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 PpE “ 1|C “ 1q ą PpE “ 1|C “ 0q

Intro Prob-Raise Three Scenarios

• Prob. Causal Models

Apt Models Conclusion

Probability-Raising

A B S PpS “ 1|B “ 1q ą PpS “ 1|B “ 0q

Intro Prob-Raise Three Scenarios

• Prob. Causal Models

Apt Models Conclusion

Probability-Raising

A B S IN PpS “ 1|dopB “ 1qq “ PpS “ 1|dopB “ 0qq

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: PpE “ 1|dopM “ 1qq ą PpE “ 1|dopM “ 0qq Scenario 3: PpE “ 1|dopM “ 1qq ă PpE “ 1|dopM “ 0qq

Intro Prob-Raise Three Scenarios

• Prob. Causal Models

Apt Models Conclusion

Three Scenarios

Scenarios 1 & 2: T M E Scenario 3 Y M T E

Intro Prob-Raise Three Scenarios

• Prob. Causal Models

Apt Models Conclusion

Three Scenarios

Scenario 1: PpE “ 1|dopM “ 1&T “ 1qq ą PpE “ 1|dopM “ 0qq Scenario 2: PpE “ 1|dopM “ 1&T “ 0qq ď PpE “ 1|dopM “ 0qq

Intro Prob-Raise Three Scenarios

• Prob. Causal Models

Apt Models Conclusion

Three Scenarios

Scenario 3: PpE “ 1|dopM “ 1&Y “ 0qq ą PpE “ 1|dopM “ 0&Y “ 0qq PpE “ 1|dopM “ 1&T “ 1&Y “ 0qq ą PpE “ 1|dopM “ 0&Y “ 0qq

Intro Prob-Raise Three Scenarios

• Prob. Causal Models

Apt Models Conclusion

Probabilistic Causal Models

Probabilistic causal model: M “ xV, dop¨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. dop¨q: function from (conjunctions of) primitive events, V “ v, to prob. dists.

• f form Pp¨|dop

V “ vqq – 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 “ VzX, Y ;

‚ some pair of possible values x, x1 of X; & ‚ some possible value y of Y s.t. PpY “ y|dopX “ x& S “ sqq ‰ PpY “ y|dopX “ x1& S “ sqq

Intro Prob-Raise Three Scenarios

• Prob. Causal Models

Apt Models Conclusion

Path-Specific Probability-Raising

Actual Causation (Simpliciter) X “ x rather than X “ x1 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 “ x1 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 “ x1 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 “ VzP fixed at their actual values

W “ w ˚, the probability of Y “ y would be higher if X “ x than if X “ x1 even if an arbitrary subset Z 1

• f the variables in

Z “ PzX, Y had taken their actual values, Z 1 “ z˚: formally, PpY “ y|dopX “ x& Z 1 “ z˚& W “ w ˚qq ą PpY “ y|dopX “ x1& W “ w ˚qq

Intro Prob-Raise Three Scenarios

• Prob. Causal Models

Apt Models Conclusion

Appropriate Models

What makes a model M “ xV, dop¨qy appropriate for assessing whether X “ x (rather than X “ x1) is an actual cause of Y “ y (for X, Y P V)?

• 1. Prob.

dists.

• f form Pp¨|dop

V “ vqq that are the output

• f dop¨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 Vi, Vj P V should have possible val-

ues Vi “ vi, Vj “ vj 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 PpE “ 1|dopM “ 1qq ą PpE “ 1|dopM “ 0qq

Intro Prob-Raise Three Scenarios

• Prob. Causal Models

Apt Models Conclusion

Appropriate Models

• 4. If X “ x (rather than X “ x1) is an actual cause of Y “ y relative to

M, there is no richer model (i.e. no model M1 “ xV1, dop¨ ¨ ¨ qy s.t. V Ă V1) satisfying 1–3 relative to which X “ x (rather than X “ x1) 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.