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| '''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 will make the actor have the happiest expectations about the outcome.
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| ==Description==
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| In a 1981 article, Allan Gibbard and William Harper explained causal decision theory as maximization of the expected utility <math>U</math> of an action <math>A</math> of an action "calculated from probabilities of [[Counterfactual conditional|counterfactuals]]":<ref name="GibbardHarper">{{Citation
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| | title = Counterfactuals and two kinds of expected utility
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| | year = 1981
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| | journal = Ifs: Conditionals, Beliefs, Decision, Chance, and Time
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| | pages = 153–190
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| | last1 = Gibbard | first1 = A.
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| | last2 = Harper | first2 = W.L.}}</ref>
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| :<math>
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| U(A)=\sum\limits_{j} P(A > O_j) D(O_j),
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| </math>
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| where <math>D(O_j)</math> is the desirability of outcome <math>O_j</math> and <math>P(A > O_j)</math> is the counterfactual probability that, if <math>A</math> were done, then <math>O_j</math> would hold.
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| ==Difference from evidential decision theory==
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| [[David Kellogg Lewis|David Lewis]] proved<ref name=Lewis1976>{{Citation
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| | doi = 10.2307/2184045
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| | title = Probabilities of conditionals and conditional probabilities
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| | year = 1976
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| | author = Lewis, D.
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| | journal = The Philosophical Review
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| | pages = 297–315| volume = 85
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| | issue = 3
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| | publisher = Duke University Press
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| | jstor = 2184045
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| }}</ref> that the probability of a conditional <math>P(A > O_j)</math> does not always equal the conditional probability <math>P(O_j | A)</math>.<ref>In fact, Lewis proved a stronger result: "if a class of probability functions is closed under conditionalizing, then there can be no probability conditional for that class unless the class consists entirely of trivial probability functions," where a ''trivial probability function'' is one that "never assigns positive probability to more than two incompatible alternatives, and hence is at most four-valued [...]."</ref> If that were the case, causal decision theory would be equivalent to evidential decision theory, which uses conditional probabilities.
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| Gibbard and Harper showed that if we accept two axioms (one related to the controversial [[principle of the conditional excluded middle]]<ref name=Shaffer2009>{{Citation
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| | title = Decision Theory, Intelligent Planning and Counterfactuals
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| | year = 2009
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| | author = Shaffer, Michael John
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| | journal = Minds and Machines
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| | pages = 61–92
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| | volume = 19
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| | issue = 1
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| | doi = 10.1007/s11023-008-9126-2
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| }}</ref>), then the [[statistical independence]] of <math>A</math> and <math>A > O_j</math> suffices to guarantee that <math>P(A > O_j) = P(O_j | A)</math>. 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.
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| <blockquote>
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| 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)
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| </blockquote> | |
| 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.
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| ==Criticism==
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| ===Counterexamples===
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| [[Newcomb's paradox]] 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.<ref name="GibbardHarper" /> However, this results in getting only $1,000, not $1,000,000. Similar concerns arise in problems like the [[prisoner's dilemma]]<ref name=Lewis1979>{{Citation
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| | title = Prisoners'dilemma is a Newcomb problem
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| | jstor = 2265034
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| | year = 1979
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| | author = Lewis, D.
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| | journal = Philosophy & Public Affairs
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| | pages = 235–240| volume = 8
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| | issue = 3
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| | publisher = Blackwell Publishing
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| }}</ref> and various other thought experiments.<ref name=Egan2007>{{Citation
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| | doi = 10.1215/00318108-2006-023
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| | title = Some counterexamples to causal decision theory
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| | url = http://www.webcitation.org/query?url=http://www.geocities.com/eganamit/NoCDT.pdf&date=2009-10-25+21:40:36
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| | year = 2007
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| | author = Egan, A.
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| | journal = The Philosophical Review
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| | pages = 93–114
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| | volume = 116
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| | issue = 1
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| | accessdate = 2009-05-28
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| |archiveurl=http://web.archive.org/web/20091025030652/http://geocities.com/eganamit/NoCDT.pdf|archivedate=2009-10-25}}</ref>
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| ===Probabilities of conditionals===
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| As Michael John Shaffer points out,<ref name=Shaffer2009 /> there are difficulties with assigning probabilities to counterfactuals. One proposal is the "imaging" technique suggested by Lewis:<ref name=Lewis1981>{{Citation
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| | doi = 10.1080/00048408112340011
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| | title = Causal decision theory
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| | url = http://www.informaworld.com/index/739194078.pdf
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| | year = 1981
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| | author = Lewis, D.
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| | journal = Australasian Journal of Philosophy
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| | pages = 5–30
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| | volume = 59
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| | issue = 1
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| | accessdate = 2009-05-29
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| }}</ref> To evaluate <math>P(A > O_j)</math>, move probability mass from each possible world <math>w</math> to the closest possible world <math>w_A</math> in which <math>A</math> holds, assuming <math>A</math> is possible. However, this procedure requires that we know what we would believe if we were certain of <math>A</math>; this is itself a conditional to which we might assign probability less than 1, leading to regress.<ref name=Shaffer2009 />
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| ==See also==
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| <div style="-moz-column-count:3; column-count:3;">
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| * [[Decision making]]
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| * [[Evidential decision theory]]
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| * [[Expected utility hypothesis]]
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| * [[Game theory]]
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| * [[Newcomb's paradox]]
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| </div>
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| ==Notes==
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| {{reflist}}
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| ==External links==
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| *[http://plato.stanford.edu/entries/decision-causal/ Causal Decision Theory] at the [[Stanford Encyclopedia of Philosophy]]
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| * [http://plato.stanford.edu/entries/logic-conditionals/ The Logic of Conditionals] at the [[Stanford Encyclopedia of Philosophy]]
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| {{DEFAULTSORT:Causal Decision Theory}}
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| [[Category:Decision theory| ]]
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The Internet is a vast open market where businesses and consumers congregate. If you are a positive thinker businessman then today you have to put your business online. This is the reason for the increased risk of Down Syndrome babies in women over age 35. So if you want to create blogs or have a website for your business or for personal reasons, you can take advantage of free Word - Press installation to get started. As soon as you start developing your Word - Press MLM website you'll see how straightforward and simple it is to create an online presence for you and the products and services you offer.
The least difficult and very best way to do this is by acquiring a Word - Press site. By using Word - Press MLM websites or blogs, you and your companies presence on the internet can be created swiftly and simply. We can active Akismet from wp-admin > Plugins > Installed Plugins. Every single Theme might be unique, providing several alternatives for webpage owners to reap the benefits of in an effort to instantaneously adjust their web page appear. If you have any questions on starting a Word - Press food blog or any blog for that matter, please post them below and I will try to answer them.
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