Causal decision theory
Encyclopedia
Causal decision theory is a school of thought within decision theory
which maintains that the expected utility of actions should be evaluated with respect to their potential causal consequences. It contrasts with evidential decision theory
, which recommends those actions that, conditional on having been performed, will make the actor have the happiest expectations about the outcome.
of an action 
of an action "calculated from probabilities of counterfactuals
":
where
is the desirability of outcome 
and 
is the counterfactual probability that, if 
were done, then 
would hold.
proved that the probability of a conditional
does not always equal the conditional probability 
. 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
and 
suffices to guarantee that 
. 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
In this case, evidential decision theory recommends that Solomon abstain from Bathsheba, while causal decision theory—noting that whether David is charismatic or uncharismatic cannot be changed—recommends sending for her.
is a classic example illustrating the potential conflict between causal and evidential decision theory: Because your choice of one or two boxes can't causally affect the Predictor's guess, causal decision theory recommends the two-boxing strategy. However, this results in getting only $1,000, not $1,000,000. Similar concerns arise in problems like the prisoner's dilemma
and various other thought experiments.
, move probability mass from each possible world 
to the closest possible world 
in which 
holds, assuming 
is possible. However, this procedure requires that we know what we would believe if we were certain of 
; this is itself a conditional to which we might assign probability less than 1, leading to regress.
Decision theory
Decision theory in economics, psychology, philosophy, mathematics, and statistics is concerned with identifying the values, uncertainties and other issues relevant in a given decision, its rationality, and the resulting optimal decision...
which maintains that the expected utility of actions should be evaluated with respect to their potential causal consequences. It contrasts with evidential decision theory
Evidential decision theory
Evidential decision theory is a school of thought within decision theory according to which the best action is the one which, conditional on your having chosen it, gives you the best expectations for the outcome...
, which recommends those actions that, conditional on having been performed, will make the actor have the happiest expectations about the outcome.
Description
In a 1981 article, Allan Gibbard and William Harper explained causal decision theory as maximization of the expected utility of an action of an action "calculated from probabilities of counterfactualsCounterfactual conditional
A counterfactual conditional, subjunctive conditional, or remote conditional, abbreviated , is a conditional statement indicating what would be the case if its antecedent were true...
":
where
is the desirability of outcome and is the counterfactual probability that, if were done, then would hold.Difference from evidential decision theory
David LewisDavid Kellogg Lewis
David Kellogg Lewis was an American philosopher. Lewis taught briefly at UCLA and then at Princeton from 1970 until his death. He is also closely associated with Australia, whose philosophical community he visited almost annually for more than thirty years...
proved that the probability of a conditional
does not always equal the conditional probability . 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
Statistical independence
In probability theory, to say that two events are independent intuitively means that the occurrence of one event makes it neither more nor less probable that the other occurs...
of
and suffices to guarantee that . 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 Solomon abstain from Bathsheba, while causal decision theory—noting that whether David is charismatic or uncharismatic cannot be changed—recommends sending for her.
Counterexamples
Newcomb's paradoxNewcomb's paradox
Newcomb's paradox, also referred to as Newcomb's problem, is a thought experiment involving a game between two players, one of whom purports to be able to predict the future. Whether the problem is actually a paradox is disputed....
is a classic example illustrating the potential conflict between causal and evidential decision theory: Because your choice of one or two boxes can't causally affect the Predictor's guess, causal decision theory recommends the two-boxing strategy. However, this results in getting only $1,000, not $1,000,000. Similar concerns arise in problems like the prisoner's dilemma
Prisoner's dilemma
The prisoner’s dilemma is a canonical example of a game, analyzed in game theory that shows why two individuals might not cooperate, even if it appears that it is in their best interest to do so. It was originally framed by Merrill Flood and Melvin Dresher working at RAND in 1950. Albert W...
and various other thought experiments.
Probabilities of conditionals
As Michael John Shaffer points out, there are difficulties with assigning probabilities to counterfactuals. One proposal is the "imaging" technique suggested by Lewis: To evaluate, move probability mass from each possible world to the closest possible world in which holds, assuming is possible. However, this procedure requires that we know what we would believe if we were certain of ; this is itself a conditional to which we might assign probability less than 1, leading to regress.External links
- Causal Decision Theory at the Stanford Encyclopedia of PhilosophyStanford Encyclopedia of PhilosophyThe Stanford Encyclopedia of Philosophy is a freely-accessible online encyclopedia of philosophy maintained by Stanford University. Each entry is written and maintained by an expert in the field, including professors from over 65 academic institutions worldwide...
- The Logic of Conditionals at the Stanford Encyclopedia of PhilosophyStanford Encyclopedia of PhilosophyThe Stanford Encyclopedia of Philosophy is a freely-accessible online encyclopedia of philosophy maintained by Stanford University. Each entry is written and maintained by an expert in the field, including professors from over 65 academic institutions worldwide...