readily accessible value

P(+ve test|cancer) Hence majority respond 80% More generally, tendency to confuse P(A|B)

with P(B|A)? (or assume that they are equivalent)

Cf. Prosecutor’s fallacy– Confuse P(DNA match | not gulity) with P(Not guilty |

DNA match)– Ignore prior of guilt

Causal account

Causal framework for judgments (Krynski & Tenenbaum, 2007)

– People fail in standard MDT because they construct a causal model that doesn’t readily accommodate the false-positive statistic P(+test|¬cancer)

Cancer

+ve Test Result

Step 1. Model construction

Causal account

Cancer

+ve Test Result

Step 2. Parameter assignment

P(cancer) = 1%

P(+test|cancer) = 80%

P(+test|¬cancer) = 10%

Does not fit into model

Causal account

Cancer

+ve Test Result

Step 3. Bayesian inference

P(cancer) = 1%

P(+test|cancer) = 80%

Typical answers neglects the base-rate

P(cancer|+test) = 80% or

= 1 – (+test|¬cancer) = 90%

Causal account

Benign cyst scenario 1% of women had breast cancer Of those with breast cancer, 80% received a +ve test result 30% of women had a benign cyst Of those with a benign cyst, 50% received a +ve test result All others received a –ve result

Cancer

+ve Test Result

Step 1. Model construction

Cyst

Causal account

Benign cyst scenario 1% of women had breast cancer Of those with breast cancer, 80% received a +ve test result 30% of women had a benign cyst Of those with a benign cyst, 50% received a +ve test result All others received a –ve result

Cancer

+ve Test Result

Cyst

Step 2. Parameter assignment

P(cancer) = 1%P(cyst) = 30%

P(+test|cancer) = 80% P(+test|cyst) = 50%

Results

Benign cyst vs. false positive scenarios– Correct responses 43% vs 16%– Base-rate neglect 4% vs 28%

Before inference people construct causal models, and need to fit parameter values to these models

The Benign cyst scenario facilitates this, whereas the false positive scenario inhibits it

Extension to other areas of probability judgment?

Asymmetry in inference– Easier to predict effects from causes than vice-

versa (in latter case need to consider alternative causes, and use Bayes rule)

General tendency to see evidence for causal mechanisms in random data– Hot-hand fallacy – Gambler’s fallacy (chance as a self-correcting

process) Cascaded inference

Counterfactual reasoningCounterfactual reasoning

Close link between causal and counterfactual Close link between causal and counterfactual thinkingthinking

Psychological accounts of counterfactual Psychological accounts of counterfactual reasoningreasoning– Mental logicMental logic– Mental models (Mental models (Johnson-Laird, 2001)– Both suppose that X causes Y closely tied to ‘If X,

then Y’ as material implication– Mental simulation (Kahneman et al.)

CBNs offer formal approach to answering CBNs offer formal approach to answering counterfactuals (counterfactuals (Pearl, 2000)Pearl, 2000)

Suppose that DSuppose that D Would D still have occurred, if A hadn’t fired?Would D still have occurred, if A hadn’t fired?

Firing squad Firing squad (deterministic case)(deterministic case)

C Captai

n

C Captai

n

A fires

A fires

B fires

B fires

Dead

Dead

U court order

U court order

Blue = Unknown

Blue = Unknown


AbductionAbduction Update beliefs on evidence D Update beliefs on evidence D

– D therefore A or B; therefore C; therefore U, A and B D therefore A or B; therefore C; therefore U, A and B

C Captai

n

C Captai

n

A fires

A fires

B fires

B fires

Dead

Dead

U court order

U court order

Green = TRUE

Green = TRUE


Action Action – Do (not-A)Do (not-A)– Set A to false; remove other links into A (graph surgery)Set A to false; remove other links into A (graph surgery)– Re-set all variables to unknown except U Re-set all variables to unknown except U

C Captai

n

C Captai

n

A fires

A fires

B fires

B fires

Dead

Dead

U court order

U court order

A fires

A fires


C Captai

n

C Captai

n

A fires

A fires

B fires

B fires

Dead

Dead

U court order

U court order

A fires

A fires

InferenceInference U is true; therefore C; therefore B; therefore DU is true; therefore C; therefore B; therefore D


C Captai

n

C Captai

n

A fires

A fires

B fires

B fires

Dead

Dead

U court order

U court order

A fires

A fires

Inference --- Inference --- D is still trueD is still true

Would D still have occurred, if A hadn’t fired?Would D still have occurred, if A hadn’t fired? Experimental study (Sloman & Lagnado, 2005) Experimental study (Sloman & Lagnado, 2005) 80% subjects say ‘yes’ 80% subjects say ‘yes’

Causal reasoning Causal reasoning

People’s counterfactual inferences obey People’s counterfactual inferences obey ‘undoing’‘undoing’

Especially with causal scenariosEspecially with causal scenarios Extended to probabilistic causationExtended to probabilistic causation Not explained on other theories of Not explained on other theories of

reasoning (mental logic, mental model reasoning (mental logic, mental model theory, probabilistic models)theory, probabilistic models)

Requires logic of causality (do-calculus)Requires logic of causality (do-calculus)

Decision makingDecision making

Importance of causal models in decision Importance of causal models in decision making (Sloman & Hagmayer, 2006) making (Sloman & Hagmayer, 2006) – Choose action that maximizes Choose action that maximizes expectedexpected utility utility– Probability of outcome given that you Probability of outcome given that you dodo action action

AA Construct a causal model of decision Construct a causal model of decision

situationsituation Use interventional probabilitiesUse interventional probabilities

Recent research has shown that of 100 men who help with the chores, 82 are in good health whereas only 32 of 100 men who do not help with the chores are. Imagine a friend of yours is married and is concerned about his health. He reads about the research and asks for your advice on whether he should start to do chores or not to improve his health. What is your recommendation?

Different possible models to explain correlation between chores and health

Subjects told either:

Chores Health

Direct cause – doing chores is additional exercise each day

Common cause – men concerned with equality issues also concerned with health issue

Chores Health

PC man

Do chores: 69% 23%

Evidential reasoning How do people reason with uncertain

evidence? How do they assess and combine

different items of evidence?– What representations do they use?– What inference processes?

How do these compare with normative theories?

Reasoning with legal evidence

Legal domain– E.g. juror, judge, investigator, media

Complex bodies of interrelated evidence– Forensic evidence; eyewitness testimony;

alibis; confessions etc Need to integrate wide variety of

evidence to reach conclusions (e.g. guilt of suspect)

Descriptive models of juror reasoning

Belief adjustment model – Hogarth & Einhorn, 1992

Story model– Pennington & Hastie, 1986, 1992

Coherence-based models– Simon, 2007; Simon & Holyoak, 2002;

Thagard, 2000

Belief adjustment model

Online judgments formed by adjusting from a prior anchor

Over-weights later items Can lead to order effects Ignores causal relations between

items of evidence

Innocent

Guilty

DECISION

Beyond reasonable doubt > C

Initial Opinion Anchor S

Innocent

Guilty

Background knowledge and assumptions

Judge’s instructions on presumption of innocence

New Evidence Item

Belief AdjustmentProcess S*

Innocent

Guilty

Trial events

(witnesses, exhibits, arguments)

Compare

S* vs Criterion C Decisio

n criterion C to convict

Utility Evaluation of decisions

Judge’s instructions on the standard of proof

Severity of the crime etc.

Belief adjustment model

Belief Adjustment algorithm Jack accused of murdering Ian

Background: Jack found out that Ian was having an affair with his girlfriend

Start with initial anchor (based on background story)

S0

Prosecution witness:

Ex-girlfriend says Jack is violent

Evidence encoded as +ve or –ve Weighted according to credibility of source

+ w1.e1

S2 = S1 - w2.e2

S1 = S0 + w1.e1 Added to anchor

Defence witness:

Sister says Jack is pacifist- w2.e2

Continue

Evidence for BAM (Hogarth & Einhorn, 1992)

Order effects when evidence is processed item-by-item Recency - over-weight final item

Jack rated more guilty with order 2

Jack accused of murdering Ian

Background: Jack found out that Ian was having an affair with his girlfriend


Ex-girlfriend says Jack is violent

Order 1

Defence witness:

Sister says Jack is pacifist

Order 2


Ex-girlfriend says Jack is violentDefence witness:

Sister says Jack is pacifist

Problems Does not capture full extent of

human reasoning– Does not address interrelations between

evidence items – Treats each item as independent– No re-evaluation of earlier items of

evidence in the light of new evidence

Story model

Evidence evaluated through story construction Stories involve network of causal relations

between events Causal narratives not arguments

– People represent events in the world, not inference process

Stories constructed prior to judgment or decision

Stories determine verdicts, and are not post hoc justifications

a) Evidence evaluation through story construction

b) Representation of possible verdicts

c) Decision by classifying best story into one verdict category

Likely to be considerable interplay between these 3 stages

Constructing a story Jurors impose a narrative structure on

trial information Engage in an active constructive

process ‘Sense-making’ by organizing

information into compelling story Heavy use of causality

– Physical– mental

Example scenario (Pennington & Hastie, 1988)

3 hour video-taped re-enactment of a criminal trial The defendant, Johnson, was charged with stabbing

another man, Caldwell, to death in a bar-room fight. Mock jurors provided with large amount of evidence

1 The first witness is a police officer: Sergeant Robert Harris2 I was on my usual foot patrol at 9:00 p.m.3 I heard loud voices from the direction of Gleason's Bar4 Johnson and Caldwell were outside the bar5 Johnson laughed at Caldwell6 Caldwell punched Johnson in the face7 Johnson raised a knife over his head8 I yelled, "Johnson, don't do it"9 Johnson stabbed Caldwell in the chest … (over 80 items)

Must decide between verdicts of guilty (of murder) or not guilty (self-defence)

Jurors’ story models elicited via think-aloud protocols

Example Story model

NB This story model promotes first-degree murder verdict

Others promote not guilty (eg self-defence)

Initiating events:

J&C argued in bar

C threatened J

J has no weapon

J leaves Psychological states:

J very angry with C

Goals:

J intends to confront C

J intends to kill C

Actions:

J goes home and gets knife

J returns to bar

C hits J

J stabs C

Consequences:

C wounded & dies

Evaluating a story Not probabilistic inferences Acceptance (with confidence level)

– Certainly true; uncertain; certainly false Certainty principles

– Coverage– Uniqueness– Coherence

Coherence Consistency

– No internal contradictions Plausibility

– fit with juror’s world knowledge etc. Completeness

– No missing parts

Evidence for story model Verbal protocols

– 85% of events causally linked Verdicts covaried with story models Recognition memory tests

– More likely to falsely remember items consistent with story model

– E.g. If murder verdict story constructed, falsely remember ‘Johnson was looking for Cardwell’

Story vs witness order

More likely to convict when prosecution evidence in story order More likely to acquit when defence evidence in story order

Defence evidence

Prosecution evidence

Story order Witness order

Story order 59 78

Witness order

31 63

% mock jurors choosing guilty verdict

Vary order of presentation of evidence to influence ease of story construction

Shortcomings Not precisely specified

– No formal or computational models of causal model construction or inference

But captures crucial insight that people use causal knowledge to represent and reason about legal evidence

Coherence-based models Process-level account Mind strives for coherent representations Elements cohere or compete Judgments emerge through interactive

process that maximizes coherence (constraint satisfaction)

Bidirectional reasoning (evidence can be re-evaluated to fit emerging conclusions)

Formal model of evidential reasoning

Bayesian networks to represent relations between bodies of evidence and hypotheses

Captures dependencies between items Permits inference from evidence to

hypotheses (and vice-versa) Increasingly used in legal contexts

Partial Bayesian net for Sacco and

Vanzetti trial

Applicable to human reasoning?

Vast number of variables Numerous probability estimates

required Complex computations

Applicable to human reasoning?

Fully-fledged BNs unsuitable as model of limited-capacity human reasoning

BUT – a key aspect is the qualitative relations between variables (what depends on what)

Judgments of relevance & causal dependency critical in legal analyses

And people seem quite good at this!– DNA match raises probability of guilt – an impartial alibi lowers it

Guilt

DNA Alibi

+ -

More realistic model People reason using small-scale

qualitative models Limited number of variables (at one

time) Require comparative rather than

precise probabilities Guided by causal knowledge Captures relevance relations Enables inferences about hypotheses

on basis of evidence

causal cognition 2: reasoning david lagnado university college london

Documents

ve result cancer

causal account cancer

ve testcancer

ve test result step

testcancer cancer

ve test result cyst

model slide

inference slide