Actual Causation: Looking Backward and Looking Forward Christopher - - PowerPoint PPT Presentation

Actual Causation: Looking Backward and Looking Forward

Christopher Hitchcock California Institute of Technology

Overview

• I’m going to talk about attempts to understand

the relation of ‘actual causation’

• Set up the problem in a familiar framework
• Some standard problems
• Approaches that seem promising, but don’t quite

work

Overview

• Offer a suggestion for a way forward
• Think about why have such a concept
• What is distinctive about it
• Solicit suggestions

Actual Causation

• By ‘actual causation’, I mean the kind of

relationship that is described by statements like:

• 1. A meteor strike in the Yucatan caused the

extinction of the dinosaurs

• 2. Sparks cast by a locomotive caused the fire that

destroyed Jacob Anderson’s house

• 3. The emission of X-rays from a charged vacuum

tube in Roentgen’s lab caused an image to appear on a screen

Actual Causation

• Actual causation has been of interest to

philosophers, and also legal theorists, because it is involved in the concepts of moral and legal responsibility

• It is also involved in the explanation of

particular events (such as the extinction of the dinosaurs)

Actual Causation

• A standard view among philosophers is that

what is distinctive about relations of actual causation is that they involve particular events

• A particular meteor struck at a particular

location at a particular time, etc.

• Particular sparks cast by a particular locomotive

caused a particular fire, etc.

Actual Causation

• This is contrasted with causal generalizations,

which relate types of events

• Large meteor impacts cause extinctions
• Sparks cause fires
• Etc.

Actual Causation

• I will suggest that another characteristic feature
• f actual causation is that it is backward-

looking as opposed to forward-looking

• Questions of actual causation tend to arise when

some event has occurred, and we retrospectively ask why it occurred

Counterfactual theory

• A well-known

approach to causation is the counterfactual theory

• Developed in detail

by the American philosopher David Lewis

Counterfactual

• To a first approximation
• C is a cause of E just in case the following

counterfactual is true: If C hadn’t occurred, E wouldn’t have occurred

• If the meteor had not struck the Yucatan (or

anywhere else on earth) the dinosaurs would not have gone extinct (when they did)

Preemption and Overdetermination

• The counterfactual definition has problems with

cases of preemption and overdetermination

• E.g., suppose Billy and Suzy are standing by

with rocks in their hands

• Suzy throws her rock at a window and it shatters

Preemption and Overdetermination

Picasso: Girl throwing rock

Preemption and Overdetermination

• If Suzy hadn’t thrown her rock, Billy would have

thrown his rock at the window and it would have shattered anyway

• Suzy preempted Billy
• Here we want to say that Suzy’s throw caused

the rock to shatter

• But the corresponding counterfactual is not true
• If Suzy hadn’t thrown, the window still would

have shattered

Structural Equation Models

• We can represent the causal structure of a case

like this…

• …including the relevant counterfactuals…
• …using structural equations models

Structural Equation Models

• We represent events in the story by variables
• E.g., we will have variable Suzy throws, which

takes the value 1 if Suzy throws, and 0 if she doesn’t

• We represent the pattern of dependence among

the variables by equations

Tools for Representing Causation

SR= 1 BR = 1 ST = SR BT = min {BR, 1 – ST} WS = max {ST, BT} Suzy Throws Billy Ready Billy Throws Window Shatters Suzy Ready

Tools for Representing Causation

• To represent counter-

factuals, we replace the original equation with a new one specifying the value of the variable SR= 1 BR = 1 ST = SR BT = min {BR, 1 – ST} WS = max {ST, BT}

Tools for Representing Causation

• To represent the

counterfactual ‘If Suzy had not thrown…’, replace the third equation SR= 1 BR = 1 ST = SR BT = min {BR, 1 – ST} WS = max {ST, BT}

Tools for Representing Causation

SR= 1 BR = 1 ST = SR BT = min {BR, 1 – ST} WS = max {ST, BT} Suzy Throws Billy Ready Billy Throws Window Shatters Suzy Ready

Tools for Representing Causation

SR= 1 BR = 1 ST = 0 BT = min {BR, 1 – ST} WS = max {ST, BT} Suzy Throws Billy Ready Billy Throws Window Shatters Suzy Ready

A Promising Approach

• There is a promising approach to defining actual

causation, developed by me, and Joe Halpern and Judea Pearl

• Look for path-specific effects

A Promising Approach

• We want to isolate the

influence along a single path

• We ‘clamp’ the other

path, by fixing the value of the variable Suzy Throws Billy Ready Window Shatters Suzy Ready Billy Throws

A Promising Approach

• We set ST to 0, while

also setting BT to 0 SR= 1 BR = 1 ST = SR BT = min {BR, 1 – ST} WS = max {ST, BT}

A Promising Approach

• We set ST to 0, while

also setting BT to 0

• Now we get WS = 0,

the window doesn’t shatter SR= 1 BR = 1 ST = 0 BT = 0 WS = max {ST, BT}

A Promising Approach

• However, this approach ends up being too

liberal

• There are path-specific effects that do not

correspond to relations of actual causation

A Promising Approach

• Question:
• Why do we have a conceptual tool for identifying

path-specific effects?

• Perhaps an answer to this question will help us

restrict the class of path-specific effects that underwrite relations of actual causation

A Hunch

• When we identify actual causes, we are

identifying ‘handles’ in the world

• Identifying targets of intervention for producing

desirable outcomes

• But this idea needs to be refined

A Hunch

• In decision theory, we evaluate potential actions
• We consider what would happen (with what

probability), if we were to perform various actions

• This is similar to considering a counterfactual

(except that it is future tensed, rather than past)

• But in decision theory, we are not interested in

path-specific effects

A Hunch

• E.g., suppose that Suzy wants, above all else, for

the window to shatter

• Should she throw the rock?
• If she throws, the window will shatter
• If she doesn’t, Billy will throw, and the window

will shatter

• Decision theory tells us that Suzy should be

indifferent between throwing and not throwing

A Hunch

• Decision theory considers only the

counterfactuals ‘If Suzy throws…’, ‘If Suzy doesn’t throw…’

• But not: ‘If Suzy doesn’t throw, and neither does

Billy…’

A Hunch

• Decision theory involves ‘cause-forward’

reasoning

• Consider a range of actions, and evaluate them

according to their consequences

A Hunch

• But consider a different kind of practical

reasoning problem

• I have some goal that I want to reach
• I reason backward from that goal, arrive at a

series of steps I will follow

• A plan
• ‘Effect-backward’ reasoning

A Hunch

• Now, when I consider which action to perform

at the beginning, I don’t think of the future as fully ‘open’, to be determined by my present action

• Rather, I must consider which action will work

best in conjunction with future actions that are part of the plan

Illustration

• We are members of a city council
• We want to make our city bicycle friendly
• We want to encourage people to ride bicycles,

and we want bicycle riders to be safe

• We are considering a mandatory helmet law
• Our goal is to decrease the proportion of

accidents that result in serious head injuries

Illustration

• But we want to do this without increasing the

number of accidents, or discouraging people from riding

• Consider the effect of a helmet law on a typical

rider

Helmet law Ride Wear helmet Other riders CCC Bicycle lanes Accident Head injury

Illustration

• There are multiple causal paths whereby a

helmet law influences the chance of a head injury

Helmet law Ride Wear helmet Other riders CCC Bicycle lanes Accident Head injury

Illustration

• But we don’t have to just implement the helmet

law and let the chips fall where they may

• We can separately intervene to undo the

undesired consequences of the law

Helmet law Wear helmet CCC Bicycle lanes Accident Head injury Other riders Ride

Illustration

• We are left with the causal path in which the

helmet law encourages the rider to wear a helmet, and wearing a helmet protects her head in case of an accident

Illustration

• If this path-specific effect is not present…
• either because the law would have no effect on

whether people wear helmets…

• or because helmets don’t provide adequate head

protection…

• then the helmet law is completely pointless

Illustration

• Suppose a particular cyclist gets in an accident,

bangs his head on the ground, but does not suffer a serious head injury

• My conjecture is that it is the very same causal

path that would be relevant to determining whether enacting the helmet law was an actual cause of the the cyclist suffering only minor injuries

A Hunch

• Judgments of actual causation involve causal

paths that remain intact when other feasible/ desirable/expected interventions are performed

• Actual causation is partly a function of our goals,

what we deem desirable, what we expect, etc.

A Hunch

• That’s OK, since there is still an objective core
• Namely the causal structure encoded in the

structural equations

• It’s only the specific relation of actual causation

that is sensitive to to our goals, desires, abilities, and expectations