Causal Reasoning

Brandon, who studies David Hume, and has probably forgotten more about his work than I will ever know, wonders about the treatment of some of Hume's issues in cognitive science. Now, since I'm no expert on Hume, I can't do much to relate cognitive research to Hume's philosophy, but I can say a little about what cognitive scientists think about causal reasoning.

More than 250 years ago, David Hume wrote:

All reasonings concerning matter of fact seem to be founded on the realtion of Cause and Effect... I shall venture to affirm, as a general proposition, which admits of no exception, that the knowledge of this relation is not, in any instance, attained by reasonings a priori; but arises entirely from experience, when we find that any particular objects are constantly conjoined with each other.

For the most part, since the inception of experimental psychology in the 19th century, this is how psychologists have believed that people reason about causes and effects, as well. To this day, the most prominent models of causal reasoning argue that the primary type of information used in detecting causes and effects is co-occurence information.

Among the co-occurence based accounts of causal reasoning in cognitive science, there have been two general types: associationist and probabilistic. Associationist models, inherited from behaviorism, argue that the processes involved in causal reasoning are similar to those involved in classical conditioning. In fact, the most widely cited associationist model of causal reasoning was originally designed to model Pavlovian conditioning¹. The model looks like this:

ΔV_C,O = αβ(λ - ΣV_S,O)

In which V_C,O represents the associative strength between a cue, C, and an outcome, O. The salience of the cue and outcome are represented by the two parameters, α and β, λ represents the outcome of a single trial (if O, λ = 1; 0 otherwise) and ΣVS,Ois the set of all cues for outcome O (for all you math people, yes, there should be a little s under the sigma, but I'll be damned if I know how to do that). In other words, the associative strength between a cue and an outcome is equal to the difference between the outcome on the present trial (λ) and the expected outcome based on all of the co-occurence information from all trials, weighted by the salience of the salience of the cue and outcome.

Needless to say, there is a problem with this model when it is used to describe causal reasoning. Under this view, the repeated co-occurence between a cue and outcome is sufficient to establish a causal connection. However, as we all know, correlation is not causation, and people are generally pretty good at distinguishing mere co-occurences from causal relationships. For instance, every morning, without fail, when I leave my apartment my nextdoor neighbor is standing outside waiting for his dog to do its business. The associative strength of the cue (me leaving in the morning) and outcome (my neighbor walking his dog) would be 1, but I've never believed that my leaving causes my neighbor to be outside walking his dog. This is because I have some knowledge of likely causes (the dog has been holding it all night, and my neighbor has to take him out first thing to make sure he doesn't pee on the carpet).

In order to capture this fact, co-occurence theories have more recently begun to model causal reasoning using Bayesian techniques. The most prominent of these is the probabilisic contrast model, and its more recent supplement, the causal power theory. The probabilistic contrast model represents causal strength (ΔP) with²

ΔP = P(E|C) - P(E|~C)

in which P(E|C) represents the probability of an event (E) occurring with a cue (C) and P(E|~C) representing the probability of the event when the cue does not occur. Thus, the causal relation between an event and a cue is determined by subtracting the probability of the event occurring without the cause from the probability of it occurring with it. Because this equation alone can ultimately lead to the same problem that doomed the associationist models (co-occurence doesn't always signal causation), the causal power theory was added onto it³. This states that the causal power of a cue, C, is a function of the causal strength ΔP divided by 1 - P(E|~C), at least in the case that C causes E to occur (there are other versions for other situations, such as when C tends to cause E not to occur). This addition helps to explain situations in which two events co-occur with a high frequency, but are not treated as causally related, by making the causal power dependent on the value of P(E|~C), or on the probability that one of the events will occur without the other. While different probabilies of one event occuring without another can yield equal causal strengths, the causal power will be different if P(E|~C) is different.

Others have dealt with the problems of the associationist and probabilistic contrast model (sans causal power theory) by introducing the concept of causal mechanisms. Consider the following (true) story⁴:

The number of never-married persons in certain British villages is highly inversely corelated with the number of field mice in the surrounding meadows. [Marriage] was considered an established cause of field mice by the village elders until the mechanisms of transmission were finally surmised: Never-married persons bring with them a disproportionate number of cats.

According to Glymour⁵, this example illustrates a co-occurence (between the number of "never-married persons" and the number of field mice) that is mediated by a mechanism (the number of cats). A mechanism is thus a cue which, if removed, will cause the correlation between another cue and an outcome to disappear. This method allows us to bring in explicit background knowledge about the relationships between different potential causes and outcomes in order to explain co-occurence relationships that are not causal.

While co-occurence theories have dominated since Hume, recent empirical evidence has called their viability into question. For instance, Dennis and Ahn⁶ have shown that the perceived causal strength between two events differs for depending on the initial information people receive. If people first receive information suggesting that one event causes another to occur, they will perceive the causal strength as being higher than if they initially receive information suggesting that the same event causes another not to occur, despite the fact that over the course of the study, participants received the same co-occurence information. In another study⁷, they showed that when participants are presented with co-occurences of two events, A and B, and co-occurences between B and a third event, C, they will infer a causal relationship between A and C, despite the fact that these two events never occurred with each other.

Due to these results, and others, researchers have begun to develop theories of causal reasoning that depend on information other than co-occurence. In these theories, co-variance information is still important, but it is secondary to, and dependent on background knowledge.The earliest of these was the causal-model theory⁸, of which Lagnado et al. wrote⁹:

According to this proposal causal induction is guided by top-down assumptions about the structure of causal models. These hypothetical causal models guide the processing of the learning input. The basic idea behind this approach is that we rarely encounter a causal learning situation in which we do not have some intuitions about basic causal features, such as whether an event is a potential cause or effect. If, for example, the task is to press a button and observe a light, we may not know whether these events are causally related or not, but we assume that the button is a potential cause and the light is a potential effect. Once a hypothetical causal model is in place, we can start estimating causal strength by observing covariation information. The way covariation estimates are computed and interpreted is dependent on the assumed causal model. (p. 6-7)

Lagnado et al. provide a (non-exhaustive) list of four possible sources of information used in causal reasoning, (statistical) covaration, temporal order, intervention (by which they mean that human action on the world is a source of both specific causal knowledge and our general conception of causality), and prior knowledge. These four sources, along with others, could be used on conjunction with each other, especially in cases where there are conflicts.

A second theory in which information about co-variation comes after, or is dependent upon, other types of knowledge is the mechanism view of Ahn and Kalish¹⁰. This view arises out of the intuition that people's concept of cause has as a component the concept of force, or causal power. They write:

We believe that the core component of the idea of "cause" is a sense of force. If A causes B, then A makes B happen, or Be had to happen given A. It was no accident. It is this sense of necessity that distinguishes genuine causal relations from mere correlations. (p. 200-201)

Under their view, prior to other types of information such as co-occurrence, we have theory-like beliefs about causes in general (specifically, that causal powers are involved in causation, and that causation is a process), and specific causal relationships. They give the example of germs causing illness, writing:

Consider getting sneezed on and getting sick. If people think the sneeze is the cause, then they also believe that there must have been a basic process or mechanism by which the sneeze forced the illness to come about. In modern Western cultures, we typically understand the mechanism to be infection; getting sneezed on infects you with germs that make you sick. A relatively elaborate notion of the mechanism might include the ideas that germs posses the causal power to make a person sick, that the person's immune system has causal powers to counteract germs, and that the person's immune system can be weakened by lack of sleep. (p. 201)

One of the benefits of this approach is that in addition to providing an explanation of causal induction, for which most of the co-occurence models are designed, it also provides a straightforward explanation of causal abduction. In abduction, we have knowledge of the occurence of an effect, and we must make an inference about its cause. These inferences will, in most cases, be constructed through a sort-of hypothesis testing process, in which we compare possible explanations, seek more information based on the hypotheses we are considering, and pick decide on our best guess. This process is likely to involve a great deal of theory-like knowledge of the interconnections between events that go beyond mere co-occurence.

In support of this view, Ahn et al.¹¹ conducted a series of experiments in which participants were able to elicit different types of information as they attempted to determine the cause of an event. In three separate experiments, participants almost always sought information about causal mechanisms, as opposed to co-occurrence information, and

To sum everything up, co-occurence theories of causal reasoning have dominated psychology for more than a century, and philosophy even longer. These theories posit that people use co-occurence information exclusively when reasoning about causal relationships. However, the day of co-occurence may be coming to an end. Recent empirical studies have produced findings that are difficult to reconcile with co-occurence theories. Instead of attempting this, some theorists have begun to develop alternative models in which co-occurence information still plays a role, but takes a back seat to other types of knowledge about causal relations. I wish I were qualified to relate these more recent views to Hume's own arguments, but I'm afraid that I would fail miserably. In closing, I will note that, considered from the perspective of philosophy, there is much in the Ahn and Kalish account that resembles the work of Wesley Salmon on causation (e.g., the focus on causal power and the treatment of causation as a process), which was developed, in large part, to overcome some of the problems raised by Hume.

¹ Rescorla, R. A., & Wagner, A. R. (1972). A theory of Pavlovian conditioning: Variations in the effectiveness of reinforcement and nonreinforcement. In A. H. Black & W. F. Prokasy (Eds.), Classical conditioning II: Current theory and research (pp.64-99). New York: Appleton-Century-Crofts.
² Cheng, P. W., & Novick, L. R. (1990). A probabilistic contrast model of causal induction. Journal of Personality and Social Psychology, 58, 545-567.
³ Cheng, P. W. (1997). From covariation to causation: A causal power theory. Psychological Review, 104, 367- 405.
⁴ Baumrind, D. (1983). Specious causal attributions in the social sciences: The reformulated stepping-stone theory of heroin use as exemplar. Journal of Personality and Social Psychology, 45, 1289-1298.
⁵ Glymour, C. (1998). Learning causes: Psychological explanations of causal explanation. Minds and Machines, 8, 39-60.
⁶ Dennis, M.J., & Ahn, W. (2001). Primacy in causal strength judgements: The effect of initial evidence for generative versus inhibitory relationships. Memory and Cognition, 29(1), 152-164.
⁷ Ahn, W., & Dennis, M.J. (2000). Induction of causal chains. Proceedings of the Twenty-second Annual Conference of the Cognitive Science Society, (pp. 19–24). Mahwah, NJ: Erlbaum.
⁸ Waldmann, M.R., & Holyoak, K.J. (1992). Predictive and diagnostic learning within causal models: Asymmetries in cue competition. Journal of Experimental Psychology: General, 121, 222-236.
⁹ Lagnado, D., Waldmann, M.R., Hagmayer, Y., & Sloman, S.A. (In Press). Beyond Covariation: Cues to Causal Structure. In A. Gopnik and L.E. Schultz (eds.). Causal Learning: Psychology, Philosophy, and Computation. In the chapter, they provide empirical justifications for the inclusion of each of these, and if you are interested in the topic, I highly recommend reading it.
¹⁰ Ahn, W., & Kalish, C.W. (2000). The role of mechanism beliefs in causal reasoning. In F.C. Keil and R.A. Wilson (eds.), Explanation and Cognition (pp. 199-226).
¹¹ Ahn W., Kalish C.W., Medin D.L,. Gelman S.A (1995). The role of covariation versus mechanism information in causal attribution. Cognition, 54(3), 299-352.