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Causal De­ci­sion Theory

TagLast edit: 1 Oct 2020 0:13 UTC by Swimmer963

Causal Decision Theory – CDT—is a branch of decision theory which advises an agent to take actions that maximizes the causal consequences on the probability of desired outcomes 1. As any branch of decision theory, it prescribes taking the action that maximizes utility, that which utility equals or exceeds the utility of every other option. The utility of each action is measured by the expected utility, the averaged by probabilities sum of the utility of each of its possible results. How the actions can influence the probabilities differ between the branches. Contrary to Evidential Decision Theory – EDT—CDT focuses on the causal relations between one’s actions and its outcomes, instead of focusing on which actions provide evidences for desired outcomes. According to CDT a rational agent should track the available causal relations linking his actions to the desired outcome and take the action which will better enhance the chances of the desired outcome.

One usual example where EDT and CDT commonly diverge is the Smoking lesion: “Smoking is strongly correlated with lung cancer, but in the world of the Smoker’s Lesion this correlation is understood to be the result of a common cause: a genetic lesion that tends to cause both smoking and cancer. Once we fix the presence or absence of the lesion, there is no additional correlation between smoking and cancer. Suppose you prefer smoking without cancer to not smoking without cancer, and prefer smoking with cancer to not smoking with cancer. Should you smoke?” CDT would recommend smoking since there is no causal connection between smoking and cancer. They are both caused by a gene, but have no causal direct connection with each other. EDT on the other hand would recommend against smoking, since smoking is an evidence for having the mentioned gene and thus should be avoided.

The core aspect of CDT is mathematically represented by the fact it uses probabilities of conditionals in place of conditional probabilities 2. The probability of a conditional is the probability of the whole conditional being true, where the conditional probability is the probability of the consequent given the antecedent. A conditional probability of B given A—P(B|A) -, simply implies the Bayesian probability of the event B happening given we known A happened, it’s used in EDT. The probability of conditionals – P(A > B) - refers to the probability that the conditional ‘A implies B’ is true, it is the probability of the contrafactual ‘If A, then B’ be the case. Since contrafactual analysis is the key tool used to speak about causality, probability of conditionals are said to mirror causal relations. In most cases these two probabilities track each other, and CDT and EDT give the same answers. However, some particular problems have arisen where their predictions for rational action diverge such as the Smoking lesion problem – where CDT seems to give a more reasonable prescription – and Newcomb’s problem – where CDT seems unreasonable. David Lewis proved 3 it’s impossible to probabilities of conditionals to always track conditional probabilities. Hence, evidential relations aren’t the same as causal relations and CDT and EDT will always diverge in some cases.

References

  1. http://​​plato.stanford.edu/​​entries/​​decision-causal/​​

  2. Lewis, David. (1981) “Causal Decision Theory,” Australasian Journal of Philosophy 59 (1981): 5- 30.

  3. Lewis, D. (1976), “Probabilities of conditionals and conditional probabilities”, The Philosophical Review (Duke University Press) 85 (3): 297–315

See also

Causal de­ci­sion the­ory is unsatisfactory

So8res13 Sep 2014 17:05 UTC
35 points
162 comments9 min readLW link

Are causal de­ci­sion the­o­rists try­ing to out­smart con­di­tional prob­a­bil­ities?

Caspar4216 May 2017 8:01 UTC
6 points
10 comments3 min readLW link

Build a Causal De­ci­sion Theorist

michaelcohen23 Sep 2019 20:43 UTC
1 point
14 comments4 min readLW link

Func­tional De­ci­sion The­ory vs Causal De­ci­sion The­ory: Ex­pand­ing on New­comb’s Problem

Geropy2 May 2019 22:15 UTC
2 points
7 comments3 min readLW link

New­comb’s Prob­lem: A prob­lem for Causal De­ci­sion Theories

[deleted]16 Aug 2010 11:25 UTC
11 points
121 comments4 min readLW link

Time­less­ness as a Con­ser­va­tive Ex­ten­sion of Causal De­ci­sion Theory

[deleted]28 May 2014 14:57 UTC
25 points
65 comments14 min readLW link

Nat­u­ral­ized in­duc­tion – a challenge for ev­i­den­tial and causal de­ci­sion theory

Caspar4222 Sep 2017 8:15 UTC
13 points
14 comments7 min readLW link

In­vi­ta­tion to com­ment on a draft on mul­ti­verse-wide co­op­er­a­tion via al­ter­na­tives to causal de­ci­sion the­ory (FDT/​UDT/​EDT/​...)

Caspar4229 May 2017 8:34 UTC
6 points
7 comments1 min readLW link

De­ci­sion The­o­ries: A Less Wrong Primer

orthonormal13 Mar 2012 23:31 UTC
97 points
174 comments9 min readLW link

An in­tro­duc­tion to de­ci­sion theory

[deleted]13 Aug 2010 9:09 UTC
25 points
29 comments6 min readLW link

An in­tro­duc­tion to New­comblike problems

So8res20 Sep 2014 18:40 UTC
23 points
5 comments7 min readLW link

[Question] What’s been writ­ten about the na­ture of “son-of-CDT”?

Liam Donovan30 Nov 2019 21:03 UTC
16 points
6 comments1 min readLW link

New­comb’s Prob­lem stan­dard positions

Eliezer Yudkowsky6 Apr 2009 17:05 UTC
7 points
22 comments1 min readLW link
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