1. Causal Cognition 2: reasoning David Lagnado University College London

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

3. 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

4. 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

5. 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

6. Use Bayes rule D = disease; ¬D = no disease T+ = positive test result P(D) = base-rate of disease P(T+|D) = true positive (hit rate) P(T+|¬D) = false positive rate – –Intuition: two ways to get a +test result, if D is true or if D is false Correct Bayesian solution

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

8. 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. Prosecutors fallacy – –Confuse P(DNA match | not gulity) with P(Not guilty | DNA match) – –Ignore prior of guilt

9. Causal account Causal framework for judgments (Krynski & Tenenbaum, 2007) – –People fail in standard MDT because they construct a causal model that doesnt readily accommodate the false- positive statistic P(+test|¬cancer) Cancer +ve Test Result Step 1. Model construction

10. 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

11. 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%

12. 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

13. 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%

14. Causal account Cancer +ve Test Result Cyst Step 3. Bayesian inference P(cancer) = 1% P(cyst) = 30% P(+test|cancer) = 80% P(+test|cyst) = 50% P(cancer|+test) = P(cancer) x P(+test|cancer) P(cancer) x P(+test|cancer) + P(cyst) x P(+test|cyst) P(cancer|+test) = 1% x 80% = 5% 1% x 80% + 30% x 50%

15. 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

16. 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 – –Gamblers fallacy (chance as a self-correcting process) Cascaded inference

17. Counterfactual reasoning Close link between causal and counterfactual thinking Close link between causal and counterfactual thinking Psychological accounts of counterfactual reasoning Psychological accounts of counterfactual reasoning –Mental 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 counterfactuals (Pearl, 2000) CBNs offer formal approach to answering counterfactuals (Pearl, 2000)

18. Suppose that D Suppose that D Would D still have occurred, if A hadnt fired? Would D still have occurred, if A hadnt fired? Firing squad (deterministic case) C Captai n A fires B fires Dead U court order Blue = Unknow n

19. Firing squad (deterministic case) Abduction Abduction Update beliefs on evidence D Update beliefs on evidence D –D therefore A or B; therefore C; therefore U, A and B C Captai n A fires B fires Dead U court order Green = TRUE

20. Firing squad (deterministic case) Action Action –Do (not-A) –Set A to false; remove other links into A (graph surgery) –Re-set all variables to unknown except U C Captai n A fires B fires Dead U court order A fires

21. Firing squad (deterministic case) C Captai n A fires B fires Dead U court order A fires Inference Inference U is true; therefore C; therefore B; therefore D U is true; therefore C; therefore B; therefore D

22. Firing squad (deterministic case) C Captai n A fires B fires Dead U court order A fires Inference --- D is still true Inference --- D is still true Would D still have occurred, if A hadnt fired? Would D still have occurred, if A hadnt fired? Experimental study (Sloman & Lagnado, 2005) Experimental study (Sloman & Lagnado, 2005) 80% subjects say yes 80% subjects say yes

23. Causal reasoning Peoples counterfactual inferences obey undoing Peoples counterfactual inferences obey undoing Especially with causal scenarios Especially with causal scenarios Extended to probabilistic causation Extended to probabilistic causation Not explained on other theories of reasoning (mental logic, mental model theory, probabilistic models) Not explained on other theories of reasoning (mental logic, mental model theory, probabilistic models) Requires logic of causality (do-calculus) Requires logic of causality (do-calculus)

24. Decision making Importance of causal models in decision making (Sloman & Hagmayer, 2006) Importance of causal models in decision making (Sloman & Hagmayer, 2006) –Choose action that maximizes expected utility –Probability of outcome given that you do action A Construct a causal model of decision situation Construct a causal model of decision situation Use interventional probabilities Use interventional probabilities

25. 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: ChoresHealth Direct cause – doing chores is additional exercise each day Common cause – men concerned with equality issues also concerned with health issue ChoresHealth PC man Do chores: 69% 23%

26. 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?

27. 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)

28. 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

29. 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

30. InnocentGuilty DECISION Beyond reasonable doubt > C Initial Opinion Anchor S InnocentGuilty Background knowledge and assumptions Judges instructions on presumption of innocence New Evidence Item Belief Adjustment Process S* InnocentGuilty Trial events (witnesses, exhibits, arguments) Compare S* vs Criterion C Decision criterion C to convict Utility Evaluation of decisions Judges instructions on the standard of proof Severity of the crime etc. Belief adjustment model

31. 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) S0S0 Prosecution witness: Ex-girlfriend says Jack is violent Evidence encoded as +ve or –ve Weighted according to credibility of source + w 1.e 1 S 2 = S 1 - w 2.e 2 S 1 = S 0 + w 1.e 1 Added to anchor Defence witness: Sister says Jack is pacifist - w 2.e 2 Continue

32. 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 Prosecution witness: Ex-girlfriend says Jack is violent Order 1 Defence witness: Sister says Jack is pacifist Order 2 Prosecution witness: Ex-girlfriend says Jack is violent Defence witness: Sister says Jack is pacifist

33. 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

34. 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

35. 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

36. 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

37. 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 Harris 2 I was on my usual foot patrol at 9:00 p.m. 3 I heard loud voices from the direction of Gleason's Bar 4 Johnson and Caldwell were outside the bar 5 Johnson laughed at Caldwell 6 Caldwell punched Johnson in the face 7 Johnson raised a knife over his head 8 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)

38. Jurors story models elicited via think-aloud protocols

39. 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

40. Evaluating a story Not probabilistic inferences Acceptance (with confidence level) – –Certainly true; uncertain; certainly false Certainty principles – –Coverage – –Uniqueness – –Coherence

41. Coherence Consistency – –No internal contradictions Plausibility – –fit with jurors world knowledge etc. Completeness – –No missing parts

42. 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

43. 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 orderWitness order Story order5978 Witness order3163 % mock jurors choosing guilty verdict Vary order of presentation of evidence to influence ease of story construction

44. 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

45. 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)

46. 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

47. Partial Bayesian net for Sacco and Vanzetti trial

48. Applicable to human reasoning? Vast number of variables Numerous probability estimates required Complex computations

49. 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 + -

50. 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