February 24, 2021

Objectives

1. Descriptive Conclusion

2. Intro to Causality

  • What is causality?
  • Counterfactuals
  • Potential Outcomes

Descriptive Claims

Evaluating Descriptive Claims:

  1. Claim \(\rightarrow\)
  2. Concept(s) \(\rightarrow\)
  3. Variable(s) \(\rightarrow\)
  4. Measure \(\rightarrow\)
  5. Draw a Conclusion \(\rightarrow\) Claim

Causality

Why causality?

Recall some of Weber’s insights:

1. science is about prediction

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

  • For us, clarity means knowing what actions achieve our goals, which do not, and how certain actions might put our values into conflict.

Why causality?

In other terms:

Science can only help answer prescriptive questions by evaluating causal claims


Without evidence for causal claims, we can’t make rational decisions about prescriptive claims

Two ways of asking causal questions

  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 millions of refugees head to Europe in 2015-2016?
  • Why are housing prices very high in Vancouver?

Two ways of asking causal questions

  1. What are the effects of causes?

We want to know what happens if we do some action or some action (the cause) happens. (Could be a specific action or not) This is about the contribution of some cause to an effect.

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

Two ways of asking causal questions

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 \[\textrm{cause} \xrightarrow{} \textrm{?}\]

What is causality?

What is causality?

all causal claims are a specific combination of two descriptive claims


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

What is causality?

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.

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

What is causality?

  • Does building a wall to keep immigrants out reduce violence 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

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

What is causality?

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

  1. One is (or will be) factual
  2. One is counterfactual

counterfactuals are the key to causality

Counterfactuals

Causality is Counterfactual

What does that mean?

Counterfactuals and Causality:

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

  • imagine an “alternate universe”

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

Spoiler Warning!

Counterfactuals:

If Gwenyth 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 remains with him

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

An exercise

This happened

Think about how you would behave under two different Public Health Code regimes:

If invited to attend a party, and the penalty, if caught, were $230, would you attend?

If invited to attend a party, and the penalty, if caught, were $2300, would you attend?

POLL

An exercise

Which of these is factual? Which is counterfactual?

\(1.\) If invited to attend a party, and the penalty, if caught, were $230, would you attend?

  • (factual): this is the actual rule in the Province

\(2.\) If invited to attend a party, and the penalty, if caught, were $2300, would you attend?

  • (counterfactual): this is not the rule in this province, but we can imagine an alternate universe in which it were.

Counterfactuals and Potential Outcomes

Counterfactuals imply potential outcomes:

If \(X\) is a variable for a possible cause and \(Y\) is a variable for what is possibly affected…

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

Counterfactuals and Potential Outcomes

potential outcomes notation:

Where \(i\) corresponds to a specific case, and \(X\) is the causal variable (and can take two values: \(1,0\)), then the potential outcomes of \(Y_i\) are:

\[Y_i(X = 1), Y_i(X = 0)\]

For case \(i\), \(X\) can only ever be \(1\) or \(0\): one potential outcome will become factual (it will happen), while the other will be counterfactual (it won’t happen)

Counterfactuals and Potential Outcomes

\(\mathrm{Love \ Life _{Gwenyth} (Catches \ the \ train )}\) \(= \mathrm{Stay \ with \ cheating \ BF}\)

\(\mathrm{Love \ Life _{Gwenyth} (Doesn't \ catch \ the \ train )}\) \(= \mathrm{Dump \ cheating \ BF}\)

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

Draw potential outcomes on the board

Counterfactuals and Causality:

And we can say that \(X\) causes \(Y\) for case \(i\) if \(Y_i(X = 1) \neq Y_i(X = 0)\):

  • \(X\) 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 for \(X\).

TO THE BOARD

Potential Outcomes: Caveat

In our example of COVID social distancing enforcement:

  • We are only imagining, as if omniscient, what you would do in the alternate universe where the penalty is $2300. We don’t actually know. Potential outcomes are what you actually would do in that alternate universe.
  • We are only asking you to imagine whether you would go to the party when invited. Potential outcomes are what you actually would do if invited.

Even if we don’t know what you would do if invited under different penalties; there are still potential outcomes of what you would do…

Example:

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

If this claim is true, what are the implied potential outcomes (of violent crime)?

Which of these potential outcomes are factual? counterfactual?

Counterfactuals and Potential Outcomes

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 \(\textrm{Murders}_{\textrm{El Paso}}(\textrm{No Wall})\)

Counterfactuals and Potential Outcomes

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

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

\[\textrm{Murders}_{\textrm{El Paso}}(\textrm{Wall}) > \textrm{Murders}_{\textrm{El Paso}}(\textrm{No Wall})\]

\[\textrm{Murders}_{\textrm{El Paso}}(\textrm{Wall}) = \textrm{Murders}_{\textrm{El Paso}}(\textrm{No Wall})\]

Counterfactuals and Potential Outcomes

“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:

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

Counterfactuals and Potential Outcomes

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

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

…How would you try to prove this?