March 9, 2021


1. What is Causality

  • Counterfactuals
  • Potential Outcomes

2. Types of causal claims

  • deterministic vs probabilistic
  • varieties of deterministic causal claims

A question for today:

From the midterm, and still a relevant policy consideration:

Do public health polices that require individuals to wear face-masks in public indoor spaces reduce COVID transmission and mortality?

  • This is a causal question.

What is causality?

What is causality?

All causal claims are counterfactual claims:

That is: they imply two descriptive claims of a specific type

  1. One descriptive claim about how the world is factually;
    • what is the factual exposure to the alleged “cause”
    • what is the factual outcome (the thing allegedly affected)
  2. One descriptive claim about how the world would be counterfactually
    • what would the outcome be if exposure to the alleged cause were different

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.

Counterfactuals and Potential Outcomes

Counterfactuals imply potential outcomes:

If \(X\) is a variable that corresponds to a possible cause and \(Y\) is a variable for what is possibly affected, and \(i\) indicates a specific case…

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

  • potential outcomes because they could happen but only one becomes factual, the others remain counterfactual.

Counterfactuals and Potential Outcomes

\(Y_i\) = COVID Deaths in a Canadian Province

\(X\) = Mandatory Face-mask Policy (yes or no)

Only one policy will be implemented; COVID deaths in the alternate world remain counterfactual (what would have happened absent face-mask policy).

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 \(X\).

  • Same as saying: \(X\) causes \(Y\) if the potential outcomes of \(Y\) are different for different values of \(X\)

Counterfactuals and Causality:

And we can say that \(\mathrm{Face \ Mask \ Policy}\) reduced \(\mathrm{COVID \ Deaths}\) for case \(BC\) if

\(\mathrm{COVID \ Deaths}_{BC}(\mathrm{Mask = Yes}) <\) \(\mathrm{COVID \ Deaths}_{BC}(\mathrm{Mask = No})\):

Counterfactuals and Causality:

All causal claims can be re-stated as counterfactual claims

  • They contain a conditional clause, starting with “If” (always in the subjunctive mood)
  • A “then” clause, stating what would happen if the conditional/“If” clause were true (always in the conditional mood)
  • May be in past, present, or future tense.

Counterfactuals and Causality:

Example: Past

“BC’s mask mandate reduced COVID fatalities.”

\[\underbrace{If \ \ BC \ \ had \ \ not \ \ imposed \ \ a \ \ mask \ \ mandate}_{\text{If-clause in Subjunctive Mood}}, \\ \underbrace{there \ \ would \ \ have \ \ been \ \ more \ \ COVID \ \ deaths.}_{\text{Then-clause in Conditional Mood}}\]

Counterfactuals and Causality:

Example: Present

“The presence of greek organizations on campus increases rates of sexual assault.”

\[\underbrace{If \ \ there \ \ were \ \ no \ \ greek \ \ organizations \ \ on \ \ campus}_{\text{If-clause in Subjunctive Mood}}, \\ \underbrace{there \ \ would \ \ be \ \ fewer \ \ sexual \ \ assaults.}_{\text{Then-clause in Conditional Mood}}\]

Counterfactuals and Causality:

Note: Counterfactual claims get increasingly complicated, the more complicated your causal claim is

  • On assignments, exam do not come up with overly complex causal 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 has Quebec had the highest rate of COVID mortality among all provinces in Canada?”

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.

  • What is the effect of the Canada Emergency Response Benefit (CERB) on consumer spending?

In groups

1. Come up with two causal claims; one corresponding each of the preceding two questions

2. Restate each causal claim as a counterfactual claim.

Varieties of Causal Claims

Two ways of asking causal questions

Usually… different kinds of causal questions are answered with different kinds of causal claims

  1. causes of effects \(\to\) deterministic causal claims
  2. effects of causes \(\to\) probabilistic causal claims

Deterministic Causal Claims

deterministic causal claims

  • claims about what happenens with certainty under specific causal conditions
  • whenever some cause (or set of causes) is present, the effect always happens
    • if the cause is present the effect is determined (unavoidable)
  • usually make these claims when we are interested in causes of effects

Deterministic Causal Claims

There are several varieties and combinations

  • necessary conditions
  • sufficient conditions
  • conjunctural/multiple causation

Necessary Conditions

necessary conditions

A causal claim that there is some cause \(C\) without which the effect cannot occur

  • A cause \(C\) must happen in order for effect \(E\) to happen.
  • Does not mean if the cause \(C\) is present, effect \(E\) must happen, only without \(C\), no \(E\).

Necessary Conditions: Example

A claim: “Without global air travel, a new infectious disease will not become a global pandemic.”

Also can be stated: “Global air travel is a necessary condition for a new disease to become a pandemic.”

Map of Air Travel in 2015


Necessary Conditions: Example

If this claim is true: “Global air travel is a necessary condition for a new disease to become a pandemic.”…

Does the graph on preceding page imply that a new infectious disease will become a pandemic?

  • No. Presence of necessary condition \(\not\to\) effect must happen. Instead, absence of necessary condition \(\to\) effect does not happen

Sufficient Conditions

(In contrast to necessary conditions)

sufficient conditions

  • cause \(C\) always produces an effect \(E\) when it is present
  • do not depend on other factors being present; cause \(C\) can produce \(E\) by itself
  • Sufficient conditions imply: every time \(C\) is present, then \(E\) will happen

Sufficient Conditions: Example

“A military coup that overthrows a democratically elected government is a sufficient condition for large public protests.”

  • This might be the case every time
  • Does not appear to depend on other factors

Generally, single causes that are sufficient conditions are rare in social sciences

Things are usually more complicated

BC vs. Washington State

Since the pandemic has begun, BC has had a 27.4 COVID deaths per 100000 people. Washington State, directly across the US border to the south, has had 67.5 COVID deaths per 100000 people.

In your group, propose an answer: What caused BC to have a lower COVID death rate than Washington State?

Complex Causality

Causality may be deterministic… there are exact conditions for when effect always/never happens.

But in reality, it is almost always complex

  • multiple factors might be necessary (conjunctural)
  • different causes produce same effect (multiple)
  • different groups of factors might, together be sufficient (multiple and conjunctural)
  • (INUS/SUIN conditions: see here)

Voting Experiment

Why do people vote?

Voting Experiment


Complex Causality

Does it make sense to say that “being shamed” is a necessary condition for voting?

  • No. Clearly some people voted in absence of shaming

Does it make sense to say that “being shamed” is a sufficient condition for voting?

  • No. Some people were shamed but did not vote.
  • It is simpler to state this probabilistically: being shamed increases likelihood of voting.

Probabilistic Causal Claims

probabilistic causal claims

are claims that the presence/absence of a cause \(C\) makes an effect \(E\) more or less likely to occur. Or cause \(C\) increases/decreases effect \(E\) on average

  • In contrast to deterministic causal claims this implies
    • effect \(E\) can happen when \(C\) is absent
    • effect \(E\) may not happen when \(C\) is present
  • NOT a claim that politics has some inherent randomness (e.g. quantum mechanics)
  • Usually make these claims when interested in effects of causes

Interlude: Coin flips:

Interlude: Coin flips: