Woodward on Invariance across Background Conditions

One of Woodward’s most important contributions to the study of causation is his introduction of the notion of invariance across background conditions. Woodward’s ideas on this topic have had a major influence on experimental research in causal cognition (including on my own work), and I thought it might be helpful to do a little bit to help bring out the importance of this contribution.

First off, what exactly is invariance across background conditions? Perhaps the easiest way to convey the basic idea is to introduce a simple example. Suppose that Samantha lives in a deeply racist society. In this society, if you have dark skin, people will deny you educational opportunities, and you will therefore be illiterate. Samantha has certain genes that give her dark skin, so she is denied educational opportunities, and she becomes illiterate. 

Suppose we now consider two different variables: Samantha’s genes (G) and her literacy (L). What we find is that, given the precise way that things are set up in the actual world, there is indeed a connection between these variables: an intervention on G will lead to a change in L. However, suppose we now consider a third variable: the presence of racism in the society (R). Then we can say that the connection between G and L is not invariant over R. There just happens to be a connection between Samantha’s genes and her literacy in the actual world because of the presence of racism, but if there weren’t any racism, there wouldn’t be any connection between these two variables. Woodward’s introduction of this concept has done a tremendous amount to shape contemporary research in causal cognition, and at this point, I think it’s fair to say that we have very strong evidence that people do indeed engage in a cognitive process that involves checking for invariance across background conditions. 

But now it seems that we face a further question. When people are thinking about the causal connection between two variables, they couldn’t possibly think about invariance across all possible background variables. They have to think about some variables and not others. So then, in people’s ordinary causal cognition, which particular variables do people consider when they are checking for invariance across background conditions?

One obvious initial hypothesis would be that the answer follows naturally from people’s beliefs about the probability of possibilities. For example, suppose that people represent the example we’ve been discussing here using a Bayes net, as follows:

P(R) = .99

P(G) = .5

P(L | R, G) = .9 – .85RG 

In this example, we are assuming that people think it is extremely improbable that the society has no racism. In other words, it is true that Samantha’s genes would have no impact on her literacy if society were not racist, but it is extremely improbable that society would not be racist, so the probability that we would be in a situation in which the causal connection between these two variables did not hold is extremely low.

Now, one natural hypothesis would be that if people think that this is the way the world actually works, they will be relatively unconcerned about whether the causal connection is invariant across that particular background variable. This hypothesis might sound plausible in theory, but actual empirical studies consistently find that things actually don’t work like that at all. Instead, it seems that we need to be thinking about a different sort of probability. We need to be thinking about probabilities of people thinking about possibilities. This is not just the same thing as the sort of probability discussed above. In certain cases, people believe  that a certain possibility is extremely improbable, but all the same, there’s a very high probability that people will think of that possibility.

Most importantly for present purposes, people’s probability  of thinking about a possibility seems to be shaped by their value judgments. If you think that a certain possibility is good or right, you will be more inclined to think of that possibility, even controlling for the degree to which you believe that there is a high probability that it will actually be realized. Thus, in our own work, we find that the probability of thinking about a given possibility x is approximately proportional to F(x)eV(x)/t, where F(x) is the person’s belief about how frequent x is, V(x) is the person’s belief about how valuable x would be, and t is a temperature parameter.

With all that in mind, let’s consider again how to apply Woodward‘s theory of invariance across background conditions to the case of a person growing up in a racist society. You might believe that it is extremely improbable that the society would not be racist, but all the same, you might believe that it would be deeply valuable for the society to not be racist. For this reason, despite your beliefs about the probabilities, you will be drawn to think about possibilities in which the society is not racist. The result is that when you are considering the connection between G and L, you will be drawn to ask whether it would still hold in possibilities in which R = 0. Since it does not, you will be inclined to think that Samantha’s genes are not genuinely the cause of her illiteracy. 

The cognitive processes here, I have been suggesting, cannot be explained just in terms of the probabilities people assign to values of the background variables. Instead, they are fundamentally bound up with the value judgments people make about values of the background variables. 

One comment

  1. James Woodward

    First of all I would like to thank Josh Knobe very much for his comments. One of the pleasures of working on causal cognition is that, as CHF tries to bring out, this topic is tailor-made for productive interactions between those who work on more theoretical or normative treatments of causation (both in philosophy and elsewhere) and empirical work on the psychology of causal cognition. Josh’s own research is a distinguished example of this: he and collaborators have developed formal models of causal judgment (particularly causal selection) and they then have tested such models as well as competitors against experimental investigations of how people actually judge. In doing so, they have discovered new “effects” in causal judgment such as “abnormal deflation” and which are predicted by their formal model (Icard et al. 2018 . One of the things that is most striking about this work is that despite the huge philosophical literature exploring people’s judgments about various scenarios, philosophers seem not to have noticed this particular effect (or for that matter, others which I discuss in CHF). This illustrates how the combination of a predictive theory and experiments can lead to empirical discoveries that likely otherwise not been made.

    Josh’s work has also emphasized that both more theoretical considerations and experimental results support a role for norms in causal judgment– this is one of the ideas in his commentary. In his example, Samantha lives in a society in which there is strong racial prejudice against people with dark skin like hers, with such people being denied access to education which produces literacy. As Josh notes, in such a case, the relation between Samantha’s genes for dark skin and her illiteracy satisfy a minimal interventionist condition for causation. Nonetheless most of us will balk at the suggestion that (1) these genes cause her illiteracy or at least regard this causal claim as (choose your word)– highly misleading or defective in some way. As Josh explains, CHF traces this judgment of defectiveness to the fact that (1) is relatively non-invariant under changes in background conditions– in a society in which there was no racial prejudice (1) would not be true.

    As an aside, let me remark that an example like this (but with prejudices against redheads) was used by the sociologist Christopher Jencks some years ago to illustrate the limitations of standard measures of heritability (h2). In Samantha’s society, illiteracy is highly heritable — h2 is close to 1.0 and there is a minimal sense in which the connection between her genes and her illiteracy is causal. But h2 is completely insensitive to considerations of invariance and in this respect fails to reflect an important part of what we care about when we make judgments about genetic causation. Examples of this sort are well known to geneticists under the characterization “reactive GXE correlation”, although in my view these are not cases of mere non-causal correlation.

    Background invariance has to do with stability of a relationship under changes in background circumstances. But, Josh asks (and this is a very good question) which background circumstances do we consider or pay attention to in making such judgments? Chapters 5 and 6 in CHF explore this question and attempt to provide a partial answer. First, I agree with Josh’s claim that this is not just a matter of considering those changes in background conditions which are most probable. The experimental evidence (some of it due to Tania Lombrozo and colleagues) supports the claim that people also attend to which background changes are thought possible, independently of their probabilities. Second I agree with Josh that “norms” including moral norms influence which possible changes in background conditions we attend to, and this is presumably part of what is at work in the Samantha example (and also one reason, as noted in response to Thomas’ commentary, it can be hard to separate the roles of normality and invariance considerations). I also think, however, that other considerations that are less naturally regarded as having to do with “norms” can also play a role– for example, as argued in CHF, in “scientific” examples, discipline-specific considerations can play a role.

    Finally note how, at least in my view, norm-based considerations enter. The judgment that such and such a causal relation is invariant under changes of sort X is an “objective” matter that does not depend on one’s moral values. Instead one’s moral values influence which changes of sort X one pays attention to.

    Icard, T., Kominsky, J. and Knobe, J. (2017) “Normality and Actual Causal Strength” Cognition 161: 80-93.

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