1. Introduction to Causality

• What is causality?
• Counterfactuals
• Potential Outcomes

Weber’s insights:

1. science is about prediction

2. science cannot tell us what to do, but it can provide clarity

If power is about giving us motivation to do something , then justifications include claims about the consequences of actions.

1. What are the causes of effects?

Want to explain something specific that has happened/we observe (the effect). Seek to attribute a cause for something we observe.

• Why did Russia invade Ukraine?
• Why are housing prices high in Vancouver?

2. What are the effects of causes?

We want to know what happens if we do some action or some action (the cause) happens. This is about the consequences of some action.

• Has BC’s housing speculation tax reduced housing prices?
• What are the effects of restricting gun ownership on gun violence?

Looking at effects of causes versus causes of effects leads to different approaches to scientific investigation

causes of effects \[\textrm{?} \xrightarrow{} \textrm{effect}\]

effects of causes \[\textrm{cause} \xrightarrow{} \textrm{?}\]

Not only is understanding causality important:

• scientific evidence for causal claims is difficult to obtain
• all the same problems as evidence for descriptive claims
• and new difficulties we must overcome

To understand the problems and solutions for providing evidence of causality, we need to know what it is.

all causal claims are a combination of two specific descriptive claims

• sometimes these descriptive claims are made explicit, often they are implied.

Why does the US have the highest rate of gun deaths among developed countries?

The US has the highest rate of gun deaths among developed countries because of its lax gun laws.

• is this a question about “causes of effects” or “effects of causes”?
• What are the two descriptive claims in this causal claim?

• Does building a wall to keep immigrants out reduce violent crime?

The border city of El Paso, Tex., used to have extremely high rates of violent crime — one of the highest in the entire country, and considered one of our nation’s most dangerous cities. Now, immediately upon its building, with a powerful barrier in place, El Paso is one of the safest cities in our country. - Donald Trump

• is this a question about “causes of effects” or “effects of causes”?
• What are the two descriptive claims in this causal claim?

The descriptive claims embedded in causal claims are of a specific type:

1. One is a claim about how the world actually is (factual)
2. One is a claim about how the world would be, if something were changed (counterfactual)

counterfactuals are the key to causality

What does that mean?

counterfactuals: are the way world would be if events had transpired differently (other than what actually took place).

• imagine an “alternate universe” or “alternate timeline”

contrasts to what is factual: the way the world is, given the events that have taken place.

If Gwyneth Paltrow’s character…

1. catches the train then she catches her boyfriend cheating, and dumps him

2. does not catch the train then she does not catch her boyfriend cheating, and stays with him

In reality, only one of these possibilities can happen. If (a) happens, it is factual, (b) is counterfactual

Which of these is factual? Which is counterfactual?

\(1.\) If you had a friend on campus who was trans/non-binary, would you vote “yes” on this measure?

\(2.\) If you did not have a friend on campus who was trans/non-binary, would you vote “yes” on this measure?

• It depends: If you actually have a trans/non-binary friend, then \(1\) is factual (\(2\) is counterfactual); If you actually don’t have a trans/non-binary friend, then \(2\) is factual (\(1\) is counterfactual)

Counterfactuals can be described with potential outcomes:

If \(X\) is a variable for a suspected cause (having a trans friend) and \(Y\) is a variable for what is possibly affected (voting for fee increase)…

then potential outcomes are the values of \(Y\) that a specific case would take for the different possible values of \(X\) (factual and counterfactual):

• If you had a friend on campus who was trans/non-binary, would you vote “yes” on this measure?
• If you did not have a friend on campus who was trans/non-binary, would you vote “yes” on this measure?

potential outcomes notation:

Where \(i\) corresponds to a specific case (e.g., you, Gwyneth Paltrow)

\(\text{Trans Friend}\) (\(X\)) is the causal variable (and can take different values, e.g. \(yes, no\)), then the potential outcomes of \(\mathrm{\$8 \ fee \ vote}\) (\(Y_i\)) are:

\[\mathrm{AMS \ fee \ vote}_{i}(\text{Trans Friend} = yes),\\ \mathrm{AMS \ fee \ vote}_i(\text{Trans Friend} = no)\]

For person \(i\), \(\text{Trans Friend}\) can only ever be \(yes\) or \(no\): one potential outcome is factual (it will happen), while the other will remain counterfactual (it won’t happen)

\(^*\) Note, I will use \(\color{red}{red}\) to indicate counterfactual potential outcomes

\(\mathrm{Love \ Life _{Gwyneth} (Catches \ the \ train )}\) \(= \mathrm{Dump \ cheating \ BF}\)

\(\mathrm{Love \ Life _{Gwyneth} (Doesn't \ catch \ the \ train )}\) \(= \mathrm{Stay \ with \ cheating \ BF}\)

We only will observe one of these two possibilities. But both could potentially have happened.

For any suspected cause \(X\), and affected variable \(Y\), and case \(i\), we denote potential outcomes as:

\[Y_i(X = ?)\]

Draw potential outcomes on the board

In our example of having transgender friends and support for trans health care:

• We are only imagining, as if omniscient, what you would do in the alternate universe where you do(do not) have a trans friend
• Potential outcomes are what you actually would do in that alternate universe.

Even if we don’t know how you would vote if you did(did not) have a trans friend, we can imagine that there is potential outcome of what you would do…

What do counterfactuals have to do with causality????

Recall that causal claims are about how some shifting some factor changes something outcome…

counterfactual causality

We can say that \(Y\) changes because of \(X\) only if, for case \(i\), \(Y_i(X = 1) \neq Y_i(X = 0)\):

• \(X\) causes \(Y\) if case \(i\) would have behaved (\(Y\)) differently (than it did factually) in the (counterfactual) alternate universe where everything was the same except \(X\) was changed.

REVISIT THE BOARD

Counterfactuals Example

“The border city of El Paso, Tex., used to have extremely high rates of violent crime — one of the highest in the entire country, and considered one of our nation’s most dangerous cities. Now, immediately upon its building, with a powerful barrier in place, El Paso is one of the safest cities in our country.” - Donald Trump

• What is the “case”?
• What is the variable for the “cause”? What is the variable for the “effect”?

Counterfactuals Example

“The border city of El Paso, Tex., used to have extremely high rates of violent crime — one of the highest in the entire country, and considered one of our nation’s most dangerous cities. Now, immediately upon its building, with a powerful barrier in place, El Paso is one of the safest cities in our country.” - Donald Trump

Which of the potential outcomes are factual? counterfactual?

Trump’s causal claim (implicitly): “The wall caused El Paso to have fewer murders”.

Trump’s counterfactual claim: “If there had been no wall, El Paso would have had more murders.”

Counterfactual claim implies two potential outcomes:

1. Number of murders in El Paso last year in the presence of the wall: \(\textrm{Murders}_{\textrm{El Paso}}(\textrm{Wall})\)
2. Number of murders in El Paso last year in the absence of the wall \(\color{red}{\textrm{Murders}_{\textrm{El Paso}}(\textrm{No Wall})}\)

If the claim is true… what are the (relative) values these potential outcomes should take?

If Trump’s causal claim is true (“The wall caused El Paso to have fewer murders”), which should be true?

\[\textrm{Murders}_{\textrm{El Paso}}(\textrm{Wall}) < \color{red}{\textrm{Murders}_{\textrm{El Paso}}(\textrm{No Wall})} \tag{1}\]

\[\textrm{Murders}_{\textrm{El Paso}}(\textrm{Wall}) > \color{red}{\textrm{Murders}_{\textrm{El Paso}}(\textrm{No Wall})} \tag{2}\]

\[\textrm{Murders}_{\textrm{El Paso}}(\textrm{Wall}) = \color{red}{\textrm{Murders}_{\textrm{El Paso}}(\textrm{No Wall})} \tag{3}\]

“The border city of El Paso, Tex., used to have extremely high rates of violent crime — one of the highest in the entire country, and considered one of our nation’s most dangerous cities. Now, immediately upon its building, with a powerful barrier in place, El Paso is one of the safest cities in our country.”

Implies:

\[\textrm{Murders}_{\textrm{El Paso}}(\textrm{Wall}) < \color{red}{\textrm{Murders}_{\textrm{El Paso}}(\textrm{No Wall})}\]

If the claim is that “The wall caused El Paso to have fewer murders”, or

\[\textrm{Murders}_{\textrm{El Paso}}(\textrm{Wall}) < \color{red}{\textrm{Murders}_{\textrm{El Paso}}(\textrm{No Wall})}\]

What kinds of evidence would help assess whether this claim is true?

Causality is counterfactual

• this is not a simple, intuitive way of thinking
• this complicates providing evidence

We will see:

• different types of causal claims
• problems in testing causal claims
• focus on solutions (for some causal claims)