Probabilistic Actual Causation Luke Fenton-Glynn l.glynn@ucl.ac.uk - PowerPoint PPT Presentation

Intro Prob-Raise Three Scenarios Prob. Causal Models Apt Models Conclusion Probabilistic Actual Causation Luke Fenton-Glynn l.glynn@ucl.ac.uk

Intro Prob-Raise Three Scenarios Prob. Causal Models Apt Models Conclusion Introduction Type (Generic) Causation: Asbestos exposure causes mesothelioma. Actual (Token) Causation: Mr. Fairchild’s exposure to asbestos caused his mesothelioma.

Intro Prob-Raise Three Scenarios Prob. Causal Models Apt Models Conclusion Introduction Egs: ‚ K-Pg Extinction ‚ Cosmic Microwave Background ‚ Collapse of Bridge 9340 on I-35W ‚ Financial Crisis ‚ Outbreak of H7N9 avian ’flu virus

Intro Prob-Raise Three Scenarios Prob. Causal Models Apt Models Conclusion Introduction Probabilities in science: ‚ Quantum Mechanics (Orthodox, GRW, etc.) ‚ Bohmian Mechanics (Prob. dist. over particle positions) ‚ Statistical Mechanics (Classical or Quantum) ‚ High-Level Sciences (Ecology, Meteorology, Genetics, Chemistry)

Intro Prob-Raise Three Scenarios Prob. Causal Models Apt Models Conclusion Probability-Raising c , e = events C , E = binary variables C “ 1 if c occurs, C “ 0 otherwise E “ 1 if e occurs, E “ 0 otherwise P p E “ 1 | C “ 1 q ą P p E “ 1 | C “ 0 q

Intro Prob-Raise Three Scenarios Prob. Causal Models Apt Models Conclusion Probability-Raising A B S P p S “ 1 | B “ 1 q ą P p S “ 1 | B “ 0 q

Intro Prob-Raise Three Scenarios Prob. Causal Models Apt Models Conclusion Probability-Raising A IN B S P p S “ 1 | do p B “ 1 qq “ P p S “ 1 | do p B “ 0 qq

Intro Prob-Raise Three Scenarios Prob. Causal Models Apt Models Conclusion Three Scenarios

Intro Prob-Raise Three Scenarios Prob. Causal Models Apt Models Conclusion Three Scenarios Scenarios 1 & 2: P p E “ 1 | do p M “ 1 qq ą P p E “ 1 | do p M “ 0 qq Scenario 3: P p E “ 1 | do p M “ 1 qq ă P p E “ 1 | do p M “ 0 qq

Intro Prob-Raise Three Scenarios Prob. Causal Models Apt Models Conclusion Three Scenarios Scenarios 1 & 2: M T E Scenario 3 Y M T E

Intro Prob-Raise Three Scenarios Prob. Causal Models Apt Models Conclusion Three Scenarios Scenario 1: P p E “ 1 | do p M “ 1& T “ 1 qq ą P p E “ 1 | do p M “ 0 qq Scenario 2: P p E “ 1 | do p M “ 1& T “ 0 qq ď P p E “ 1 | do p M “ 0 qq

Intro Prob-Raise Three Scenarios Prob. Causal Models Apt Models Conclusion Three Scenarios Scenario 3: P p E “ 1 | do p M “ 1& Y “ 0 qq ą P p E “ 1 | do p M “ 0& Y “ 0 qq P p E “ 1 | do p M “ 1& T “ 1& Y “ 0 qq ą P p E “ 1 | do p M “ 0& Y “ 0 qq

Intro Prob-Raise Three Scenarios Prob. Causal Models Apt Models Conclusion Probabilistic Causal Models Probabilistic causal model: M “ x V , do p¨qy V : a set of variables V “ v for V P V is a primitive event V generates field of events: Boolean closure of set of primitive events. do p¨q : function from (conjunctions of) primitive events, � V “ � v , to prob. of form P p¨| do p � dists. V “ � v qq – prob. dist. that would result from intervening upon � V to set � V “ � v

Intro Prob-Raise Three Scenarios Prob. Causal Models Apt Models Conclusion Probabilistic Causal Models Graphical representation of a probabilistic causal model: Variables in V are nodes Directed edge (‘arrow’) from X to Y ( X , Y P V ) iff there is ‚ some possible assignment of values � S “ � s to the variables in � S “ V z X , Y ; ‚ some pair of possible values x , x 1 of X ; & ‚ some possible value y of Y s.t. P p Y “ y | do p X “ x & � s qq ‰ P p Y “ y | do p X “ x 1 & � S “ � S “ � s qq

Intro Prob-Raise Three Scenarios Prob. Causal Models Apt Models Conclusion Path-Specific Probability-Raising Actual Causation (Simpliciter) X “ x rather than X “ x 1 is an actual cause of Y “ y iff X “ x & Y “ y are the actual values of X & Y and X “ x rather than X “ x 1 is an actual cause of Y “ y relative to an appropriate model M .

Intro Prob-Raise Three Scenarios Prob. Causal Models Apt Models Conclusion Robust Path-Specific Probability-Raising Actual Causation (Model-Relative) X “ x rather than X “ x 1 is an actual cause of Y “ y relative to a model M iff there is a path P in M s.t., when we hold all variables in W “ V z P fixed at their actual values � � W “ � w ˚ , the probability of Y “ y would be higher if X “ x than if X “ x 1 even if an arbitrary subset � Z 1 Z 1 “ � of the variables in � Z “ P z X , Y had taken their actual values, � z ˚ : formally, Z 1 “ � P p Y “ y | do p X “ x & � z ˚ & � W “ � w ˚ qq ą P p Y “ y | do p X “ x 1 & � W “ � w ˚ qq

Intro Prob-Raise Three Scenarios Prob. Causal Models Apt Models Conclusion Appropriate Models What makes a model M “ x V , do p¨qy appropriate for assessing whether X “ x (rather than X “ x 1 ) is an actual cause of Y “ y (for X , Y P V )? of form P p¨| do p � 1. Prob. dists. V “ � v qq that are the output of do p¨q when � V “ � v is the input must be the ‘true’ prob. (objective chance?) dist. that would result from intervening upon � V to set � V “ � v . 2. No two different variables V i , V j P V should have possible val- ues V i “ v i , V j “ v j that represent states of affairs that are logically/metaphysically related. 3. The values of each variable should form a partition.

Intro Prob-Raise Three Scenarios Prob. Causal Models Apt Models Conclusion Appropriate Models M E P p E “ 1 | do p M “ 1 qq ą P p E “ 1 | do p M “ 0 qq

Intro Prob-Raise Three Scenarios Prob. Causal Models Apt Models Conclusion Appropriate Models 4. If X “ x (rather than X “ x 1 ) is an actual cause of Y “ y relative to M , there is no richer model (i.e. no model M 1 “ x V 1 , do p¨ ¨ ¨ qy s.t. V Ă V 1 ) satisfying 1–3 relative to which X “ x (rather than X “ x 1 ) is not an actual cause of Y “ y .

Intro Prob-Raise Three Scenarios Prob. Causal Models Apt Models Conclusion Conclusion Actual causation consists in there being at least one apt model rel- ative to which there is robust path-specific probability-raising.