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| title | chunk | source | category | tags | date_saved | instance |
|---|---|---|---|---|---|---|
| Causal decision theory | 1/2 | https://en.wikipedia.org/wiki/Causal_decision_theory | reference | science, encyclopedia | 2026-05-05T14:37:31.280571+00:00 | kb-cron |
Causal decision theory (CDT) is a school of thought within decision theory which states that, when a rational agent is confronted with a set of possible actions, one should select the action which causes the best outcome in expectation. CDT contrasts with evidential decision theory (EDT), which recommends the action which would be indicative of the best outcome if one received the "news" that it had been taken.
== Informal description == Informally, causal decision theory recommends the agent to make the decision with the best expected causal consequences. For example: if eating an apple will cause you to be happy and eating an orange will cause you to be sad then you would be rational to eat the apple. One complication is the notion of expected causal consequences. Imagine that eating a good apple will cause you to be happy and eating a bad apple will cause you to be sad but you aren't sure if the apple is good or bad. In this case you don't know the causal effects of eating the apple. Instead, then, you work from the expected causal effects, where these will depend on three things:
how likely you think the apple is to be good or bad; how happy eating a good apple makes you; and how sad eating a bad apple makes you. In informal terms, causal decision theory advises the agent to make the decision with the best expected causal effects.
== Formal description == In a 1981 article, Allan Gibbard and William Harper explained causal decision theory as maximization of the expected utility
U
{\displaystyle U}
of an action
A
{\displaystyle A}
"calculated from probabilities of counterfactuals":
U
(
A
)
=
∑
j
P
(
A
>
O
j
)
D
(
O
j
)
,
{\displaystyle U(A)=\sum \limits _{j}P(A>O_{j})D(O_{j}),}
where
D
(
O
j
)
{\displaystyle D(O_{j})}
is the desirability of outcome
O
j
{\displaystyle O_{j}}
and
P
(
A
>
O
j
)
{\displaystyle P(A>O_{j})}
is the counterfactual probability that, if
A
{\displaystyle A}
were done, then
O
j
{\displaystyle O_{j}}
would hold.
== Difference from evidential decision theory == David Lewis proved that the probability of a conditional
P
(
A
>
O
j
)
{\displaystyle P(A>O_{j})}
does not always equal the conditional probability
P
(
O
j
|
A
)
{\displaystyle P(O_{j}|A)}
. (see also Lewis's triviality result) If that were the case, causal decision theory would be equivalent to evidential decision theory, which uses conditional probabilities. Gibbard and Harper showed that if we accept two axioms (one related to the controversial principle of the conditional excluded middle), then the statistical independence of
A
{\displaystyle A}
and
A
>
O
j
{\displaystyle A>O_{j}}
suffices to guarantee that
P
(
A
>
O
j
)
=
P
(
O
j
|
A
)
{\displaystyle P(A>O_{j})=P(O_{j}|A)}
. However, there are cases in which actions and conditionals are not independent. Gibbard and Harper give an example in which King David wants Bathsheba but fears that summoning her would provoke a revolt.
Further, David has studied works on psychology and political science which teach him the following: Kings have two personality types, charismatic and uncharismatic. A king's degree of charisma depends on his genetic make-up and early childhood experiences, and cannot be changed in adulthood. Now, charismatic kings tend to act justly and uncharismatic kings unjustly. Successful revolts against charismatic kings are rare, whereas successful revolts against uncharismatic kings are frequent. Unjust acts themselves, though, do not cause successful revolts; the reason uncharismatic kings are prone to successful revolts is that they have a sneaky, ignoble bearing. David does not know whether or not he is charismatic; he does know that it is unjust to send for another man's wife. (p. 164)
In this case, evidential decision theory recommends that David abstain from Bathsheba, while causal decision theory—noting that whether David is charismatic or uncharismatic cannot be changed—recommends sending for her. When required to choose between causal decision theory and evidential decision theory, philosophers usually prefer causal decision theory.
== Thought experiments == Different decision theories are often examined in their recommendations for action in different thought experiments.
=== Newcomb's paradox ===
In Newcomb's paradox, there is a predictor, a player, and two boxes designated A and B. The predictor is able to reliably predict the player's choices— say, with 99% accuracy. The player is given a choice between taking only box B, or taking both boxes A and B. The player knows the following:
Box A is transparent and always contains a visible $1,000. Box B is opaque, and its content has already been set by the predictor: If the predictor has predicted the player will take both boxes A and B, then box B contains nothing. If the predictor has predicted that the player will take only box B, then box B contains $1,000,000. The player does not know what the predictor predicted or what box B contains while making the choice. Should the player take both boxes, or only box B? Causal decision theory recommends taking both boxes in this scenario, because at the moment when the player must make a decision, the predictor has already made a prediction (therefore, the action of the player will not affect the outcome). Conversely, evidential decision theory (EDT) would have recommended that the player takes only box B because taking only box B is strong evidence that the predictor anticipated that the player would only take box B, and therefore it is very likely that box B contains $1,000,000. Conversely, choosing to take both boxes is strong evidence that the predictor knew that the player would take both boxes; therefore we should expect that box B contains nothing.
== Criticism ==