How, whether, why: Causal judgments as counterfactual contrasts
Tobias Gerstenberg1 (tger@mit.edu), Noah D. Goodman2 (ngoodman@stanford.edu),David A. Lagnado3 (d.lagnado@ucl.ac.uk) & Joshua B. Tenenbaum1 (jbt@mit.edu)
1 Department of Brain and Cognitive Sciences, Massachusetts Institute of Technology, Cambridge, MA 02139
2 Department of Psychology, Stanford University, Stanford, CA 94305
3 Experimental Psychology, University College London, London WC1H 0AP

Abstracta) clip 7b) clip 12c) clip 23

E

How do people make causal judgments? Here, we propose
a counterfactual simulation model (CSM) of causal judgmentthat unifies different views on causation. The CSM predicts
that people’s causal judgments are influenced by whether acandidate cause made a difference to whether the outcome occurred as well as to how it occurred. We show how whethercausation and how-causation can be implemented in terms ofdifferent counterfactual contrasts defined over the same intuitive generative model of the domain. We test the model in an
intuitive physics domain where people make judgments about
colliding billiard balls. Experiment 1 shows that participants’counterfactual judgments about what would have happened if
one of the balls had been removed, are well-explained by anapproximately Newtonian model of physics. In Experiment 2,
participants judged to what extent two balls were causally responsible for a third ball going through a gate or missing thegate. As predicted by the CSM, participants’ judgments increased with their belief that a ball was a whether-cause, ahow-cause, as well as sufficient for bringing about the outcome.
Keywords: causality; counterfactuals; mental simulation; intuitive physics.

highlight the second type. Here, we propose a model thatcombines these different views by showing how each type ofdifference-making can be captured in terms of different counterfactual contrasts defined over the same generative model ofthe domain (cf. Schaffer, 2005; Woodward, 2011).

Introduction

Model

How do people make causal judgments? What role docounterfactual thoughts about what might have been play?
Philosophers have proposed many different frameworks forthinking about causality. Some have argued that causation
is fundamentally about dependence – what it means for C tohave caused E is that E did somehow depend on C (Lewis,
2000; Woodward, 2003). Others maintain that causation isabout processes: C caused E if there was a (physical) process that started with C and produced E (Dowe, 2000). Stillothers argue for a pluralistic view and point to two or moredifferent concepts of causation (Beebee, Hitchcock, & Menzies, 2009; Hall, 2004). If one takes a look at the empiricalevidence, one also gets the impression that people’s causal
judgments are very much a mixed bag. Some studies findthat people’s judgments are strongly influenced by information about the exact way in which C brought about E (Lombrozo, 2010; Walsh & Sloman, 2011; Wolff, 2007), whereas
others find that people mostly care about counterfactual dependence – whether E would still have happened if C had
been absent (Chang, 2009; Gerstenberg, Goodman, Lagnado,& Tenenbaum, 2012, 2014).
Our aim in this paper is to unify these different views. We
argue that the core notion that underlies people’s causal judgments is that of difference-making. However, there are several ways in which a cause can make a difference to the effect. It can make a difference to whether the effect occurred,and it can make a difference to how the effect occurred (cf.
Lewis, 2000). While dependence-theories traditionally focus on the first type of difference-making, process-theories

The counterfactual simulation model (CSM) explains people’s causal judgments in terms of counterfactual contrasts
operating over an intuitive domain theory. Here, we illustrate the workings of the model by focusing on people’s intuitive understanding of physics. In previous work, we haveshown that people’s causal judgments in situations which feature a single collision event, are well-captured by assumingthat they compare what actually happened, with what they
think would have happened if the candidate cause had been
removed from the scene (Gerstenberg et al., 2012, 2014). We
now extend the CSM to handle more complex situations thatinvolve the interaction of several candidate causes. We will
see that people’s causal judgments in these more complex
cases can be explained if we assume that people consider different kinds of counterfactual contrasts.
Let us illustrate these different contrasts via the example ofa simple causal chain (see Figure 1a). Ball E and ball A are
initially at rest. Ball B then enters the scene from the right,
hits ball A which subsequently hits ball E, and E goes throughthe gate. To what extent are balls A and B responsible for E’s
going through the gate?
Whether-dependence First, we may consider what would
have happened if either ball had been removed from thescene. That is, we assess whether each ball’s presence madea difference to whether or not ball E went through the gate.
Formally, we define the probability that a candidate cause C
was a whether-cause of a target event e as

A

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causal chain #1

causal chain #2

double preventiond) clip 3e) clip 15f) clip 16

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joint causation

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overdetermination

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preemption

Figure 1: Diagrams of a selection of clips shown in the experiment.

PW (C, e) = P(e0 6= e|S, remove(C)).

(1)

We first condition on what actually happened in the situation S – whether ball E went through the gate, the movementsof the candidate cause balls, as well as the positioning of thewalls and the gate. We then consider a counterfactual situation in which the candidate cause had been removed fromthe scene (remove(C)), and evaluate the probability that theoutcome would have been different from what it actually was(e0 6= e). The more certain we are that the outcome event
would have been different, the greater our subjective degreeof belief that C was a whether-cause.
In the causal chain, ball B is a whether-cause of E’s going
through the gate. If B had been removed from the scene, ball
E would have just remained at rest in front of the gate (seeFigure 2a). Ball A, in contrast, is not a whether-cause. If A
had been removed, ball E would still have gone through thegate – it would have been knocked in by B.
How-dependence If whether-causation was all that matteredthen ball A shouldn’t receive any responsibility at all for E’s
going through the gate. However, there clearly is a sense inwhich ball A made a difference to the outcome. For one, it
was ball A that actually knocked E through the gate – there
was direct transfer of force from A to E. So while ball A
didn’t make a difference to whether E went through the gate,
it clearly made a difference to how E went through the gate.
We define the probability of how-causation as
PH (C, ∆e) = P(∆e0 6= ∆e|S, change(C)).

(2)

whether-causeEA

how-cause
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sufficient-cause
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robust-cause
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(a)
(b)
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Figure 2: Illustration of the different types of counterfactual contrasts applied to ball B.

how-cause. The CSM thus predicts that B will be judged
more responsible for the outcome than A.
Sufficiency Our test for whether-causation captures whether
the candidate cause’s presence was necessary for the outcome
to occur. It has also been argued that sufficiency is an important aspect of causation: we prefer causes that bring about
the outcome without requiring any other causes (Woodward,2006). Again, we define sufficiency in terms of a counterfactual contrast. The probability that a candidate cause wassufficient for bringing about the outcome is
PS (C, e) = P(e0 = e|S, remove(\C)).

(3)

After having conditioned on what happened (S), we assess
the probability that the same outcome (broadly construed)
would still have happened (e0 = e) in a counterfactual situation in which we removed all other candidate causes apartfrom the cause under consideration (remove(\C)).2
In the causal chain, ball B was a sufficient cause of E’s
going through the gate (see Figure 2c). Even if we had removed the other candidate cause (ball A) from the scene, ball
E would still have gone through the gate. Ball A, in contrast,
was not sufficient. If B had been removed from the scene, E
would not have gone through the gate.
Robustness Finally, it has also been argued that people’s
causal judgments are influenced by robustness (Lewis, 1986;
Lombrozo, 2010; Woodward, 2006). Causal relationships arerobust to the extent that they would have continued to holdeven if the conditions had been somewhat different. We define the probability that a cause was robust as

Again, we first condition on what actually happened (S).
Now, we consider a different kind of counterfactual contrast.
Rather than imagining what would have happened if the candidate cause had been removed from the scene, we simulate
what would have happened if the cause had been somewhat
different (change(C)). In our domain of colliding billiard
balls, we may think of the change operation as a small perturbation applied to a ball’s spatial position.1 We then assess
whether the outcome event would have been different from
how it actually was (∆e0 6= ∆e).
Note that there is an important difference in how the outcome event is construed depending on whether we assess PW
or PH . For PW , we construe the outcome event (e) broadly:
did E go through the gate or did it not. For PH , in contrast, weconstrue the outcome event (∆e) finely: exactly how, where,
and when did E go through the gate. In the causal chain, ballB does qualify as a how-cause of E’s going through the gate(see Figure 2b). If B’s spatial location had been somewhat different, E would have gone through the gate differently from
how it actually did. For the same reason, Ball A also qualifies
as a how-cause of E’s going through the gate.
So far, the CSM has two components: whether-causationand how-causation. In our running example, ball B is botha whether-cause and a how-cause, whereas ball A is only a

After having observed what actually happened (S), we consider whether the same outcome (broadly construed) would
still have happened (e0 = e) even if the other candidate causes
had been somewhat different (change(\C)). In the causal
chain, the robustness of each of the candidate causes is somewhat compromised. Considering the robustness of ball B,
there is a good chance that E would not have gone throughthe gate in a counterfactual situation in which ball A’s position was changed. More generally, the longer a causal chain,
the less robust each of the candidate causes becomes. A small
perturbation to any one of the balls would be sufficient for the
chain to fail.

1 We could also consider changes to C’s velocity, direction of
motion, or mass. What sorts of changes are relevant will be dictatedby people’s intuitive understanding of what factors might make adifference (a change in color, for example, is unlikely to be considered).

2 What objects are included in the set of candidate causes is anempirical question. In our experiments reported below, we stipulate
the set of candidate causes. Generally, people might have different
intuitions about which causes are worth considering (e.g. whether
or not the wall should be included in the set).

PR (C, e) = P(e0 = e|S, change(\C)).

(4)

Putting it all together
Now we have all the puzzle pieces we need. The CSM predicts that ‘good’ causes are whether-causes and how-causesthat are sufficient for bringing about the outcome in a robust way. The prototypical case which meets all of theserequirements is the Michottean launching event (Michotte,
1946/1963). In a launching clip, ball E is initially at rest,ball C enters the scene and collides with ball E, causing it to
move. C is a whether-cause of E’s motion (E wouldn’t have
moved if C had been removed from the scene); C is a howcause of E’s motion (E would have moved differently if C’s
initial position had been changed); C is a sufficient cause of
E’s motion (in this case, sufficiency is trivial as there are noalternative candidate causes that could be removed); and C isa robust cause of E’s motion (again, there are no alternativecauses whose position could have been somewhat different).
With all the puzzle pieces in our hands, we still need to saysomething about how to put them together. Before applying
the different counterfactual contrasts, we need to determine
the set of candidate causes in a particular situation. We only
consider causes that actually made a difference. We define
the probability that a cause made a difference as
PDM (C, ∆e) = P(∆e0 6= ∆e|S, remove(C)).

(5)

A cause made a difference if the outcome event (finely construed) would have been different had the candidate cause
been removed from the scene. The CSM predicts that only
if our subjective degree of belief is high that the cause madea difference, do we continue to consider the other aspects of
causation (PW , PH , PS , and PR ).
Before discussing the experimental tests of the model, let
us briefly illustrate the CSM’s predictions by applying it tosome example cases. Figure 1c depicts a ‘double prevention’scenario. E is headed toward the gate. Ball A threatens toknock E off the path. Ball B, however, knocks ball A out of
the way. B thus prevents A from preventing E (hence ‘double
prevention’). Let us focus on ball B’s causal status: B madea difference in the actual situation. B is a whether-cause (Ewould not have gone through the gate if B had been removed)
but not a how-cause (E would have gone through the gate
in exactly the same way even if we had perturbed B’s initial
position somewhat). B was sufficient for E’s going throughthe gate (E would have gone through the gate even if ball A
had been removed), and B was a robust cause (E would most
likely have gone through the gate even if A’s position had
been changed).3
Finally, let’s consider the ‘preemption case’ shown in Figure 1f. Here E is at rest in front of the gate and ball A knocks
E through the gate shortly before ball B would have done thesame (hence, A preempts B from unleashing its causal power).
Ball A made a difference according to Eq. 5 whereas ball B
3 Note that whether B qualifies as being sufficient and robust depends on whether we include latent causes, such as the cause of E’s
motion, in the set of candidate causes. If we included the cause of
E’s motion in the set, then B would not be sufficient and its robustness would be lower.

did not. Ball A was not a whether-cause since E would havegone through the gate even if ball A had been removed. Ball A
does qualify as a how-cause though, and it was also sufficientand robust.

Experiment 1: Counterfactual judgments
The CSM assumes that people consider different counterfactual contrasts when making causal judgments. To test theplausibility of this assumption, we first need to make surethat people are capable of simulating the relevant counterfactuals. In this experiment, we directly asked participants tomake counterfactual judgments about whether ball E would
have gone through the gate if either ball A or ball B had been
removed from the scene.

Modeling counterfactual judgments
We model people’s counterfactual judgments by assuming that their intuitive understanding of the domain approximately follows the laws of Newtonian physics. This ‘Noisy
Newtons’ approach has been applied successfully in a rangeof situations (e.g. Battaglia, Hamrick, & Tenenbaum, 2013;
Sanborn, Mansinghka, & Griffiths, 2013) and we have shownin previous work that people’s counterfactual judgments for
simple collision cases are well-explained within this framework (Gerstenberg et al., 2012, 2014).
In order to predict participants’ counterfactual judgments,
we use the same physics engine that was used to generate
the actual clips and generate counterfactual situations by simply removing the candidate ball from the scene. Whether or
not ball E would have gone through the gate in this situation
follows deterministically from each ball’s initial position andvelocity. However, people don’t have direct access to the outcome in the counterfactual world. They need to make useof their intuitive physical theory to mentally simulate what
would have happened.
We capture people’s uncertainty by introducing noise in the
counterfactual simulation from the point at which the candidate ball would have collided with one of the other balls (cf.
Smith & Vul, 2013). At each time step in the simulation, we
introduce a small random perturbation drawn from a Gaussian
distribution to the other ball’s velocity. For example, consider
the causal chain #2 shown in Figure 1b. Would ball E havegone through the gate if ball A had not been present in thescene? To simulate people’s judgments, we remove ball A
from the scene, and add noise to ball E’s velocity from thepoint at which balls A and E would have collided. In thiscase, the chances that E ends up going through the gate in
the noisy simulation are low (it would only go through if thenoise happened to sufficiently perturb ball E’s velocity down
towards the gate). To simulate the counterfactual of whether
E would have gone through the gate if B had not been present
in the scene, we remove B from the scene and introduce noise
to E’s velocity at the time at which B and E would have collided. Here the chances that E would have gone through thegate is high. Since B only collides with E shortly before it entered the gate, a very large perturbation to E’s velocity would

Methods

100

Counterfactual judgments

be required to prevent E from going through the gate.
We fit the Noisy Newton model to people’s judgments byfinding the value for the noise parameter which leads to thehighest correlation with people’s judgments. The noise parameter refers to the value of the standard deviation (SD) of
the Gaussian distribution from which the random perturbations to a ball’s velocity are drawn. The greater the SD themore noise is introduced into the simulations. For each levelof SD, we generate two samples of 1000 noisy worlds: one inwhich ball A is removed, and one in which ball B is removed.
We then determine the probabilities p(e0 6= e|S, remove(A))
and p(e0 6= e|S, remove(B)) by counting the number of worlds
in which the outcome would have been different from what it
actually was.

16B
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r = 0.88

7A

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Figure 3: Scatterplot of the Noisy Newton model (SD = 1.6◦ ) andparticipants’ mean counterfactual judgments. ◦ = cases in which ball
E would have missed, 4 = cases in which E would have gone in.

Participants & Design 80 participants (Mage = 33.4,
SDage = 10.1, 34 female) were recruited via Amazon Mechanical Turk. Half of the participants answered counterfactuals involving ball A, the other half involving ball B. Eachparticipant saw 32 clips.4
Procedure Participants viewed each clip twice before answering the question: “Would ball E have gone through thegate if ball A/B had not been present?”. Participants indicatedtheir response on a slider whose endpoints were labeled “definitely no” and “definitely yes”. The midpoint was labeled“unsure”. After having answered the question, participantsreceived feedback by viewing the same clip again whereby
either ball A or ball B was turned into a ‘ghost ball’ that didn’t
collide with the other balls and stopped moving at the point at
which it would have first collided. This was done to remind
participants of what the actual clip had looked like. On average, it took participants 18.1 (SD = 4.63) minutes to complete
the experiment.

factual situation in which one of the balls had been removed
from the scene. In previous work, we had shown that participants’ counterfactual simulations were accurate for simple
cases with two balls (Gerstenberg et al., 2012), and situations that involved additional objects such as bricks or teleports (Gerstenberg et al., 2014). Here, we show that people’s
mental simulations of counterfactuals are well-captured by a
Noisy Newton model even in more complex situations thatinvolve the collisions of several balls.

Results

Participants & Design 41 participants (Mage = 33.7,
SDage = 10.5, 21 female) were recruited via Amazon Mechanical Turk. This experiment used the same set of 32 clips
as in Experiment 1. In half of the clips ball E went throughthe gate, whereas in the other half it missed.
Procedure Participants viewed each clip three times before
answering the question: “To what extent were A and B responsible for E (not) going through the gate?”. The question
was adapted based on the outcome of the clip. Participants indicated their responses on two separate sliders, one for eachball. The endpoints of the sliders were labeled “not at all”
and “very much”. On average, it took participants 21.2 (SD =4.96) minutes to complete the experiment.

Figure 3 shows a scatter plot of participants’ mean counterfactual judgments and the predictions by the best-fitting
Noisy Newton model. For example, participants thought that
there was a high chance that ball E would have gone throughthe gate if ball A had been removed in clip 7 (see Figure 1a)and the model correctly captures this. It also correctly predicts that people consider it unlikely that E would have gonein, if ball A (or B) had been removed in clip 3 (see Figure 1d).
The model that explains participants’ counterfactual judgments best, uses a noise parameter of SD = 1.6◦ and results in a correlation of r = 0.88 with RMSE = 19.05. A
deterministic physics model (i.e. SD = 0◦ ) does worse withr = 0.82, RMSE = 30.28. The correlation of the Noisy Newton model with participants’ judgments decreases, for noise
values greater than 1.6◦ .

Discussion
The results of Experiment 1 demonstrate that people are capable of simulating what would have happened in a counter4 You can take a look at the clips here:
http://web.mit.edu/tger/www/demos/contrasts.html

Experiment 2: Causal responsibility judgments
Experiment 1 established that people are able to mentally
simulate what would have happened in different counterfactual situations. In Experiment 2 we now want to see how
the different counterfactual contrasts that the counterfactual
simulation model (CSM) postulates, influence people’s causal
judgments.

Methods

Results
In order to evaluate participants’ causal responsibility judgments, we will consider three different versions of the CSM
which differ in terms of the number of counterfactual contrasts they consider. The simplest model, CSMW , tries to
explain participants’ judgments merely in terms of whetherdependence. Another version of the model, CSMWH , also
considers how-dependence. Finally, the CSMWHS model in-clip 7
causal chain #1
100

W− H+ S−

clip 12causal chain #2

W+ H+ S+W+ H+ S+W− H+ S−

clip 23
double prevention
W− H− S−

W+ H− S+

Table 2: Probabilities of the different counterfactual contrasts forthe subset of cases shown in Figure 1. PW and PS are based onparticipants’ counterfactual judgments in Experiment 1.

Causal responsibility

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7
Ball A B

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clip 3
joint causation

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clip 15
overdetermination

W+ H+ S−W− H+ S+W− H+ S+

clip 16preemption
W− H+ S+W− H− S−A
CSMWHS

B

75
50

12
A

23
B A B

3
A

15
B

A

B

16
A B

PDM 100 100 100 100 0 100 100 100 100 100 100 0
PW 15 80 73 6 0 74 85 78 16 13 21 0
PH 100 100 100 100 0 0 100 100 100 100 100 0
PS 20 85 94 27 0 80 22 15 87 84 97 0

25
0
A

B
legend:

A
data

CSMW

B
CSMWH

Figure 4: Mean causal responsibility ratings (white bars) and model
predictions of different versions of the CSM (shaded bars) for a selection of cases. Error bars denote ±1SEM. The labels above thebars indicate each ball’s causal status. For example, Ball A in clip 7
is neither a whether-cause nor sufficient but a how-cause.

cludes sufficiency as an additional component. Table 1 shows
the weights that the different models put on the different predictors and Table 2 shows the probabilities of the different
counterfactual contrasts for the subset of cases shown in Figure 1. Figure 4 shows participants’ causal responsibility judgments together with the predictions of the three different versions of the CSM for the same selection of clips.
To get PW and PS , we simply used participants’ counterfactual judgments from Experiment 1. To determine PH , weran the physics model and generated a sample of situations inwhich we applied a small perturbation to the candidate ball.
We then checked the proportion of cases in which E went
through the gate differently from how it actually did. In cases
in which the ball made no difference to the actual outcome(i.e. PDM = 0), the other predictors were capped at 0.
The CSMW , which only considers whether-causation asa predictor, struggles with several situations. In the causal
chain #1 (Clip 7), participants gave a high rating to ball B but
also a relatively high rating to ball A, even though PW (A, e)
is very low (see Table 1). Further, the model overpredicts ratings to ball B in the double prevention case (Clip 23). WhilePW (B, e) is high in this case, participants’ judgment was relatively low. Finally, it struggles with the cases in which theoutcome is overdetermined and where each ball individually
made no difference to whether E went through the gate (Clips
15 and 16). Over the set of 32 cases, the CSMW accounts formerely 50% of the variance in participants’ judgments. This
clearly shows that participants’ causal responsibility judgments in these clips cannot be explained merely in terms ofTable 1: Regression results for different versions of the CSM.

PW
PH
PS
Constant
R2
F Statistic

CSMW
0.59∗∗∗

CSMWH
0.40∗∗∗
0.30∗∗∗

CSMWHS
0.36∗∗∗
0.22∗∗∗
0.32∗∗∗
23.18∗∗∗
9.99
3.46∗
0.50
0.69
0.82
61.56∗∗∗
66.54∗∗∗
90.68∗∗∗(df = 1; 62)(df = 2; 61)(df = 3; 60)
Note: ∗ p<0.1; ∗∗ p<0.05; ∗∗∗ p<0.01

whether-dependence.
A model which also considers how-dependence significantly improves the fit to participants’ judgments with 69%
variance accounted for overall. As Figure 4 shows, it correctly predicts a higher rating for ball A in the causal chain#1 and a lower rating for ball B in the double prevention
case. It also gets closer to participants’ judgments in situations in which the outcome was overdetermined. However,
the CSMWH predicts a relatively large difference between the
joint causation case (Clip 3) and the overdetermination case
(Clip 15). In the joint causation case, PW is high for bothballs, and they both also made a difference to how E went
through the gate. In the overdetermination case, both balls
made a difference to how E went through the gate while PW
is very low. In contrast to this prediction, the results show thatparticipants’ judgments are almost identical in the two cases.
The CSMWHS explains this pattern of results by assumingthat participants’ also care about sufficiency. While in thecase of joint causation, both causes are necessary but neither
is sufficient, in the case of overdetermination, neither cause isnecessary but they each are individually sufficient. By taking
both aspects into account, the CSMWHS correctly predicts thatparticipants’ judgments are similarly high in both situations.
Overall, the CSMWHS accounts for 82% of the variance inparticipants’ judgments (see Figure 5 for participants’ judgments for the full set of 32 different clips together with thepredictions of the CSMWHS ).
The results also provide some evidence for the role of robustness in people’s causal judgments (see Figure 2d). The
CSMWHS predicts incorrectly that participants’ judgments
should be lower for ball A in the preemption case (Clip 16)
than for ball B in the causal chain #1 (Clip 7). In the causal
chain, ball B is not a robust cause of E’s going through thegate. If A’s position had been somewhat different then E
might not have gone through the gate. Conversely, in thepreemption case, ball A is a very robust cause of E’s going
through the gate. Randomly perturbing the position of thealternative cause B, doesn’t affect the robustness of the relationship between A and E.

Discussion
The results of Experiment 2 show that we can explain participants’ causal responsibility judgments to a high degreeof quantitative accuracy by assuming that people are sensitive to a number of different factors when making their judgments. A model that considers whether-dependence, how-¬E|AB, ¬E|A, ¬E|B, ¬E

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Figure 5: Mean causal responsibility (red = negative outcome, green = positive outcome) and model predictions (black bars). Error bars denote±1SEM. Note: The labels on top of each pair of clips indicate the actual outcome and the outcome in different counterfactual situations. For
example, in Clips 11 and 12, ball E actually went through the gate (E|AB), it would have also gone through if only ball A had been present(E|A). However, it would not have gone through if only ball B (¬E|B), or neither ball A nor ball B had been present (¬E).

dependence, and sufficiency best explains participants’ judgments. Even though there was some evidence for the importance of robustness in people’s judgments, including it as aseparate predictor did not significantly increase the model’s
fit.

General discussion

Causality and counterfactuals are close kin. In this paper,
we have shown how to explain people’s causal responsibility
judgments in terms of different counterfactual contrasts defined over an intuitive domain theory. We applied the counterfactual simulation model (CSM) to modeling judgments
about collisions between several billiard balls within the domain of intuitive physics. Experiment 1 showed that people’s counterfactual judgments closely follow the predictionsof a noisy Newtonian model. In Experiment 2, we demonstrated that people’s causal judgments are tightly linked totheir counterfactual judgments. In previous work, in which
we looked at less complex stimuli that featured a single collision event only, we found that participants’ causal judgments
were closely related to their subjective degree of belief thatthe candidate cause made a difference to whether the outcome occurred (Gerstenberg et al., 2012, 2014). By considering a more challenging set of situations, we found thatparticipants’ causal judgments go beyond simple whetherdependence. When making causal judgments, people alsocare about whether the cause influenced how the outcome
happened and, whether they believe that the cause was sufficient (and robust) for bringing about the outcome.
The CSM defines a space of four counterfactual contrasts
by applying two basic operations, remove and change, to different targets – either the candidate cause, or the alternativecauses. While some have argued for the existence of two fundamentally different types of causation (e.g Hall, 2004), theCSM provides a framework of unification by showing how

these different causal conceptions can be understood as different counterfactual contrasts operating over the same intuitive domain theory (Schaffer, 2005). Here we have focusedon applying the CSM to people’s causal judgments in the domain of intuitive physics. However, the counterfactual contrasts that the CSM postulates are defined on a sufficiently
general level such that the model can be applied to any domain for which we are able to write down a generative model.
In future work, we will apply the CSM to modeling people’s
causal judgments in other domains such as interactions between social agents.
Acknowledgments This work was supported by the Center for
Brains, Minds & Machines (CBMM), funded by NSF STC award
CCF-1231216 and by an ONR grant N00014-13-1-0333.

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