Causal Models of Decision Making:
Choice as Intervention
York Hagmayer ([email protected])
Department of Psychology, University of Göttingen, Gosslerstr. 14
37073 Göttingen, Germany
Steven A. Sloman ([email protected])
Cognitive & Linguistic Sciences, Brown University, Box 1978
Providence, RI
Abstract
reflect causal relations is not considered. In fact, in games
of chance, the probabilities are often independent of the
choice made. The probability of red in roulette is
determined by the number of red, black and green fields, not
(unfortunately) by what you bet on. But in real world
contexts the probabilities are fixed by underlying causal
structures. An evidential relation may reflect a causal
relation (climate → heating costs) or just a spurious relation
due to a common cause (shoveling snow ↔ heating costs).
This distinction is critical for good decision making.
Whereas moving southward reduces your heating costs,
failing to shovel does not. Evidential expected utility theory
has no means to represent this distinction.
Recent philosophical and computational theories are
able to distinguish causal and spurious relations by
explicitly representing causal structure (e.g., Pearl, 2000,
Woodward, 2003). A spurious relation is a statistical
relation between two events that is not due to a direct causal
connection between them but rather to a common cause. A
causal relation from A to B differs from a spurious relation
in that it allows A to influence B by means of an
intervention on A. Interventions on causes increase the
probability of their effects; interventions on spuriously
related events do not change the probability of those other
events. Causal Bayes net theories (e.g. Pearl, 2000, Spirtes,
Glymour & Scheines, 2000) therefore distinguish
observational probabilities, reflecting the statistical relation
between observed events, and interventional probabilities
that represent the effect of intervention. This distinction is
critical to decision making, because choice entails action,
i.e. intervention. Therefore, if the goal of a decision is to
increase the probability of getting a desired outcome, then
interventional probabilities have to be used to calculate
expected utilities and not evidential utilities. For example,
the evidential probability relating shoveling snow and
heating costs is fairly high. Despite this fact, moving should
be preferred, because the interventional probability of low
heating costs after moving is higher than the interventional
probability of low heating costs after reducing shoveling.
Note that in games of pure chance, evidential and
Causal considerations must be relevant to making decisions.
Nevertheless, traditional decision theories like evidential
expected utility theory do not have the means to distinguish
causal from merely evidential relations. As a result, they fail
to distinguish cases where a choice influences consequences
from cases where a choice does not affect consequences even
though they are correlated. Therefore a causal model theory
of choice is introduced built on the causal Bayes net
framework. The theory claims that people decide using causal
models of the decision situation. Choice is represented as an
intervention. Two experiments are presented testing
predictions of the theory.
Introduction
People who shovel a lot of snow have higher heating bills
than those who shovel less. Would you therefore
recommend to a friend who wants to reduce his heating bill
that he should stop shoveling snow? Probably not.
Shoveling less snow would make sense if it reduced heating
costs. But the reason that shoveling snow and heating costs
are correlated is presumably not that one is a cause of the
other; it’s rather that both are effects of the climate.
Stopping would merely reduce the effort, without affecting
the underlying cause, and thus would do nothing to change
the target effect, the amount paid. Therefore you would
probably recommend moving south to someone worried
about heating expenses. The example shows that it is not
evidential relations but causal considerations that are crucial
to good decision making. Yet the study of decision making
has been dominated by evidential expected utility theory, a
theory that fails to account for causal considerations.
Evidential expected utility theory is the primary gold
standard for good decision making. The theory is built on
the gambling metaphor; the rational decision-maker is
conceived of as someone playing a game like roulette which
has a set of possible outcomes, each with some probability
of occurring and each with some value or utility for the
decision maker. The best options are the ones that have the
highest likelihoods of delivering the most goods, those with
the highest expected utility. Whether these likelihoods
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A causal modeling framework for decision making
Causal Bayes nets (e.g., Pearl, 2000) offer a formal
framework for representing and reasoning about causal
systems using causal models, a form of graphical
representation of both deterministic and probabilistic causal
systems. They also allow distinguishing observation from
intervention, which is critical for modeling choice.
Furthermore, they specify when and how interventional
probabilities, i.e., the probabilities of events resulting from
intervention, can be derived from observational evidence.
Observations are represented by a conventional
conditional probability (e.g., the probability that an
individual has low heating costs given that he doesn’t
shovel snow). To represent interventions, Pearl (2000)
proposes a special operator called do. An intervention
do(X=x) has the effect of setting the variable X to the value
x and, less obviously, removes any links from other
variables to X in the causal model. In other words an
intervention disconnects the manipulated event from its
usual causes. For example, preventing someone from
shoveling snow is an action by an agent that constitutes an
intervention. Its relevance to heating costs is represented by
the interventional probability that someone has low heating
costs given that we stop them. To represent the intervention
in a causal model, we add a node for the intervention and
set shoveling to no.
Critically, we also disconnect
shoveling from its normal cause (climate) because we have
determined shoveling directly so other causes become
irrelevant (see Figure 1).
interventional probabilities coincide, because causal
structure is irrelevant to the outcome. This might help
explain why evidential expected utility theory has ignored
this distinction.
Two major conclusions can be drawn: (i) decisions
require causal models, and (ii) choices involve
interventions. Based on these insights we will propose a
causal model theory of choice. First we offer a cursory
review of previous work on causal decision making and an
informal introduction to causal Bayes nets. After outlining
our theory, we will report two preliminary experiments
testing some predictions of our account.
Causal Decision Making
Philosophers have proposed several theories that are
sensitive to causal structure (e.g. Nozick, 1995). These
theories all use something other than evidential conditional
utility to determine expected utilities. Instead they take the
causal consequences of choice into account (cf. Meek &
Glymour, 1994). For example, Nozick (1995) suggests
calculating causal expected utilities based on probabilities
that reflect the causal impact of the choices made.
Despite the fact that issues of causality have framed
debates about decision making in philosophy for 35 years,
little work has been done on this topic in psychology. The
influence of causality has been recognized in judgments of
probability (e.g., Tversky & Kahneman, 1980) and has been
the central issue in studies of attribution and explanation
(e.g., Ahn, Kalish, Medin & Gelman, 1995, Kelley, 1967).
Related work has also been done in the study of reasoning
(e.g., Mandel, 2003; Sloman & Lagnado, 2005) and
learning (e.g., Lagnado & Sloman, 2004; Waldmann &
Hagmayer, 2005). In the domain of decision making per se,
there is some evidence that people are persuaded by causal
considerations. Pennington and Hastie (1993) showed that
juries can be swayed by presenting evidence in an order
consistent with a causal story. Studies on natural decision
making (Klein, 1998) have also shown that people tend to
build a causal model to simulate the consequences of a
potential action and proceed if the results turn out to be
satisfying. Several studies have found that there is an
asymmetry between acts of omission and commission (e.g.
Baron, 1992). People seem to prefer omission to
commission given identical negative consequences, because
they regard actions as more causally efficacious and
therefore experience more regret when acting. Research has
also found that people tend to neglect alternative causal
models when making decisions, and sometimes rely on only
one (e.g., Dougherty, Gettys & Thomas, 1997). Finally
there is some evidence that people sometimes deviate from
the optimal use of causal knowledge in their decisions and
deceive themselves in a self-serving manner (Quattrone &
Tversky, 1984). Our theory accommodates these findings
and specifies boundary conditions for the use of causal
models in decision making.
Observation
Climate
Shovel
Snow
Heating
Costs
Intervention
Intervention
= Stop
Shoveling
= No
Climate
Heating
Costs
Figure 1: Causal models representing
observation and intervention
The observation model also shows that the evidential
relation between shoveling and heating costs is merely
correlational. It is a result of the common cause structure of
the model. The intervention model shows that by virtue of
removing the link shoveling snow is rendered independent
of climate and heating costs. This inferential procedure of
“undoing” a causal link captures the intuition that shoveling
snow is no longer indicative of the climatic conditions
because shoveling is no longer influenced by the climatic
conditions. Therefore, it's also no longer related to heating
costs.
Based on the causal model and its parameters, i.e., the
conditional probabilities reflecting the causal links in the
model, evidential relations between the events in the model
can be inferred. More important, based on the modified
interventional model the interventional probabilities that
would result from an intervention can be computed (see
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value assigned by choice, and (iii) undoing is implemented,
i.e., the manipulated variable is cut off from its normal
causes. Figure 3 shows the choice model for insulating.
Insulating would cut the connection between climate and
amount of heat lost. Therefore the link connecting climate
and heat loss has been deleted.
Pearl, 2000, for a detailed description of how to do so in the
general case).
A causal model theory of choice
The theory described here offers an analysis of the activity
of a decision maker. It rests on two basic assumptions:
(i) decisions involve deliberation concerning the outcomes
of causal processes and (ii) choice can be conceived as an
intervention on a causal structure. The decision maker is
hypthosized to go through three phases of decision making:
Climate:
Cold
Choice Intervention:
Insulate
Heat Loss:
Low
Phase 1. World model construction
In this phase the decision maker first instantiates her goals
as a distribution of preferred causal consequences (e.g., low
heating costs). She then identifies the causal factors that are
relevant to determining those consequences (e.g., climate
and heat loss). Next these factors are separated into those
that are determined by the decision maker’s choice options
(e.g., heat loss) and other factors that are not (e.g., climate).
These other factors comprise any other relevant variable in
the context.
Next the decision maker constructs a causal model of the
decision environment describing how these factors bring
about causal consequences. The construction of the world
model may be facilitated if the given information already
conforms to a causal model (see Pennington & Hastie,
1993). Finally she updates her model of the world by
assigning all known values of factors and letting probability
propagate to obtain a posteriori probability values for all
states (methods for doing this can be found in, e.g., Halpern,
2003). For example, if the house is situated in the northern
part of the United States, the factor climate is set to cold
and the probability of low heating costs is decreased. Figure
2 shows such a partly instantiated causal model of the world
for our heating example. In accordance with causal Bayes
net theories, we assume that graphs are acyclic: Effects do
not affect their causes.
Climate:
Cold
Heat Loss
Shoveling Snow:
Yes
Heating Costs
Figure 3: Choice model constructed by the decision maker
If more than one choice is available, a separate model for
each choice has to be constructed. However, previous
research (Klein, 1998) points out that people tend to
construct a single causal model and consider one choice
option at a time.
Phase 3. Choice
The probability of relevant consequences is calculated for
each option based on the choice model. Thus interventional
probabilities are used to infer the likelihood of
consequences given each choice option. The choice is made
by maximizing the likelihood of getting the most favorable
causal consequences. First, the decision maker compares the
probability distribution over the causal consequences that
would obtain if no action were taken with the consequences
resulting from action. When expected outcomes of omission
and commission are equal, the default choice is to not act,
because any kind of action incurs some cost. This prediction
conforms to the omission bias found in previous research
(e.g. Baron, 1992). Second, if different actions are available
the consequences of these options are compared to each
other. For the sake of simplicity, we assume that choice
involves utility maximization: The action with the highest
causal expected utility is chosen. The critical claim of the
theory is that expected utilities are calculated using
interventional probabilities and that utilities are determined
by causal consequences. Computing both interventional
probabilities and causal consequences requires a causal
model. It is this dependence on a causal model that we deem
crucial; the assumption of utility maximization might be
substituted with a more psychologically realistic choice rule.
As it stands, the framework assumes causal as opposed to
evidential expected utility maximization. The experiments
reported in this paper will investigate this crucial prediction.
Shoveling Snow:
Heating Costs
Yes
Figure 2: World model constructed by the decision maker
Phase 2. Choice model construction
In order to evaluate the consequences of a potential action
an intervention model must be set up. In an intervention
model, the variable being intervened on is disconnected
from its normal causes. This is because a state variable set
by choice is no longer diagnostic of its other natural causes,
given that the choice is made deliberately. In other words,
the logic of intervention applies to choice. The choice
model differs from the decision maker’s model in three
ways: (i) a choice-intervention node is added to represent
the intervention, (ii) the manipulated variable is given the
Boundary conditions
A critical assumption made by the proposed theory is that
choice equals an imaginary intervention in a causal model.
When a choice variable is set by intervention, this variable
has no diagnostic value for its other (normal) causes. Thus
the theory implies undoing effects. In order to obtain such
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way the evidential relation was presented. In Experiment 2
we manipulated the strength of the evidential relation. The
strength of the evidential relation affects the causal expected
utility given a direct causal link structure but not given a
common cause structure. Therefore we expected
participants to be sensitive to this manipulation only if they
assumed a direct causal influence of the given variable upon
the desired effect. The common core of both experiments
was that participants were informed about the existence of
an unknown albeit plausible evidential relation. They were
also informed about the causal model underlying the
evidential relation. Either the relation could be traced back
to a causal link or to a common cause. Note that both causal
models imply the existence of an evidential relation. Thus
none of the models challenged the existence or validity of
the evidential relation. Participants in both experiments had
to decide whether an action should be pursued to achieve a
desired outcome. Based on our theory we expected to
observe undoing effects in both experiments.
undoing effects several conditions must be met. First the
decision maker has to fully consider the causal structure of
the environment before making a choice. There is evidence
however, that people do not always engage in elaborated
reasoning (e.g. Petty & Cacioppo, 1986). Unmotivated or
stressed participants may rely on evidential relations and
neglect causal structure. Second the decision maker has to
assume that her interventions are strong. Only interventions
that are made deliberately and completely determine the
value of the choice variable are strong. Otherwise the
variable intervened on is not completely disconnected from
its causes and remains diagnostic. The cases of selfdeception described by Quattrone and Tversky (1984) might
serve as an example. Voters may assume that their decision
to vote was not a fully deliberate choice but caused by some
factor that also affects other voters’ decision to go to the
polls. Third, undoing requires that the decision maker does
not engage in analogical reasoning when predicting the
actions taken by other persons. For example, an assumption
made by some participants in games offering identical
payoffs to all players is that other players will make the
same choice. Reasoning of this sort has been described as
the Stackelberg heuristic (Colman & Bacharach, 1997).
Experiment 1
The goal of Experiment 1 was to provide evidence that
participants are sensitive to causal structure and to the
implications of the intervention resulting from their choice.
Participants received four scenarios about familiar everyday
activities and their evidential relation to desired outcomes.
For example participants read the following story:
Recent research has shown that of 100 men who help
with the chores, 82 are in good health whereas only 32
of 100 men who do not help with the chores are.
Imagine a friend of yours is married and is concerned
about his health. He read about the research and asks for
your advice on whether he should start to do chores or
not to improve his health. What is your
recommendation? Should he start to do the chores or
not?
In two experimental conditions we added a causal
explanation for the evidential relation to the scenario.
Participants were either informed that
Research discovered that the cause of this finding was
that doing the chores is an additional exercise every day
(Direct cause condition).
or that
Research discovered that the cause of this finding was
that men who are concerned about equality issues are
also concerned about health issues and therefore both
help to do the chores and eat healthier food (Common
cause condition).
Participants were given a forced choice either to
recommend acting or to recommend not acting. The other
three scenarios concerned the relation between exercise and
caloric consumption, high risk sports and drug abuse, and
chess and academic achievement. The evidential relations in
all four scenarios were very strong. The probability of the
desired outcome was 40-50% higher for persons taking the
action than for persons who did not.
We also manipulated the way the evidential relation was
presented to investigate whether presentation format affects
participants’ decisions. Participants either received
information about conditional frequencies as in the example
Testing the theory
As an initial test of the theory, we focus on whether choices
are construed as imaginary interventions on causal models.
If so, undoing effects should result. We therefore
confronted participants with an evidential relation between a
variable and a desired outcome and asked whether they
would recommend manipulating the variable in order to
achieve the outcome. Different causal models explained the
given relation, either a common-cause structure or a direct
causal link. Given a common-cause model, an intervention
would imply undoing and therefore independence of the
variable intervened on and the desired outcome. In contrast,
a direct causal link implies that an intervention would
activate the causal relation and therefore increase the
probability of the outcome in accordance with the evidential
relation. Thus despite the fact that the evidential relation is
identical in both cases, action should only be recommended
given a direct causal relation.
To test the generality of these predictions we constructed
two experiments using different methodologies to
investigate undoing effects. Experiment 1 was conducted on
the world-wide-web, while Experiment 2 was conducted in
the lab. New scenarios were constructed for each
experiment. In addition, further factors that may affect
participants’ answers were investigated. In Experiment 1 the
way the evidential relation was presented was manipulated.
As outlined earlier, deriving interventional expected utilities
requires Bayesian reasoning based on causal models. While
some researchers have found that Bayesian reasoning is
impaired with probabilities but facilitated by frequencies
(Gigerenzer & Hoffrage, 1995), others have found that such
inferences are possible based on qualitative information
alone (Sloman & Lagnado, 2005). Therefore the evidential
relation was either described in a frequency format, in a
probability format or just qualitatively. We expected
participants to generate undoing effects regardless of the
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containing a certain substance have a higher crop yield than
other soils. The yield was either 65% higher (strong
evidential relation) or only 6.5% higher than with other soils
(weak evidential relation). It was explained that the relation
was either due to soil fungi that released the substance and
also provided nutrients for the crops (common-cause model)
or that the substance stimulates the growth of fungi that
release nutrients for the crops (causal-chain model). Note
that in contrast to Experiment 1 the same events were part
of both causal models. We also added a control condition in
which no causal model explaining the evidential relation
was provided. Participants in all conditions were asked to
give advice to an agrochemical company contemplating
whether to add the substance to a fertilizer. Answers were
given on a rating scale ranging from 0 (“substance should
definitely not be added”) to 100 (“substance should
definitely be added”). The second scenario concerned the
relation between the presence of certain molecules and the
amount of insulin produced in bioreactors.
Based on our theory we expected participants to
recommend not adding the substances when the evidential
relation could be traced back to a common-cause model
regardless of the strength of the evidential relation. In
contrast, we expected participants to consider the strength
of the evidential relation when presented with a causalchain model. In this case the evidential probabilities
conform to the interventional probabilities. Thus the causal
expected utilities are higher when the evidential relation is
strong than when it is weak. Therefore participants should
recommend acting, but more emphatically given a strong
relation. For the control condition, we speculated that
participants would take the evidential relation into account,
because conversational maxims (Grice, 1975) imply that
given information is relevant for subsequent questions.
Therefore the results in this condition should mirror the
ones in the causal-chain condition.
Seventy-two students from the University of Göttingen
responded to the two scenarios. The order of scenarios and
conditions was completely counterbalanced. As the answers
to both scenarios were highly similar they were combined
for further analysis. The results are depicted in Figure 5.
given above or they were informed about the increase in
probability (“men doing the chores are 50% more likely to
be in good health than men who do not”) or they were just
informed that there is an evidential relation without any
specific numbers (“men doing the chores are substantially
more likely to be in good health than men who do not”).
This factor was manipulated between participants.
The study was run online. Participants were recruited
at various psychology websites and through university
newspaper advertisements. They were rewarded for
participation with a small chance (about 1/50) to win a
small amount of money (about $50). Each participant
received the four scenarios with either a common-cause
model or a direct-cause model. The order of models and
scenarios was completely counterbalanced. Eighty-one
participants made a total of 324 decisions. Because there
were no apparent differences between the four scenarios the
results were aggregated for further analysis. The results for
the six experimental conditions are depicted in Figure 4.
80
70
60
50
40
30
20
10
0
Common Cause
Frequency
Direct Cause
Percent
Qualitative
Figure 4: Results Experiment 1.
Percentage of recommendations to act.
Overall only 23% of the participants given a commoncause model recommended acting in comparison to 69% of
the participants given a direct causal link. The difference
between causal models turned out to be significant in all
three conditions, χ2frequency=18.8, p<.01, χ2percent=16.3, p<.01,
χ2qualitative=16.9, p<.01. These results show that most
participants took the causal structure into account when
making their decisions. They did not simply base them on
the evidential relation.
100
80
60
40
20
0
Experiment 2
The causal model theory of choice claims that people base
their decisions upon causal expected utilities calculated
using interventional instead of evidential relations.
Experiment 1 showed that participants are sensitive to the
causal structure underlying an evidential relation and to
undoing effects. However, it did not test whether
participants are sensitive to the magnitude of the
interventional probability implied by the causal model and
the observed evidential relation. In Experiment 2 we
therefore manipulated the strength of the evidential relation
as well as the structure of the causal model generating the
data and again looked for undoing effects.
Two scenarios describing biological processes were
used. In the first scenario participants read that soils
Common
Causal Chain
Control
Cause
Weak Relation Strong Relation
Figure 5: Mean recommendations in Experiment 2.
0 = Action not recommended
100 = Action strongly recommended
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An analysis of variance with ‘causal model’ and
‘evidential relation’ as between-participants factors yielded
a significant main effect for causal model, F(2,138) = 28.5,
p<.01, MSE = 725.9. No other effect was significant.
Participants recommended action in the causal-chain and in
the control condition, but advised omission in the common
cause condition.
Contrary to our prediction, no effect of the strength of
the evidential relation was observed in the causal-chain
condition. This finding may be due to the scenarios chosen.
A 6.5% increase in crop yield or insulin production is
already a big effect in real terms. Therefore the results may
reflect a ceiling effect. The written justifications also
pointed in this direction. Almost all participants assuming a
causal-chain model strongly recommended adding the
substance. Those who did not referred to other reasons like
unknown side-effects to justify their advice. Therefore we
expect to find the predicted effect in future experiments
using a more sensitive task.
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Concluding Remarks
Traditional evidential expected utility theory does not have
the means to distinguish amongst evidential relations
reflecting causal relations and spurious relations implied by
common causes. However, the results of previous research
have shown that participants distinguish between different
causal models and their implications (e.g., Sloman &
Lagnado, 2005, Waldmann & Hagmayer, 2005).
Furthermore the results of the two experiments presented in
this paper show that this distinction also affects participants’
decisions.
The causal model theory of choice aims to integrate
causal Bayes nets with an assessment of preference in order
to develop an understanding of human choice. Its central
claim is that people make decisions based on causal models
which they use to infer the probability of desired
consequences that result from interventions in the form of
choices. Causal Bayes net theories provide the formal tools
to model this process and to calculate causal expected
utilities. The results of these two experiments add to the
existing support in the literature for these claims. Further
research will reveal the generality of these conclusions and
afford further specification of the process of choice.
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