1. NPHS 1530 Causation, Liability and Correlation
Unit 1 (Part 2)

2. Statistical Relevance (or Conditional Dependence) Models of Causation
Cause  Effect relationships can be inferred from conditional probability statements
Example: “Smoking is a cause of lung cancer.”
Identify the probability of developing lung cancer in a clearly defined population (age, sex, etc.): P(Effect) or P(E)
Identify the conditional probability of lung cancer in matched group of smokers: P(Effect|Cause) or P(E|C)
Identify the conditional probability of lung cancer in matched group of non-smokers: P(Effect | Absent Cause) or P(E|~C)

3. Statistical Relevance (or Conditional Dependence) Models of Causation
Cause  Effect relationships can be inferred from two conditional probability statements (Simple Statistical Relevance (SSR) criteria)
Probability of lung cancer in smokers is greater than the probability of lung cancer in the general population: P(Effect|Cause) > P(Effect) or P(E|C) > P(E)
Probability of lung cancer in smokers is greater than the probability of lung cancer in non-smokers: P(Effect|Cause) > P(Effect |Absence of Cause) or P(E|C) > P(E|~C)

4. Simple Statistical Relevance (SSR) Model & Problems with Regularity Theory (1)
Imperfect regularity: “Smoking tobacco is a cause of lung cancer.”
Confirm assertion that P(E|C) > P(E|~C); where C is ‘smoking tobacco’ and E is ‘diagnosis of lung cancer’
Irrelevance: “Salt that has been hexed by a sorcerer invariable dissolves when placed in water.”
Falsify assertion that P(E|C) > P(E|~C); where C is ‘hexing by a sorcerer’ and E is ‘salt’s property of dissolving in water.
Validate irrelevance condition: P(E|C) = P(E|~C)=P(E).

5. Simple Statistical Relevance Model (SSR) & Problems with Regularity Theory (2)
Asymmetry: “Smoking is a cause of lung cancer but lung cancer does not cause one to smoke.”
Confirm assertion that P(E|C) > P(E|~C); where C is ‘smoking tobacco’ and E is ‘diagnosis of lung cancer’
Difficulties with second condition: relationships between P(C|E) , P(C|~E) and P(C) do not address issue

6. Simple Statistical Relevance (SSR) Model & Problems with Regularity Theory (3)
Spurious regularities: “A rapid drop in barometric pressure  (1) drop in a column of mercury and (2) a storm (with a short delay).”
Let C designate ‘a rapid drop in barometric pressure)
Let E1 designate a ‘drop in a column of mercury’
Let E2 designate ‘a storm (with short delay)’
We will find that P(E1|C) > P(E1|~C), P(E2|C) > P(E2|~C), P(E1|E2) > P(E1|~E2) and P(E2|E1) > P(E2|~E1)
Difficulty with spurious correlations.

7. Simple Statistical Relevance (SSR) Model & Problems with Regularity Theory (3)
P(E1|C) > P(E1|~C), P(E2|C) > P(E2|~C), P(E1|E2) > P(E1|~E2) and P(E2|E1) > P(E2|~E1)
Drop in barometric pressure C
Drop in a column of mercury E1
Storm (after a short delay) E2

8. Statistical Relevance Model & Common Cause Principle
Want to establish that the drop in barometric pressure is a common cause of E1 and E2
Drop in barometric pressure C
Drop in a column of mercury E1
Storm (after a short delay) E2
Drop in barometric pressure C
Drop in a column of mercury E1
Storm (after a short delay) E2

9. Common Cause Principle: Conjunctive Fork
‘Effects’ are correlated: (1) P(E1 & E2) > P(E1)P(E2)
‘Cause’ occurs intermittently: (2) 0<P(C)<1
‘Effects’ (when ‘cause’ present) are independent statistically : (3) P(E1&E2|C) = P(E1|C)P(E2|C)
‘Effects’ (when ‘cause’ absent) are independent statistically : (4) P(E1&E2|~C) = P(E1|~C)P(E2|~C)
SSR for E1: (5) P(E1|C) > P(E1|~C)
SSR for E2: (6) P(E2|C) > P(E2|~C)
Drop in barometric pressure C
Drop in a column of mercury E1
Storm (after a short delay) E2

10. Common Cause Principle: Conjunctive Fork –Numerical Example
Let P(C)=0.3, P(E1|C)=1 and P(E2|C)=0.6. Therefore, P(E1)=0.3, P(E2)=0.18, P(E1&E2|C)=0.6, and P(E1&E2|~C)=0
(1) P(E1 & E2) > P(E1)P(E2): (0.6)(0.3) > (0.3)(0.18)
(2) 0<P(C)<1: P(C)=0.3
(3) P(E1&E2|C) = P(E1|C)P(E2|C): 0.6 = (0.6)(1)
(4) P(E1&E2|~C) = P(E1|~C)P(E2|~C): 0 = (0)(0.6)
(5) P(E1|C) > P(E1|~C)
(6) P(E2|C) > P(E2|~C)
Drop in barometric pressure C
Drop in a column of mercury E1
Storm (after a short delay) E2

11. Statistical Relevance Model & Common Cause Principle
Want to establish that the drop in barometric pressure is a common cause of E1 and E2
Drop in barometric pressure C
My big toe aches E1
Storm (after a short delay) E2
Drop in barometric pressure C
My big toe aches E1
Storm (after a short delay) E2

12. Common Cause Principle: Conjunctive Fork –Numerical Example (1)
Let P(C)=0.3, P(E1|C)=0.8 and P(E2|C)=0.6, P(E1)=0.5, P(E2)=0.18, P(E1&E2|C)=0.6, and P(E1&E2|~C)=0 (Common Cause solution)
(1) P(E1 & E2) > P(E1)P(E2)? (0.5)(0.18) > (0.5)(0.18)-FALSE
(2) 0<P(C)<1? P(C)=0.3
(3) P(E1&E2|C) = P(E1|C)P(E2|C)? 0.6 = (0.6)(0.8)-FALSE
(4) P(E1&E2|~C) = P(E1|~C)P(E2|~C)? 0 = (0.2)(0.4) -FALSE
(5) P(E1|C) > P(E1|~C) and (6) P(E2|C) > P(E2|~C)
Drop in barometric pressure C
My big toe aches E1
Storm (after a short delay) E2

13. Problems with Common Cause Principle
Multiple common causes
‘Effects’ are not distinct
Implicit or latent underlying factors
Often factor in application of ‘scientific’ evidence to public policy
Role of poverty in crime
Role of industry and agricultural activity in global warming

14. Criteria in Response to Problems with Common Cause Principle
[Nancy Cartwright 1979] Invariance with background context (B):
C causes E if and only if the probability of the effect, in the presence of the cause and any context B, exceeds the probability of the effect when C is absent but B present.
C causes E if and only if P(E|C&B)>P(E|~C&B) for all contexts B
Note that this is an inductive extension – proof by asserting lack of counterexample

15. Criteria in Response to Problems with Common Cause Principle
[Ellery Ells 1991] Causal Relations Taxonomy
C is a positive cause of E if and only if P(E|C&B)>P(E|~C&B) for all contexts B
C is a negative cause (inhibitor/preventer) of E if and only if P(E|C&B)<P(E|~C&B) for all B
C is a causally neutral for E (or irrelevant) if and only if P(E|C&B)=P(E|~C&B) for all contexts B
C is a mixed (or interacting) cause of E if it is none of the above.

16. Statistical Relevance Model of Scientific Explanation (Wesley Salmon)
Given some population A, an attribute (characteristic, feature, response, etc.) C is statistically relevant to another attribute B if and only if P(B|A&C) ≠ P(B|A).
C is irrelevant if and only if P(B|A&C) = P(B|A).
Example: All males who take birth control pills regularly fail to get pregnant.
We also observe that pills prevent pregnancy: P(Pregnancy/take pills)<P(Pregnancy|~take pills)

17. Statistical Relevance Model of Scientific Explanation (Wesley Salmon)
Example: All males who take birth control pills regularly fail to get pregnant.
Consider a population of people, T, which has subpopulations termed Male and Female.
P(Pregnancy|T & Male & “takes birth control pills”) = P(Pregnancy|T & Male)  pills are irrelevant
P(Pregnancy|T & Female & “takes birth control pills”) ≠ P(Pregnancy|T & Female), assuming not all women take pills

18. Is it necessary (or possible) to establish causation?
Single causal factors
Multiple causal factors
Contingencies
Interactions

19. Concepts from Formal Logic and Philosophy of Jurisprudence
Legal definitions for ‘factual causation’
‘But-for’ criterion
INUS (Insufficient but Non-redundant element of an Unnecessary but Sufficient set of conditions) criterion
NESS (Necessary Element of a Sufficient Set of conditions) criterion (a form of INUS condition)

20. Examples for Criminal or Civil Liability
Two hunters independently and simultaneously shoot and kill a third person.
Two contractors independently and simultaneously fail to deliver critical logistical support on time, resulting in a disaster.
Intuitive solution?

21. Examples for Criminal or Civil Liability
Intuitive solution? Both caused harm.
But-for conclusion: Action of NEITHER party was necessary for the outcome, thus neither caused the harm.
Case 1: The third party would not have been killed, but for the action of Hunter 1 (or 2).
Case 2: Disaster would have been averted but for the inaction of contractor 1 (or 2).

22. Examples for Criminal or Civil Liability
Intuitive solution? Both caused harm.
NESS conclusion: Action of EITHER party was a necessary element of a sufficient set of conditions for the outcome, thus both caused the harm.
Case 1: The action of Hunter 1 (or 2) was a necessary component leading to the killing of the third party.
Case 2: The inaction of contractor 1 (or 2) was a necessary element, given the scenario (set of conditions) for producing the disaster.

23. Examples for Criminal or Civil Liability
Intuitive solution? Both caused harm.
NESS conclusion: Action of EITHER party was a necessary element of a sufficient set of conditions for the outcome, thus both caused the harm.
Case 1: The action of Hunter 1 (or 2) was a necessary component leading to the killing of the third party.
Case 2: The inaction of contractor 1 (or 2) was a necessary element, given the scenario (set of conditions) for producing the disaster.

24. Extension of Examples
The ability of two hunters to own guns is a cause of them independently and simultaneously shooting and killing a third person.
Sarah Palin’s graphic with targeted congressional districts is a causal factor in the attempted assassination of a member of Congress.
Are the additional conditions causes or irrelevancies?
What do we need to know to make the determination?

25. Overdetermination Example(s):
Multiple health hazards (e.g., neurotoxins and carcinogens) from a ‘Superfund’ toxic waste clean-up site.
Contributions of genetics, product availability and personal choice to public health issues.
Cigarettes or chewing tobacco
Alcohol
Fats and soft drinks as causes of obesity

26. Overtaking Causes or Causal Preemption
Special cases of overdetermination
Examples:
Victim with lethal blood alcohol level is injured fatally in a barroom brawl. Who is culpable for the death?
‘Assisted suicide’ of a terminally ill patient.
Driver dozes off and strikes road debris that fell previously from a truck hauling scrap metal. The impact of the debris causes tire blowout, in the absence of a Jersey barrier on a four lane road, the car swerves into oncoming traffic and causes a fatal head-on collision.

27. Overtaking causes or Causal Preemption
Concept of ‘Proximate Cause’: How proximate need a cause be?

28. Assignment
Describe the causal arguments from the Chapter 4 of the Macondo Well Blowout Report (next 2 PowerPoint slides) in terms of:
But-for reasoning
INUS and NESS reasoning
Proximate Cause identification
Overtaking Causes / Causal Preemption
Regularity and Statistical Relevance criteria

29. Macondo Well Blowout Report (Chapter 4, released 6 JAN 11)
…the Macondo blowout was the product of several individual missteps and oversights by BP, Halliburton, and Transocean, which government regulators lacked the authority, the necessary resources, and the technical expertise to prevent.
We may never know the precise extent to which each of these missteps and oversights in fact caused the accident to occur. Certainly we will never know what motivated the final decisions of those on the rig who died that night.
What we nonetheless do know is considerable and significant: (1) each of the mistakes made on the rig and onshore by industry and government increased the risk of a well blowout; (2) the cumulative risk that resulted from these decisions and actions was both unreasonably large and avoidable; and (3) the risk of a catastrophic blowout was ultimately realized on April 20 and several of the mistakes were contributing causes of the blowout.

30. Macondo Well Blowout Report (Chapter 4, released 6 JAN 11)
The immediate cause of the Macondo blowout was a failure to contain hydrocarbon pressures in the well. Three things could have contained those pressures: the cement at the bottom of the well, the mud in the well and in the riser, and the blowout preventer.
But mistakes and failures to appreciate risk compromised each of those potential barriers, steadily depriving the rig crew of safeguards until the blowout was inevitable and, at the very end, uncontrollable. 

31. Assignment Guidelines
Cut-and-paste examples of each causal reasoning concept and state succinctly why. For example, for the NESS, identify the necessary element and the sufficient set of conditions in the applicable statements.
Due: Next Thursday before class.

32. Concepts from Formal Logic and Philosophy of Jurisprudence
Honoré, Antony, "Causation in the Law", The Stanford Encyclopedia of Philosophy (Winter 2010 Edition), Edward N. Zalta (ed.), URL = <
Menzies, Peter, "Counterfactual Theories of Causation", The Stanford Encyclopedia of Philosophy (Fall 2009 Edition), Edward N. Zalta (ed.), URL = <

33. Concepts from Formal Logic and Philosophy of Jurisprudence
Hitchcock, Christopher, "Probabilistic Causation", The Stanford Encyclopedia of Philosophy (Fall 2010 Edition), Edward N. Zalta (ed.), URL = <
Woodward, James, "Scientific Explanation", The Stanford Encyclopedia of Philosophy (Spring 2010 Edition), Edward N. Zalta (ed.), URL = <