I have a hard time understanding what counterfactuals are actually useful for. To me, they seem to be answering the wrong question. In your book, you give at least a couple of different reasons for when one would need the answer to a counterfactual question, so let me tackle these separately:

1. Legal questions of responsibility. From your text, I infer that the American legal system says that a defendant is guilty if he or she caused the plaintiff's misfortune. You take this to mean that if the plaintiff had not suffered misfortune had the defendant not acted the way he or she did, then the defendant is to be sentenced. So we have a counterfactual question that needs to be determined to establish responsibility. But in my mind, the law is clearly flawed. Responsibility should rest with the predicted outcome of the defendant's action, not with what actually happened. Let me take a simple example: say that I am playing a simple dice-game for my team. Two dice are to be thrown and I am to bet on either (a) two sixes are thrown, or (b) anything else comes up. If I guess correctly, my team wins a dollar, if I guess wrongly, my team loses a dollar. I bet (b), but am unlucky and two sixes actually come up. My team loses a dollar. Am I responsible for my team's failure? Surely, in the counterfactual sense yes: had I bet differently my team would have won. But any reasonable person on the team would thank me for betting the way I did. In the same fashion, a doctor should not be held responsible if he administers, for a serious disease, a drug which cures 99.99999% of the population but kills 0.00001%, even if he was unlucky and his patient died. If the law is based on the counterfactual notion of responsibility then the law is seriously flawed, in my mind.

   A further example is that on page 323 of your book: the desert traveler. Surely, both Enemy-1 and Enemy-2 are equally 'guilty' for trying to murder the traveler. Attempted murder should equal murder. In my mind, the only rationale for giving a shorter sentence for attempted murder is that the defendant is apparently not so good at murdering people so it is not so important to lock him away... (?!)

2. The use of context in decision-making. On page 217, you write "At this point, it is worth emphasizing that the problem of computing counterfactual expectations is not an academic exercise; it represents in fact the typical case in almost every decision-making situation." I agree that context is important in decision making, but do not agree that we need to answer counterfactual questions.

   In decision making, the things we want to estimate is P(future | do(action), see(context) ). This is of course a regular do-probability, not a counterfactual query. So why do we need to compute counterfactuals?

   In your example in section 7.2.1, your query (3): "Given that the current price is P=p₀, what would be the expected value of the demand Q if we were to control the price at P=p₁?". You argue that this is counterfactual. But what if we introduce into the graph new variables Qtomorrow and Ptomorrow, with parent sets (U₁, I, Ptomorrow) and (W,U)2,Qtomorrow), respectively, and with the same connection-strengths d₁, d₂, b₂, and b₁. Now query (3) reads: "Given that we observe P=p₀, what would be the expected value of the demand Qtomorrow if we perform the action do(Ptomorrow=p₁)?" This is the same exact question but it is not counterfactual, it is just P(Qtomorrow | do(Ptomorrow=p₁), see(P=P₀)). Obviously, we get the correct answer by doing the counterfactual analysis, but the question per se is no longer counterfactual and can be computed using regular do( )-machinery. I guess this is the idea of your 'twin network' method of computing counterfactuals. In this case, why say that we are computing a counterfactual when what we really want is prediction (i.e. a regular do-expression)?

3. In the latter part of your book, you use counterfactuals to define concepts such as 'the cause of X' or 'necessary and sufficient cause of Y'. Again, I can understand that it is tempting to mathematically define such concepts since they are in use in everyday language, but I do not think that this is generally very helpful. Why do we need to know 'the cause' of a particular event? Yes, we are interested in knowing 'causes' of events in the sense that they allows us to predict the future, but this is again a case of point (2) above.

   To put it in the most simplified form, my argument is the following: Regardless of if we represent individuals, businesses, organizations, or government, we are constantly faced with decisions of how to act (and these are the only decisions we have!). What we want to know is, what will likely happen if we act in particular ways. So we want to know is P(future | do(action), see(context) ). We do not want nor need the answers to counterfactuals.

Where does my reasoning go wrong?

Author reply

1. Your first question doubts the wisdom of using single-event probabilities, rather than population probabilities in deciding legal responsibility. Suppose there is a small percentage of patients that are allergic to a given drug, and the manufacturer nevertheless distributes the drug with no warning about possible allergical reaction. Wouldn't we agree that when an allergic patient dies he is entitled to compensation? Normally, drug makers take insurance for those exceptional cases, rather than submit the entire population to expensive tests prior to taking the drug -- it pays economically. The physician, of course, is exonerated from guilt, for he/she just followed accepted practice. But the law makes sure that someone pays for the injury if one can prove that, counterfactually, the specific death in question would not have occured had the patient not taken the drug.
2. Your second question deals with decisions conditioned on observations. Or, as you put it:

   "In decision making, the things we want to estimate is P(future | do(action), see(context)). This is of course a regular do-probability, not a counterfactual query. So why do we need to compute counterfactuals?"

   The answer is that, in certain cases, the variables entering into "context" are CONSEQUENCES of the "action", and the expression P(y|do(x), z) is defined as the probability of y given that we do X=x and LATER observe Z=z, which is not the probability of y given that we first observe Z=z and then do X=x.

   This confusion disappears of course when we have a sequential, time-indexed model. But, working with static models as in my book, we we we do not have the language to express the probability P of Y=y given that we first observe Z=z and then do X=x. Counterfactuals give us a way of expressing this probability, by writing

   P = P (y_x | z). Note that P = P (y_x | z) = P(y|do(x), z) if z is a non descendant of x.

   I have elaborated on this point in
   Pearl, J., ``The logic of counterfactuals in causal inference (Discussion of `Causal inference without counterfactuals' by A.P. Dawid),'' Journal of American Statistical Association, Vol. 95, No. 450, 428--435, June 2000.

3. Your third question seeks a decision-theoretic interpretation of the "actual cause" -- there is none. The "actual cause" is defined solely by human intuition. It is a linguistic notion often used in practical discourse, and the task of Chapter 10 is to capture that intuition mathematically.

Thanks for your illuminating questions. I hope that they, together with my attempted answers will help other readers with similar difficulties.

Best wishes,
========Judea Pearl

Date: February 22, 2006
From: Dr. Patrik Hoyer (University of Helsinki, Finland)
Subject: The meaning of counterfactuals

On Question 1
My view on your example is that if the drug company followed the law in doing all the required tests, not "cutting corners," not silencing early results showing strange results, not hiding information, etc etc, then I would not consider the company responsible for the death. Rather, I would consider it an accident, similar to the damage cause by an earthquake, a tornado, or a car-crash due to an elk crossing the street. Nobody would be legally responsible for the death, but of course the family could get insurance money from a private (or public-sector) insurance against accidental death.

Of course, had the company deliberatly tried to silence strange test results, or not done all the tests required, or in some other way broken the law for how medicines should be developed, then the company (and in particular the people responsible for the practice within the company) should be held responsible.

On question 2
My notion of causality is strongly tied to the notion of time, so I have a hard time with your explanation.

First, isn't a "sequential, time-indexed model" really what we would like? At least it fits nicely with my intuition about causality; much better than any 'static' model. So, if counterfactuals are not needed in such a model then in my mind they are not needed at all...

Second, again my intuition of causality is so strongly connected to time that I can't understand how one can first observe Z and then do X if Z is a descendant of X. If this is physically possible then I would call the new controlled variablel X' and then of course Z is not a descendant of X' (since Z happens before X') and again we can get by with regular do-probabilities.

Author Reply On Question 2
A static model IS a short-hand notation for a "sequential, time-indexed model". When an engineer draws a circuit diagram, he is building a static model, which saves miles and miles of drawing the sequential model equivalent. The meaning of the static model is

where M_i stand for the model at time t_i, and M₁ = M₂ = ....M_n

Now, suppose in M₂ we have a chain of gates we observe Z₃ at time t3 and we want to know the causal effect of X4 on Y₅ . We can do this exercise through do-calculus, with all the necessary indices and the replicated models. But we can do it much nicer in the static model, using counterfactuals. P(Y_x = y | z) will give us the correct answer.

Isn't it a nice invention??

You say:

So, if counterfactuals are not needed in such a model then in my mind they are not needed at all...

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