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Ev­i­den­tial De­ci­sion Theory

TagLast edit: 26 Sep 2020 19:33 UTC by Swimmer963

Evidential Decision Theory – EDT – is a branch of decision theory which advises an agent to take actions which, conditional on it happening, maximizes the chances of the desired outcome. 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. Causal Decision Theory – CDT – says only through causal process one can influence the chances of the desired outcome 1. EDT, on the other hand, requires no causal connection, the action only have to be a Bayesian evidence for the desired outcome. Some critics say it recommends auspiciousness over causal efficacy2.

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 wound recommend against smoking, since smoking is an evidence for having the mentioned gene and thus should be avoided.

CDT uses probabilities of conditionals and contrafactual dependence to calculate the expected utility of an action – which track causal relations -, whereas EDT simply uses conditional probabilities. 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 usual cases these two probabilities are the same. However, David Lewis proved 3 its’ 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 diverge depending on the problem. In some cases EDT gives a better answers then CDT, such as the Newcomb’s problem, whereas in the Smoking lesion problem where CDT seems to give a more reasonable prescription.

References

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

  2. Joyce, J.M. (1999), The foundations of causal decision theory, p. 146

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

Blog posts

See also

Ev­i­den­tial De­ci­sion The­ory, Selec­tion Bias, and Refer­ence Classes

Qiaochu_Yuan8 Jul 2013 5:16 UTC
33 points
128 comments6 min readLW link

Does Ev­i­den­tial De­ci­sion The­ory re­ally fail Solomon’s Prob­lem?

AlexMennen11 Jan 2011 4:53 UTC
13 points
19 comments1 min readLW link

Is Ev­i­den­tial De­ci­sion The­ory pre­sump­tu­ous?

Tobias_Baumann2 Feb 2017 13:41 UTC
5 points
39 comments1 min readLW link

What’s Wrong with Ev­i­den­tial De­ci­sion The­ory?

aaronde23 Aug 2012 0:09 UTC
25 points
54 comments5 min readLW link

[Question] What is an Ev­i­den­tial De­ci­sion The­ory agent?

Chris_Leong5 Dec 2019 13:48 UTC
9 points
1 comment1 min readLW link

The Smok­ing Le­sion: A prob­lem for ev­i­den­tial de­ci­sion theory

[deleted]23 Aug 2010 9:01 UTC
3 points
101 comments1 min readLW link

An in­tro­duc­tion to de­ci­sion theory

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

The Differ­ence Between Clas­si­cal, Ev­i­den­tial, and Time­less De­ci­sion Theories

DanielLC26 Mar 2011 21:27 UTC
6 points
32 comments1 min readLW link

An­thropic un­cer­tainty in the Ev­i­den­tial Black­mail problem

Johannes_Treutlein14 May 2017 16:43 UTC
8 points
1 comment1 min readLW link
(casparoesterheld.com)

New­comb’s Prob­lem stan­dard positions

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