Stories and statistics: What can the Sally Clark case tell us about the psychology of evidential reasoning?
David LagnadoDavid Lagnado
Division of Psychology and Division of Psychology and Language SciencesLanguage Sciences
University College LondonUniversity College London
Evidential reasoning
How do people assess and combine How do people assess and combine evidence to make decisions? evidence to make decisions? – Legal, Medical, Financial, Social …Legal, Medical, Financial, Social …
Cognitive science approachCognitive science approach– What kinds of representations?What kinds of representations?– What kinds of inference patterns?What kinds of inference patterns?
How do these compare with normative or How do these compare with normative or formal methods of evidential reasoning?formal methods of evidential reasoning?– Bayesian networks now used to model Bayesian networks now used to model
complex forensic evidence (Taroni et al, 2006)complex forensic evidence (Taroni et al, 2006)
Reasoning with legal Reasoning with legal evidenceevidence
Legal domainLegal domain– E.g. juror, judge, investigator, mediaE.g. juror, judge, investigator, media
Complex bodies of interrelated Complex bodies of interrelated evidenceevidence– Forensic evidence; witness testimony; Forensic evidence; witness testimony;
alibis; confessions etcalibis; confessions etcNeed to integrate wide variety of Need to integrate wide variety of
evidence to reach singular conclusion evidence to reach singular conclusion (e.g. guilt of suspect)(e.g. guilt of suspect)
Story model (Pennington & Hastie, 1986, 1991, 1992)
Evidence evaluated through story Evidence evaluated through story construction construction – ‘‘Stories involve human action sequences in Stories involve human action sequences in
which relationships of physical causality and which relationships of physical causality and intentional causality between events are intentional causality between events are central’central’
Jurors use prior causal knowledge and Jurors use prior causal knowledge and expectations about story structure to fill in expectations about story structure to fill in gaps in evidencegaps in evidence
Active ‘sense-making’ process to construct Active ‘sense-making’ process to construct an account of what happenedan account of what happened
Evidential Reasoning
Reasoning Reasoning fromfrom evidenceevidence– Use the evidence to Use the evidence to
construct ‘most construct ‘most plausible’ account plausible’ account of what happenedof what happened
– Generate a causal Generate a causal story based on the story based on the evidenceevidence
Reasoning Reasoning aboutabout evidenceevidence– Assessing the Assessing the
strength/reliability/vstrength/reliability/validity of the alidity of the evidenceevidence
– How well does the How well does the evidence support the evidence support the putative putative hypotheses/stories?hypotheses/stories?
think-aloud protocols from jurors in simulated trials suggest that they predominantly engage in former
Continuum? Individual variability in competence at juror Individual variability in competence at juror
reasoning (Kuhn et al., 1994) and evidential reasoning (Kuhn et al., 1994) and evidential reasoning in general (Kuhn, 1991)reasoning in general (Kuhn, 1991)
SATISFICING
Construct single story
using evidence
SATISFICING
Construct single story
using evidence
THEORY-EVIDENCE CO-ORDINATION
Construct multiple storiesEvaluate against evidence
and alternatives
THEORY-EVIDENCE CO-ORDINATION
Construct multiple storiesEvaluate against evidence
and alternatives
Group deliberation helps shift --->
Requires ability to reflect on one’s own reasoning?
Stories: blessing or curse?
Story is concrete and categoricalStory is concrete and categorical Describes a singular causal processDescribes a singular causal process
Hard to simultaneously Hard to simultaneously compare/evaluate multiple compare/evaluate multiple stories (cf Wigmore)stories (cf Wigmore)
Danger of neglecting Danger of neglecting alternative accountsalternative accounts
Evidence often Evidence often gathered/interpreted for a gathered/interpreted for a single story (confirmation single story (confirmation bias)bias)
The ‘truth’ might not make The ‘truth’ might not make a good storya good story
Economy of representationEconomy of representation Easy to communicateEasy to communicate Clear-cut basis for decision Clear-cut basis for decision
and actionand action Identify key variables to Identify key variables to
blameblame
Binocular rivalry
Switch between two coherent percepts (green vs red)
Even when inputs are mixed
Switch between two coherent stories(prosecution vs defence)
Even when evidence is mixed
Sally Clark case
Sally & Stephen Clark married, both solicitorsSally & Stephen Clark married, both solicitors Son Christopher born in 1996Son Christopher born in 1996
– Died suddenly at home aged 11 weeksDied suddenly at home aged 11 weeks– Sally alone with child; noticed he was unwell; Sally alone with child; noticed he was unwell;
ambulance called, but he could not be ambulance called, but he could not be resuscitatedresuscitated
Postmortem (Dr Williams): Postmortem (Dr Williams): – Death from natural causes - lung infection Death from natural causes - lung infection
(and bruises consistent with resuscitation (and bruises consistent with resuscitation attempts) attempts)
– Body was crematedBody was cremated
Sally Clark case
Harry born in 1997Harry born in 1997– Died suddenly at home aged 8 weeksDied suddenly at home aged 8 weeks– Stephen at home with Sally; but Sally alone with child Stephen at home with Sally; but Sally alone with child
when discovered unwell; ambulance called, but he could when discovered unwell; ambulance called, but he could not be resuscitatednot be resuscitated
Postmortem (Dr Williams): Postmortem (Dr Williams): – Suspicious - death from shaking? Suspicious - death from shaking? – Re-examined death of Christopher Re-examined death of Christopher – Concluded it too was unnatural, with evidence of Concluded it too was unnatural, with evidence of
smothering smothering
Sally Clark charged with murder of both children Sally Clark charged with murder of both children
Prosecution case
Christopher & Harry were smotheredChristopher & Harry were smothered– Nb change from Dr Williams’ initial claims of Nb change from Dr Williams’ initial claims of
shaking for Harry (error in diagnosis of retinal shaking for Harry (error in diagnosis of retinal haemorrhages)haemorrhages)
Neither died from SIDS because there were Neither died from SIDS because there were unexplained injuries unexplained injuries
Numerous similarities between the two Numerous similarities between the two deaths deaths – ‘‘which would make it an affront to commonsense which would make it an affront to commonsense
to conclude that either death was natural, and it to conclude that either death was natural, and it was beyond coincidence for history to so repeat was beyond coincidence for history to so repeat itself’ itself’
Prosecution case
‘‘SimilaritiesSimilarities’’– Babies died at similar agesBabies died at similar ages– Both found unconscious in same room; at same Both found unconscious in same room; at same
time; shortly after feedtime; shortly after feed– Mother alone with child when found unwellMother alone with child when found unwell– Father either away or due to go awayFather either away or due to go away– (Medical evidence of previous abuse & (Medical evidence of previous abuse &
deliberate injury)deliberate injury)
How unlikely are these given that mother How unlikely are these given that mother is innocent? (beyond coincidence?) is innocent? (beyond coincidence?)
Prosecution case: Injuries to Christopher
Blood in lungs
Blood in lungs
Torn frenulum
Torn frenulum BruisesBruises
SmotheringSmothering
nosebleednosebleed
Prior smothering
Prior smothering
Both fresh & older blood
Between lip and jaw
Small marks on arms and legs
Prosecution case:Injuries to Harry
Old fracture & dislocation
Hypoxic damage to
brain
Hypoxic damage to
brain
Haemorrhages in eyelids
Haemorrhages in eyelids
Haemorrhages to eyes
Haemorrhages to eyes
SmotheringSmothering Shaking/ prior abuse
Shaking/ prior abuse
Rib injuriesRib injuries Spinal injuriesSpinal injuries
Spinal bleeding & swollen cord
Prosecution case:Credibility of witnesses
Sally Clark states she found Harry slumped in bouncy chair
Sally Clark states she found Harry slumped in bouncy chair
Harry slumped in bouncy chair?
Harry slumped in bouncy chair?
Police surgeon says impossible for baby of 8 weeks to slump in bouncy chair
Police surgeon says impossible for baby of 8 weeks to slump in bouncy chair
Sally Clark reliabilitySally Clark reliability
Sally’s testimony in doubt
Sally Clark alone with Harry
Sally Clark alone with Harry
Stephen Clark states he returned home at 5.30/5.45pm
Stephen Clark states he returned home at 5.30/5.45pm
Taxi records show Stephen Clark returned home at 8.10pm
Taxi records show Stephen Clark returned home at 8.10pm
Opportunity/ Motive
Sally Clark smothered Harry
Sally Clark smothered Harry
Stephen Clark reliability
Stephen Clark reliability
Stephen lying to protect wife
Stephen’s testimony in doubt
Professor Sir Roy Meadow (Paediatrics)Professor Sir Roy Meadow (Paediatrics) Report – Report – ‘‘Sudden unexpected deaths in Sudden unexpected deaths in
infancyinfancy’’ Risk factors – age of mother (<26), smoker in Risk factors – age of mother (<26), smoker in
household, no wage earnerhousehold, no wage earner None applied to Clark family None applied to Clark family
Chance of one SIDS in family= 1 in 8,543Chance of one SIDS in family= 1 in 8,543 Chance of two SIDS = 1/8543 x 1/8543 Chance of two SIDS = 1/8543 x 1/8543
= 1/73 million= 1/73 million ‘‘……by chance that happening will occur by chance that happening will occur
about once every hundred yearsabout once every hundred years’’
Prosecution case:Statistical evidence
Defence case
Sally Clark did not kill her childrenSally Clark did not kill her children– They died of natural but unexplained causesThey died of natural but unexplained causes– Medical evidence amounts only to suspicionMedical evidence amounts only to suspicion
Two of prosecution experts said cause of Two of prosecution experts said cause of deaths deaths ‘‘unascertainedunascertained’’
Case hinges upon Dr WilliamCase hinges upon Dr William’’s reliability s reliability and competence and competence
Blood in lungs
Blood in lungs
Torn frenulum
Torn frenulum BruisesBruises
Resuscitationattempts
Resuscitationattempts
Reliability of Dr WilliamsReliability of Dr Williams
Postmortem effects
Postmortem effects
Report of Torn
frenulum
Report of Torn
frenulum
Report of Bruises
Report of Bruises
HaemoderosisHaemoderosis
Report from police & hospital
Report from police & hospital
Change of opinionPoor conduct of postmortemLow quality photos etc
Change of opinionPoor conduct of postmortemLow quality photos etc
Defence case: Injuries to Christopher
NB distinguish event from reports of event
Defence case: Injuries to Harry
Hypoxic damage to
brain
Hypoxic damage to
brain
Haemorrhages to eyelids
Haemorrhages to eyelids
Haemorrhages to eyes
Haemorrhages to eyes
Natural causes
post-death
Natural causes
post-death
PostmortemPostmortem
Rib injuriesRib injuries Spinal injuriesSpinal injuries
Reliability of Dr WilliamsReliability of Dr Williams
Change of opinionPrior error with slidesChange of opinionPrior error with slides
Stephen Clark states he returned home at 5.30/5.45pm
Stephen Clark states he returned home at 5.30/5.45pm
Sally Clark alone with Harry
Sally Clark alone with Harry
Stephen Clark reliability
Stephen Clark reliability
Taxi records show Stephen Clark returned home at 8.10pm
Taxi records show Stephen Clark returned home at 8.10pm
Opportunity/ Motive
Sally Clark smothered Harry
Sally Clark smothered HarryStephen very
unlikely to lie to protect wife if she killed their children
Stephen admitted lack of knowledge, and mentioned taxi records
Stephen admitted lack of knowledge, and mentioned taxi records
Explain Stephen testimony mistake
Defence case: Statistical evidence
2 SIDS death = significantly greater than 1/73 million
Mother >26No smokersWage earner
Mother >26No smokersWage earner
SIDS death1SIDS death1 SIDS death2SIDS death2
genetic or environmental
factors
genetic or environmental
factors
Calculation Calculation for two for two deaths deaths ignores ignores possible possible genetic & genetic & environmentaenvironmental factors l factors
Estimate for Estimate for probability of probability of one SIDS one SIDS death death questionablequestionable
Known risk factors
UNKNOWN risk factors
Deaths are not independent (so cannot simply square)
Verdict
Sally Clark found guilty by 10-2 Sally Clark found guilty by 10-2 majoritymajority
Imprisoned for lifeImprisoned for life
First Appeal:Statistical evidence Statistical evidence
misleadingmisleading Non independenceNon independence
– 1/73 million figure flawed1/73 million figure flawed– Probabilities are not independent Probabilities are not independent
RelevanceRelevance– Probability of two SIDS deaths insufficientProbability of two SIDS deaths insufficient– needs to be compared against probability that mother needs to be compared against probability that mother
murders both her children murders both her children – Estimated incidence of this is much lower than of two SIDS Estimated incidence of this is much lower than of two SIDS
deathsdeaths
‘it is clearly inadequate to concentrate on a single cause of death. If we make an assessment of the probability of two babies in one family both dying from SIDS, we must equally make a similar assessment of the probability of two babies in one family both being murdered (and so on, for any other causes that may be under consideration)…’ Dawid (2002)
EvidenceEvidence
SIDSSIDS MurderMurder
Two alternative causes of the deathsTwo alternative causes of the deaths
(exclusive but not exhaustive – other causes possible, also possible that one SIDS, one murdered etc)(exclusive but not exhaustive – other causes possible, also possible that one SIDS, one murdered etc)
Prior probability of SIDS is low
Prior probability of murder is even lower
Prior to other/medical evidence, probability of double SIDS greater than probability of double murder
Evidence of 2 deaths
Appeal dismissed
Court of appeal judgmentCourt of appeal judgment– No need for expert statisticians to give oral testimony No need for expert statisticians to give oral testimony
––““it was hardly rocket scienceit was hardly rocket science””– Defence already pointed out flaws in statisticsDefence already pointed out flaws in statistics– What matters is that probability of two SIDS deaths is What matters is that probability of two SIDS deaths is
very low, not exact figurevery low, not exact figure– Statistic might have had larger impact on jury than it Statistic might have had larger impact on jury than it
should have, but case against Sally Clark was should have, but case against Sally Clark was nevertheless overwhelmingnevertheless overwhelming
"In the context of the trial as a whole, the point on statistics "In the context of the trial as a whole, the point on statistics was of minimal significance and there is no possibility of the was of minimal significance and there is no possibility of the jury having been misled so as to reach verdicts that they jury having been misled so as to reach verdicts that they might not otherwise have reached."might not otherwise have reached."
Second appeal
Discovery of new evidenceDiscovery of new evidence– Harry had bacterial infection Harry had bacterial infection – Known by Dr Williams but not disclosed at trial!Known by Dr Williams but not disclosed at trial!– (When jury asked about blood tests for Harry, (When jury asked about blood tests for Harry,
Williams said Williams said nono relevantrelevant test results) test results)
Plausible cause of Harry’s death Plausible cause of Harry’s death – according to 11 independent expertsaccording to 11 independent experts– Also casts doubt on ChristopherAlso casts doubt on Christopher’’s death due to s death due to
unreliability of Dr Williamsunreliability of Dr Williams
Harry’s death
Hypoxic damage to
brain
Hypoxic damage to
brain
Hemorrhages to eyelids
Hemorrhages to eyelids
Hemorrhages to eyes
Hemorrhages to eyes
Natural causes
post-death
Natural causes
post-death
PostmortemPostmortem
Rib injuriesRib injuries Spinal injuriesSpinal injuries
Reliability of Dr WilliamsReliability of Dr Williams
Failure to disclose
etc
Failure to disclose
etc
Bacterial infectionBacterial infection
Micro-biological
tests
Micro-biological
tests
Conclusions about Christopher
Second appeal
Conviction declared unsafeConviction declared unsafe– Sally Clark released 2003Sally Clark released 2003
PostscriptPostscript– Several other similar convictions involving Several other similar convictions involving
Meadow subsequently overturnedMeadow subsequently overturned– Meadow struck off medical register 2005; Meadow struck off medical register 2005;
reinstated on appeal 2006reinstated on appeal 2006– Williams guilty of serious misconduct 2005Williams guilty of serious misconduct 2005
Sally dies 2007Sally dies 2007
Lessons
Various repercussions for legal domainVarious repercussions for legal domain– Expert witnesses Expert witnesses – (expert in child health not an expert in statistics)(expert in child health not an expert in statistics)– Interpretation and presentation of statistical Interpretation and presentation of statistical
evidence evidence
For evidential reasoningFor evidential reasoning– Understanding statistical evidenceUnderstanding statistical evidence– Role of causal networksRole of causal networks– Reliability of evidence (and experts)Reliability of evidence (and experts)– Stories and blameStories and blame
Statistical evidence
Well-documented problems when people reason Well-documented problems when people reason with probabilities (Kahneman, 2012)with probabilities (Kahneman, 2012)– Base rate neglect; prosecutor's fallacy; conjunction Base rate neglect; prosecutor's fallacy; conjunction
errorserrors
In contrast people are good at qualitative causal In contrast people are good at qualitative causal reasoningreasoning
One approach that reconciles these findingsOne approach that reconciles these findings– People need suitable causal models for appropriate People need suitable causal models for appropriate
probabilistic reasoning (Krynski & Tenenbaum, 2007; probabilistic reasoning (Krynski & Tenenbaum, 2007; Sloman, 2005; Lagnado, 2011)Sloman, 2005; Lagnado, 2011)
Classic probability problems facilitated with Classic probability problems facilitated with causal modelscausal models
Medical diagnosis problem(Krynski & Tenenbaum, 2007)
Given +test people grossly Given +test people grossly overestimate probability of canceroverestimate probability of cancer
(Neglect low base rate) (Neglect low base rate) Mistaken use of false positive Mistaken use of false positive
probabilityprobability Low false + Low false + high probability of high probability of
cancer cancer
+ TEST+ TEST
CancerCancer CystCyst
+ TEST+ TEST
CancerCancer
Alternative cause of +test made Alternative cause of +test made explicit explicit
People give better estimates of People give better estimates of probability of cancer probability of cancer
Improved probabilistic reasoning Improved probabilistic reasoning given suitable causal model given suitable causal model
shown for several classic problems shown for several classic problems
Statistical evidence
To avoid errors in Sally Clark caseTo avoid errors in Sally Clark case– Need suitable (causal) model to Need suitable (causal) model to
understand probabilities understand probabilities – Need to consider (probability) of Need to consider (probability) of
alternative causesalternative causes– Need to combine via Bayes ruleNeed to combine via Bayes rule
Misleading categories
Case framed as murder vs SIDSCase framed as murder vs SIDS Exclusive but not exhaustive Exclusive but not exhaustive Tempting to reason: not-SIDS -> murderTempting to reason: not-SIDS -> murder But other natural explanations possible (eg But other natural explanations possible (eg
infections etc)infections etc) Key to represent alternative causes …Key to represent alternative causes …
EvidenceEvidence
NaturalNatural UnnaturalUnnatural
EvidenceEvidence
other naturalother natural smothersmother
Other …Other …SIDSSIDS
Non-independence
Main focus on flawed assumption of Main focus on flawed assumption of independence of SIDS deathsindependence of SIDS deaths– Judges, lawyers, media, etc Judges, lawyers, media, etc
People understand independence/non-People understand independence/non-independence when framed causallyindependence when framed causally– Possible unobserved common causes of SIDS deathsPossible unobserved common causes of SIDS deaths– Eg genetic or environmental factorsEg genetic or environmental factors
SIDS1SIDS1
Genetic or environmental
Genetic or environmental
SIDS2SIDS2
Understanding/using probability
Second error –Second error –– How is probability of SIDS relevant to How is probability of SIDS relevant to
probability that Sally is guilty of murder?probability that Sally is guilty of murder?– Need to use Bayes rule Need to use Bayes rule – Requires comparison with prior probability of Requires comparison with prior probability of
child murder child murder
Danger of prosecutor's fallacyDanger of prosecutor's fallacy– Assume that 1 in 73 million figure applies to Assume that 1 in 73 million figure applies to
probability that Sally Clark is innocentprobability that Sally Clark is innocent– Eg P(2deaths|not guilty) = P(not guilty|Eg P(2deaths|not guilty) = P(not guilty|
2deaths)2deaths)
Statistical evidence Probabilistic reasoning improved by explicit Probabilistic reasoning improved by explicit
causal models (Krynski &Tenenbaum,2007)causal models (Krynski &Tenenbaum,2007) Avoid MeadowAvoid Meadow’’s second error by explicitly s second error by explicitly
representing probability of double murder?representing probability of double murder?
EvidenceEvidence
SIDSSIDS MurderMurderPrior of double SIDS is low
Prior for double murder is even lower
Ongoing empirical work on improving Bayesian reasoning using causal models
Representing alternative cause and its prior probability should improve probabilistic judgments
Causal networks
Key role of causal reasoning borne out by Key role of causal reasoning borne out by Sally Clark caseSally Clark case
But story model needs to be developedBut story model needs to be developed Formal means for representing causal models Formal means for representing causal models
and inferenceand inference Include representation of evidence and Include representation of evidence and
reliability (and their interrelations)reliability (and their interrelations) Move closer to theory-evidence co-ordinationMove closer to theory-evidence co-ordination Even if people don’t always do this- they can!Even if people don’t always do this- they can!
Legal idioms Evidential reasoning in terms of Evidential reasoning in terms of
causal building blockscausal building blocks– Capture generic inference patternsCapture generic inference patterns– Reusable and combinableReusable and combinable– Qualitative causal structureQualitative causal structure– Based on Bayesian networksBased on Bayesian networks– Akin to schema/scriptsAkin to schema/scripts
Fenton, Lagnado & Neil, 2012Fenton, Lagnado & Neil, 2012
Legal idioms
Evidence idiomEvidence idiom Evidence Evidence depends on depends on HypothesisHypothesis Evidence is more likely if hypothesis is trueEvidence is more likely if hypothesis is true Observed evidence raises the probability of Observed evidence raises the probability of
hypothesishypothesis
BruisesBruises
Smother Smother
EvidenceEvidence
Hypothesis Hypothesis Smothering causes bruises(probabilistically)
Explaining away Explaining away – EEvidence is often rebuttedvidence is often rebutted
Legal idioms
BruisesBruises
Smother Smother ResuscitationResuscitation
Stephen reportStephen report
Evidence for alternative cause of bruises
Legal idioms
Distinguish event from reportDistinguish event from report
EventEvent
HypothesisHypothesis
ReportReport
BruisesBruises
Christopher smotheredChristopher smothered
Williams report of bruises
Williams report of bruises
Police / hospital report of NO
bruises
Police / hospital report of NO
bruises
Legal idioms Evidence – Reliability idiomEvidence – Reliability idiom
Evidence EEvidence E
Hypothesis HHypothesis H ReliabilityReliability
Williams reportWilliams report
BruisesBruises Reliability of Williams
Reliability of Williams
Impact of evidence on hypothesis is modulated by its reliability
Williams slide errors
Williams slide errors
Legal idioms
Reliability of witness reports Reliability of witness reports – Separate factors for reliabilitySeparate factors for reliability
Williams reportWilliams report
BruisesBruises Reliability of Williams
Reliability of Williams
VeracityVeracity
Is Williams honest?
ObjectivityObjectivity
Is Williams biased?
CompetenceCompetence
Is Williams mistaken?
From Schum (2001)
Legal idioms
Opportunity idiomOpportunity idiom
Sally smothers Harry
Sally smothers Harry
Sally alone with HarrySally alone with Harry
Stephen reportStephen report
ReliabilityReliability
Opportunity is often a pre-condition of guilt
Legal idioms
Motive idiomMotive idiom
Motive is typically a pre-condition of guilt
Sally murders baby
Sally murders baby
Sally career driven
Sally career driven
Sally resentfulSally resentful
Letters to parents
Letters to parents
evidence
Use of ironyUse of irony
rebuttal
Combining idioms – alibi evidence
Stephen lying to protect wife?
Stephen memory error?
ReliabilityReliability
Sally smothered Harry
Sally smothered Harry
Sally alone with HarrySally alone with Harry
Opportunity
Taxi record 8.10Taxi record 8.10Stephen report 5.30
Stephen report 5.30
Conflicting Evidence reports
Status of framework
NormativeNormative– Formal model to capture appropriate probabilistic Formal model to capture appropriate probabilistic
inference (and support theory-evidence co-ordination) inference (and support theory-evidence co-ordination)
DescriptiveDescriptive– Do people’s inferences conform to the model?Do people’s inferences conform to the model?– Qualitatively? Quantitatively?Qualitatively? Quantitatively?– Empirical studies suggest good fit to qualitative Empirical studies suggest good fit to qualitative
patternspatterns
PrescriptivePrescriptive– Guide to interpreting complex evidence and improving Guide to interpreting complex evidence and improving
inference (shift towards TEC)inference (shift towards TEC)
The big picture
Combining network fragments into a Combining network fragments into a large-scale modellarge-scale model
Cognitive Economy?
How do people do this?How do people do this?– Lab-based studies support the claim that they Lab-based studies support the claim that they
use idioms for small-scale problems (Lagnado, use idioms for small-scale problems (Lagnado, 2011; Lagnado et al., 2012)2011; Lagnado et al., 2012)
– But how does this scale-up?But how does this scale-up? Story-tellingStory-telling
– Use of narrative to simplify?Use of narrative to simplify?– Reasoning Reasoning from from but not but not aboutabout evidence evidence
Stories and BlameStories and Blame
Stories constructed from causal networksStories constructed from causal networks Cohesive narrative to explain eventsCohesive narrative to explain events To attribute blame for negative outcomesTo attribute blame for negative outcomes But focus of stories can compromise But focus of stories can compromise
proper theory-evidence co-ordination proper theory-evidence co-ordination
Stories and BlameStories and Blame
At trialAt trial Prosecution presented one cohesive Prosecution presented one cohesive
story – story – Sally smothered both babiesSally smothered both babies Explains most of the medical evidenceExplains most of the medical evidence Explains unreliability of Stephen & Sally testimonyExplains unreliability of Stephen & Sally testimony ‘‘SupportedSupported’’ by statistical evidence by statistical evidence
Defence did not present one single Defence did not present one single story, but numerous disconnected story, but numerous disconnected pieces to explain the different injuries pieces to explain the different injuries etcetc
Possible line of juror reasoning?
Jurors reject SIDS due to extreme rarityJurors reject SIDS due to extreme rarity Neglect low base-rate of smothering Neglect low base-rate of smothering
because this was never raised at trial because this was never raised at trial Accept smothering because:Accept smothering because:
– it gives it gives ‘‘simplesimple’’ explanation of injuries explanation of injuries– (and explains inconsistent testimonies)(and explains inconsistent testimonies)– Assigns blame to someone Assigns blame to someone
A A ‘‘plausibleplausible’’ story? story?
Importance of causal story that Importance of causal story that assigns blame?assigns blame?
At second appealAt second appeal– New New ‘‘storystory’’ in which Harry died from in which Harry died from
infection and Dr Williams & Meadow infection and Dr Williams & Meadow were blamedwere blamed
Aftermath & MediaAftermath & Media– Professor MeadowProfessor Meadow’’s statistical errors are s statistical errors are
highlighted highlighted
Stories and BlameStories and Blame
Importance of clarity in evidential Importance of clarity in evidential reasoningreasoning– For jurors, lawyers, judges, experts, media …For jurors, lawyers, judges, experts, media …
How can this be improved?How can this be improved?– Shift from single casual story to theory-Shift from single casual story to theory-
evidence co-ordinationevidence co-ordination– Use peopleUse people’’s capacity for causal reasoning to s capacity for causal reasoning to
support better probabilistic inference? support better probabilistic inference? – Introduce formal methods eg Bayesian networks Introduce formal methods eg Bayesian networks
etc to help model and evaluate evidence? etc to help model and evaluate evidence? – Ongoing research! Ongoing research!
Lessons for evidential reasoning
Thank you!
Collaborators Collaborators – Norman Fenton (QMUL)Norman Fenton (QMUL)– Martin Neil (QMUL)Martin Neil (QMUL)
Evidence projectEvidence project– Philip DawidPhilip Dawid– William TwiningWilliam Twining
BAYES RULE (odds version)
P(2deaths|guilty) = 1P(2deaths|~guilty) =1/73million (ignoring error of non-independence)
P(guilty) = 1/84million (based on stats for double child murders – but perhaps should just consider guilty = at least one murder)
P(guilty|2deaths) = 0.009
Nbp/1-p = odds
P = odds/(1+odds)
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