Causal Analysis in Theory and Practice

May 31, 2010

An Open Letter from Judea Pearl to Nancy Cartwright concerning “Causal Pluralism”

Filed under: Discussion,Nancy Cartwright,Opinion,structural equations — moderator @ 1:40 pm

Dear Nancy,

This letter concerns the issue of “causal plurality” which came up in my review of your book “Hunting Causes and Using Them” (Cambridge 2007) and in your recent reply to my review, both in recent issue of Economics and Philosophy (26:69-77, 2010).

My review:

Cartwright Reply:

I have difficulties understanding causal pluralism because I am a devout mono-theist by nature, especially when it comes to causation and, although I recognize that causes come in various shades, including total, direct, and indirect causes, necessary and sufficient causes, actual and generic causes, I have seen them all defined, analyzed and understood within a single formal framework of Structural Causal Models (SCM) as described in Causality (Chapter 7).

So, here I am, a mono-theist claiming that every query related to cause-effect relations can be formulated and answered in the SCM framework, and here you are, a pluralist, claiming exactly the opposite. Quoting:

“There are a variety of different kinds of causal systems; methods for discovering causes differ across different kinds of systems as do the inferences that can be made from causal knowledge once discovered. As to causal models, these must have different forms depending on what they are to be used for and on what kinds of systems are under study.

If causal pluralism is right, Pearl’s demand to tell economists how they ought to think about causation is misplaced; and his own are not the methods to use. They work for special kinds of problems and for special kinds of systems – those whose causal laws can be represented as Pearl represents them. HC&UT argues these are not the only kinds there are, nor uncontroversially the most typical.

I am very interested in finding out if, by committing to SCM I have not overlooked important problem areas that are not captured in SCM. But for this we need an example; i.e., an example of ONE problem that cannot be formulated and answered in SCM.

The trouble I have with the examples sited in your reply is that they are based on other examples and concepts that are scattered on many pages in your book and, thus, makes it hard to follow. Can we perhaps see one such example, hopefully with no more than 10 variables, described in the following format:

Example: An agent is facing a decision or a question.

Given: The agent assumes the following about the world: 1. 2. 3. ….
The agent has data about …., taken under the following conditions.
Needed: The agent wishes to find out whether…..

Why use this dry format, you may ask, when your book is full with dozens of imaginative examples, from physics to econometrics? Because if you succeed in showing ONE example in this concise format you will convert one heathen to pluralism, and this heathen will be grateful to you for the rest of his spiritual life.

And if he is converted, he will try and help you convert others (I promise) and, then, who knows? life on this God given earth would become so much more enlightened.

And, as Aristotle used to say (or should have) May clarity shine on causality land.


Judea Pearl


  1. I don’t know if this is connected at all to your debate with Cartwright, but I was wondering how you see the following sorts of problems fitting with the DO calculus. Suppose an agent wants to know what the world would be like if a variable were removed from a system — not just have its value set to zero or to a default value, but removed from the system altogether. How is that specified in the DO calculus? Or suppose an agent wants to know what the world would be like if a variable were denatured, say by adding a new value to the admissible values for that variable. Does the DO calculus consider these kinds of “second-order” questions?

    Comment by Jonathan Livengood — July 8, 2010 @ 8:44 am

  2. To be concrete, suppose Agent is thinking about a small election — say for the graduate student representative of a smallish department having ~25 students. Agent thinks that everyone will try to maximize expected utility and (to make things simpler) also thinks that everyone votes independently of everyone else. Moreover, Agent has lots of data about the preferences of the potential voters. Agent wants to know what difference it will make to the outcome of the election if a third candidate is added to the ballot (which currently includes only two candidates). I can see two ways of modeling this scenario. Way #1: start with a graph that has an edge from each voter to a node for the outcome and then add a new variable describing the number of candidates to be admitted, also with an edge into the outcome. Way #2: start with the same graph as in Way #1 but allow interventions on the nature of the outcome variable. Way #2 seems preferable to me, but it doesn’t look like a problem that is well-described by setting a variable to a value. Is there a strong reason to prefer something along the lines of Way #1? Or am I making a mistake (in Way #2) with respect to how the DO calculus works?

    Comment by Jonathan Livengood — July 12, 2010 @ 12:50 pm

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