Cause and Intent: Social Reasoning in Causal Learning
Noah D. Goodman, Chris L. Baker, Joshua B. Tenenbaum{ndg, clbaker, jbt}@mit.edu
MIT, Dept. of Brain and Cognitive Sciences
Abstract
The acquisition of causal knowledge is a primary goal of childhood; yet most of this knowledge is known already to adults.
We argue that causal learning which leverages social reasoning is a rapid and important route to knowledge. We present
a computational model integrating knowledge about causality
with knowledge about intentional agency, but using a domaingeneral mechanism for reasoning. Inference in this model predicts qualitatively different learning than an equivalent model
based on causality alone or a hybrid causal-encoding model.
We test these predictions experimentally with adult participants, and discuss the relation of these results to the developmental phenomenon of over-imitation.
Keywords: Causal learning, social cognition, Bayesian modeling, imitation.

Introduction
How do children acquire conceptual knowledge? One answer
is that children are adept at rational inference from direct
experience with the world—children as scientists (Gopnik,
Meltzoff, & Kuhl, 1999). Human culture suggests another answer: the quickest route to conceptual knowledge may be bylearning what others already know (Tomasello, 1999; Gergely& Csibra, 2006). Indeed, a vast majority of the knowledge
that a child will acquire is already known by adults in theirsociety. This suggests that children come equipped with social learning mechanisms to encode the knowledge of adults(Lyons, Young, & Keil, 2007). We suggest a middle groundbetween these two views: that an understanding of intentional
agency makes it possible to use social context as a source ofevidence to enable rapid learning without requiring dedicatedpsychological mechanisms.
Among the most profound achievements of human knowledge is an understanding of causal structure in the world; notcoincidentally, causality has been a major area of research
into children’s ability to learn from evidence (Gopnik et al.,2004). In this paper we therefore focus on the acquisitionof causal knowledge in a social, but non-linguistic, setting.
To explore the hypothesis that social learning emerges fromthe interaction, under domain-general inference processes,of existing conceptual structures, we construct a computational model integrating social and causal representations.
Recent modeling of human causal reasoning has focused on
the causal Bayes nets approach (Pearl, 2000; Gopnik et al.,2004). This view helps explain how causal learning can succeed based on observed co-occurance between events andwell-chosen interventions. The interventions, however, aretreated as unexplained actions on a system. In contrast, recent
models of intuitive psychology have focused on the selection of actions by agents given their goals and beliefs (Baker,
Tenenbaum, & Saxe, 2007; Goodman et al., 2006), but treatedthe structure of the world as background knowledge available to all agents. We combine these modeling approaches byconstructing a model of intuitive psychology in which beliefs
about the causal structure of the world are represented andused for action selection, and showing how such an intuitive
theory of causal-agency can explain the source of interventions and speed causal learning.
We test this model experimentally by studying adult intuitions in a set of scenarios that provide both social and causal
information. These scenarios are chosen to distinguish between the combined social-causal model and two alternatives:a similar causal-only model, and a hybrid gated-inference
model. We then use these results to explain a puzzling phenomenon of imitation-based learning in children.

Computational modeling
Our goal is to construct a formal model which simultaneously
represents knowledge about causality and knowledge about
intentional agency, and to explore how Bayesian inference
over the combination differs from inference over each piecein isolation. Knowledge can be represented as probabilistic generative models; Bayesian inference then “inverts” thisgenerative knowledge, specifying appropriate beliefs about
latent states given observed evidence. We begin by recallingstandard generative models capturing (aspects of) causality
and intentional agency, then describe how they may be integrated, and finally describe predictions of the resulting model.
Causality A causal Bayes net (CBN) model describes theprobability P(E|A, S) of observing a set of events E, given
the causal structure S, and the interventions, or exogenous
actions, A (Fig. 1a). More formally, a CBN consists of a directed acyclic graph on a set of variables, together with a
specification of the probabilistic dependence of each variable
on its parents in the graph. The variables represent eventsor states, and the edges represent the fact of a causal dependence. For some variables there is an intervention: an exogenous event that forces the variable to a particular value,irrespective of the values of its parents. We will assume thatthe dependencies between variables are described by noisyor functions (each parent is a sufficient cause) or noisy-andfunctions (parents are jointly sufficient and individually necessary); the causal strength of these dependencies, ε, is a fixedparameter. (See Pearl (2000) for more about the formalism
and uses of causal Bayes nets.)
Agency Bayesian decision theory (Berger, 1985) describes
the choices made by a rational agent facing a stochastic decision problem (SDP) (Fig. 1b). A SDP consists of a set of
possible actions the agent may take, a utility function U(E),Causalstructure

Causal Bayes net:
Causalstructure(a)

Events=Belief aboutcausal structure

Desiredoutcome(events, costs)

Stochastic decision process:Actions

Beliefs(b)

Desires

Actions

Actions(c)

EventsFigure 1: Schematic representations of generative models for causality (a), intentional agency (b), and the social-causal combination (c).
Equality between the true causal structure and an agent’s belief about causal structure embodies the knowledgeable agent assumption.

capturing the agent’s desires (reward for each possible outcome E), and a belief function PB (E|A), capturing the agent’s
beliefs about how the world works (the likely outcomes of anaction A). Bayesian decision theory specifies that the agent
should choose an action to maximize her expected utility:
EPB (E|A)U(E). If we assume that agents are only approximately rational, and hence only softly maximize expectedutility:
P(A|U, PB ) ∝ eβ·EPB (E|A)U(E) ,(1)
where the parameter β determines the amount of decision
noise.
Eq. 1 can be used to model the intuitive theory of intentional agency of a person who makes the rational agent assumption (Baker et al., 2007).
Integration In order to capture reasoning about an intentional agent choosing actions based on their causal knowledge, we construct a model which integrates the above approaches to causality and agency. We first assume that theobserved agent represents the world in terms of causal Bayesnet S: the set of outcomes is the set of all possible events(variable values), the set of actions is all combinations of interventions, and the belief function is described by the CBNdependency: PB (E|A)=P(E|A, S). Further, we assume thatthe utility function of the agent splits into a cost, C , for eachintervention made, and a reward, R , for each desired event
achieved.1
This CBN-based stochastic decision problem describes a
simple theory of mind for reasoning about a causal agent—
the intuitive theory one person has about another person’s
causal knowledge, desires, and actions. Note that a person might represent the causal structure of the world via a
CBN, and represent another agent’s beliefs via a second CBN(wrapped inside a SDP). When the interventions that enter
the person’s own causal reasoning are the actions of the otheragent, they need not be treated as unexplained events. Fig. 1c
1 The model described in this section can be easily extended tocapture temporal effects by using dynamic Bayes nets and Markov
decision process models.

represents a combined model in which the interventions of
the CBN have been identified with the actions of the SDP.
We will simplify by making the knowledgeable agent assumption: the beliefs of the observed agent about the causal
structure of the world reflect the true (but unknown to theobserving agent) causal structure of the world. While thisis clearly not always the case, people, and especially children, are often in situations where they can observe the actions of an expert on a novel-to-the-observer causal system.
In Fig. 1c this is represented with the equality between thetrue causal structure of the world and the observed agent’s
beliefs about the causal structure. (It is possible to relax thisassumption, leading to a model which incorporates explicit
reasoning about belief formation and update; see Goodman
et al. (2006) for a related model.)Given this setup, Bayesian inference can be used to infer a causal structure from observation of events and actions
in two ways: assuming only causal knowledge (causal-onlyinference), and assuming both causal and social knowledge(social-causal inference). For causal-only inference, the posterior over causal structures is given by:
Pc (S|A, E) ∝ P(E|A, S)P(S),(2)

where P(S) is the prior probability over causal structures—
we take this to be given by an independent prior probability
P(vi →v j ) that each potential edge is in S.
For social-causal inference the joint posterior over causal
structure, S, and the (unknown) utility function, U, of theagent performing the actions is given by:
Ps-c (S,U|A, E) ∝ P(A, E|S,U)P(S)P(U)∝ P(E|A, S)P(A|S,U)P(S)P(U),(3)

where P(A|S,U) is given by Eq. 1. (Note that the same causal
structure, S, enters both the CBN term and the SDP term of
Eq. 3—this is the knowledgeable agent assumption.) We assume a uniform prior on sets of desired events, which determines P(U). If we are interested in the causal structure alone,

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Posterior probability(c)Causal−only modelSocial−causal modelSocial−causal, strong prior

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Figure 2: Model predictions: the social-causal (a) and causal-only (b) models (both with uniform causal prior: P(A→C)=P(B→C)=0.5),
and (c) the social-causal model with prior disfavoring cause B: P(B→C)=0.15. (In all cases R =6, C =1, ε=0.85.)

Ps-c (S|A, E) = ∑ P(S,U|A, E).

(4)U

Predictions We describe the simplest scenario in which thecausal-only and social-causal models make qualitatively different predictions about causal learning. Imagine a situation
with three causal variables: two potential causes, A and B,
and one potential effect, C. Simultaneous interventions on
A and B are observed, and activation of C follows. To thecausal-only model this is confounded evidence, and it is unable to distinguish possible causal relations2 (Fig. 2b). If weassume, however, that the simultaneous interventions on A
and B are the actions of a knowledgeable agent, the socialcausal model makes the (strong) inference that both A and B
are required to bring about C (Fig. 2a). This inference follows from the tradeoff of costs and goals in the social-causal
model. Informally: the agent wishes to minimize action cost
while achieving a desired outcome, because each interventions has a cost, the most parsimonious inference is that theagent believes both actions are required to bring about her
desired outcome—if her goal is to bring about C, this meansthat she must believe the causal structure is A&B→C.
If the prior probability of cause B is significantly less thanthat of cause A (i.e. P(B→C)P(A→C)) the social-causal
inference model overrides the social inference, instead concluding that A is the only cause of C; Fig. 2c. However,prior beliefs integrate continuously, coming to dominate theinference when they are fairly strong, but influencing inference even when they are weak (Fig. 3). This graded behavior
contrasts with another possible mechanism for incorporating
causal knowledge, the gated-encoding model, in which social context is used for inference, but prior beliefs serve as
a gating mechanism, forming the “boundary conditions” forattention to social context (Lyons et al., 2007).
2 The causal-only model exhibits a slight preference for the structure AorB→C because the evidence is most likely given this structure: either of the events is a sufficient cause of C.

The social-causal inference model has a number of freeparameters—the causal strength ε, the action cost C , the goal
reward R , and the decision noise β—that affect quantitative predictions. However, the qualitative predictions seen in
Figs. 2 and 3 hold over a wide range of parameters. These
predictions differ from the predictions of a causal-only inference model (which is unable to use social information to deconfound ambiguous evidence), and a gated-encoding model(which fails to continuously integrate prior causal knowledge
with social information).
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we can marginalize over these utility functions:

A only
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Figure 3: The graded effect of prior knowledge on inferences of thesocial-causal model.

Experiment: Causal learning in social context
In the following experiment we test the qualitative predictionsof the social-causal model that critically distinguish it fromthe other possible models: that people will use social context
as a source of information to disambiguate confounded causal
evidence (Fig. 2a), that this relies on a knowledgeable agent
assumption (Cf. Fig. 2b), and that this interacts (in a gradedfashion) with prior causal knowledge (Figs. 2c and 3). We
constructed scenarios in which a knowledgeable agent performed two actions (simultaneously) and an effect followed(the Social condition). To show that inferences follow fromrational- and knowledgeable-agent assumptions, and not extraneous non-social factors of the scenarios, we controlledfor mere agency by manipulating the knowledgeability of theactor about the causal system—in the Self condition we described the actions as being taken by “you” (the participant).
Finally, to explore the effect of prior causal knowledge weconstructed a third variant of the scenarios (the Prior condition) in which one of the two actions was relatively implausible as a cause of the effect. To verify that these causes
were implausible we followed the main experiment by eliciting plausibility judgments for each potential causal relation.

MethodParticipants Participants were fifteen members of the MIT
community who received a small compensation for their time.
Materials We constructed a series of scenarios based on the
abstract causal scenario described above. Each scenario consisted of three sentences: (1) setup of scenario, (2) agent/you
performs two actions simultaneously, (3) effect follows. Eachscenario had three variations differing only in the second sentence: in the Social condition the agent performed two equivalent actions, in the Self condition “you” (the reader) perform
two equivalent actions, in the Prior condition the agent performs two dissimilar actions, one of which is an implausible
cause of the effect. In order to rule out the hypothesis that social reasoning effects are peculiar to a single domain (e.g. artifacts), we constructed scenarios drawn from three different
domains: mechanical (artifact), biological, and chemical. In
each domain we constructed three different scenarios, for a
total of nine scenarios. Each of the nine scenarios had threevariants: one for each of the three conditions.
For example, one Social condition scenario in the biological domain was:A (and not B)
B (and not A)
Either A or B (or both together)
Both A and B together (but not either one alone)
C is unrelated to A and B,
with A, B, and C were replaced with the appropriate events.
The order of the response options was consistent for each participant, but randomized between participants.3 Following
the main portion of the experiment participants were asked
to rate the plausibility (on a seven-point scale) of each action
causing the corresponding effect.

Results and discussion

Your coworker simultaneously drinks a yellow liquidand pours a blue liquid on the flowers.

Fifteen (out of 135) responses failed to sum to 100 (neverby more than 10); these responses were normalized to 100.
Ratings on the plausibility check were left blank on two responses; these were omitted from our analyses.
In no condition was there a significant effect of domain; we
collapse across domains for the remaining analyses. Fig. 4
summarizes the causal structure inferences of participants ineach of the three conditions.
Consistent with the predictions of the social-causal model(Fig. 2a), bets placed on “A and B” in the Social condition
were significantly greater than bets placed on any other option (vs. “A only”: t(44)=8.58, p<0.001; vs. “B only”:
t(44)=8.59, p<0.001; vs. “A or B”: t(44)=3.25, p<0.01;
vs. “no relation”: t(44)=8.47, p<0.001). (All t-tests are twotailed and, where appropriate, correlated-samples.) Thus, incontrast to the predictions of a causal-only learning model,
participants infered that A and B together cause C, despite
confounded evidence. To verify that this inference was basedon social context information, we compare the Social condition to the Self condition, in which the knowledgeable agent
assumption should be weakened. Indeed, the “A and B” bets
were significantly less in the Self condition than in the Social
condition (t(44)=3.34, p<0.001), and in the Self condition
there was no longer a significant difference between “A andB” and “A or B” responses (t(44)=1.71, p=0.094)4 .
The prior plausibility check confirmed that the causal relations intended to be implausible were significantly lessplausible than those intended to be plausible (t(44)=19.27,
p<0.001). As predicted (Fig. 2c), prior plausibility affectedcausal structure inferences: the bets on “A and B” were significantly greater in the Social condition than in the Prior condition (t(44)=5.11, p<0.001). Thus participants used priorProcedure Participants were assigned to conditions suchthat each participant received one scenario in each condition in each domain (assignments were counterbalanced ina latin square design). The order of scenarios was randomized between participants. After reading each scenario participants were asked for their causal structure inferences (“Whatcauses C?”) in the form of bets (which were required to sum
to $100—hence, providing a natural elicitation of probability
judgments). The five options were of the form:

3 To verify that participants were considering each scenario, we
inserted an attention check at a random position within the experiment packet. This page looked visually similar to other pages but
contained instructions to write only “I have read the instructions”
and proceed. No participant failed this check.
4 In the Self condition there was a trend toward “A and B” bets.
Informal debriefing suggested that some participants misunderstood
the fictional assumption of the scenario, treating “themselves” asknowledgeable agents. If this was the case, we would expect toobserve a mixture of the causal-only model with the social-causal
model; this is consistent with the observed trend.

You work at a genetically-engineered plants nursery, andone of your coworkers is tending to some almost-deadflowers that you havent seen before. Your coworker simultaneously pours a yellow liquid and a blue liquid on
the flowers. By the end of the day, the flowers are growing again.
In the Self condition the middle sentence was changed to:
One day when your coworker is gone, you find a yellow
liquid and a blue liquid in his supplies and simultaneously pour them on the flowers.
In the Prior condition the middle sentence was changed to:

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(c)
Self condition

Likelihood rating

Social condition

Prior condition

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Figure 4: The mean bet (likelihood rating) placed on each of the five possible causes of C. The Social condition (a) confirms the socialcausal model predictions (Fig. 2a). The Prior condition (c) confirms predictions of the social-causal model with strong prior (Fig. 2c). The
Self condition (b) reflects a reversion to the causal-only model (Fig. 2b), as expected, but seems to be mixed with residual social-causal
inferences—see Footnote 4.
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causal knowledge to inform inferences, even when social context information was available. To see whether this is a graded
integration of information sources, as predicted by the socialcausal model (Fig. 3), or an all-or-nothing gating effect ofprior knowledge, we exploit natural variation among the scenarios. The relationship between the plausibility rating of aparticipant and their bet on “A and B” in the corresponding
scenario, can be used to further examine the effect of priorknowledge on inferences. Pooling Social and Prior scenarios, prior plausibility ratings explain 43% of the variance inbets (r=0.66, p<0.001), as shown in Fig. 5.5 Within conditions, causal structure inferences remain significantly correlated with the variation in plausibility judgments (r=0.46,
p<0.01 within the Social condition, r=0.56, p<0.001 within
the Prior condition). This result indicates that participants
continuously integrate prior causal knowledge with social
context information, rather than using prior causal knowledge
as a gate on social inference.

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Figure 5: The mean bet (likelihood rating) of participants on “A
and B” according to their plausibility rating for B as a cause of C.
The graded effect of prior knowledge confirms the model predictions(Fig. 3).

Over-imitation
The results of the previous sections show that generic inference abilities, combined with an understanding of causality
and agency, can result in rapid learning of causal knowledge.
Yet where there is rapid learning there is the possibility of going rapidly astray—are there situations in which social-causal
inference might lead to incorrect conclusions?
A number of authors have reported that children seem toover-imitate adults, copying even actions which are, to adults,
clearly superfluous to bringing about an effect (Horner &Whiten, 2005; Lyons et al., 2007; Meltzoff, 1995). For instance Horner and Whiten (2005) present a “puzzle box” tochildren and demonstrate a series of actions which culminate
in retrieving a prize from within the box. The box is transparent, and some of these actions are plausibly related to the
5 The correlation is higher for group means (r=0.85); we are,however, primarily interested in the relationship within individual
participants.

outcome, but one is not (for example, touching a rod to the topof the box). When invited to retrieve the prize, children perform all the actions, including the superfluous one. Chimps
in a similar experiment did not over-imitate, leaving out the
implausible action. Lyons et al. (2007) investigated a number of possible explanations for over-imitation in children but
found it to be remarkably robust; the only manipulation theyreport that reversed children’s over-imitation was removal ofphysical contact between cause and (potential) effect (Lyons
et al., 2007, Expt. 2b). On the basis of these findings Lyons etal. (2007) suggest that over-imitation reflects an “automaticcausal encoding” mechanism, with “boundary conditions” toswitch off this encoding (such as physical contact).
Our modeling results indicate that a separate principle(such as automatic causal encoding) needn’t be invoked to
explain children’s over-imitation. If children’s prior beliefs
are weaker than adults’ (and, like adults, contact-causality isamongst the strongest priors), then over-imitation behavior
follows as the result of domain-general probabilistic inference, assuming that children use social context as a source ofevidence. Our experimental results, which demonstrate similar inferences in adults, further support this interpretation by
showing that the interaction between prior causal knowledge
and social inference is not a gating mechanism (as suggested
by “boundary conditions” on automatic causal encoding), but
a graded integration as required by Bayesian inference.
It is interesting to ask what the differences between chimps
and children mean, in light of this interpretation. The causalonly model predicts little over-imitation, since even a small
amount of prior bias dominates the inference. This suggeststhat chimps too are acting rationally on the basis of causal
structure inferences, but are failing to use social information
to guide these inferences. That is, the quixotic over-imitationof children may reflect a deep understanding of other minds,
while the lack of this behavior in chimps might reflect poor
theory of mind.

flower). Different inferences might be licensed when theagent has a social goal, such as communication or pedagogy(e.g. teaching how to revive a flower—see Shafto and Goodman (2008)). Further work will be required to distinguishlearning based on inference of concrete goals from that basedon social goals.
We have suggested that rapid social learning follows fromdomain-general inference abilities and an intuitive theoryof other minds. This emerged naturally in our computational model by considering a powerful inference mechanism (Bayesian inference) operating over complex knowledge structures. Since the compositionality of concepts is a
crucial feature of human cognition, it is likely that other important aspects of human thought also lurk in the interactions
between representations that are well understood in isolation.
Studying the effects of such interaction is thus an especially
important and potentially fruitful direction for computational
cognitive science.

Conclusion

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Roots of human sociality: Culture, cognition, and human interaction, ed. NJ Enfield & SC Levenson.
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A., Wellman, H., et al. (2006). Intuitive Theories of Mind: A
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We have presented a computational model of the social acquisition of causal knowledge. This model integrates existing
Bayesian approaches to causal reasoning and intuitive psychology. It predicts qualitatively different inferences aboutcausal structure, given social context, than an equivalentmodel based on causality alone, and predicts that prior causal
knowledge will be integrated into inferences in a graded fashion. We verified these predictions experimentally with adultparticipants, and discussed the relation of these results to thedevelopmental phenomenon of over-imitation.
While research on imitation and social cognition has
stressed the tendency of children to gain knowledge directlyfrom adults, research on causal learning has focused on theability of children to extract causal structure from observationand interaction directly with causal systems. Our results suggest that social context may provide a crucial, and often ignored, source of information that children use to learn causal
knowledge. However, the ability to learn from disparate
sources of evidence raises an important empirical question:
to what extent do children actually rely on social evidence(vs. observation, exploration, etc.) in acquiring causal knowledge? Our results indicate that social learning depends on aknowledgeable-agent assumption, thus it is reasonable to startby asking when children are aware that adults have knowledge that they themselves lack. Kushnir, Wellman, and Gelman (2008) have recently shown that children are sensitive tothe knowledgeability of others, and treat intentional actions
by knowledgeable agents as more informative about causal
structure than actions by unknowledgeable agents. This isconsistent with our experimental results; our modeling results
show that such inferences are an appropriate response to social context, rather than a rough heuristic, or incorrect bias.
Throughout this paper, social context consisted of observed
actions of an agent with a concrete goal (e.g. reviving a

References