Evidential decision theory

School of thought within decision theory

Evidential decision theory (EDT) 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 with the highest news value, that is, the action which would be indicative of the best outcome in expectation if one received the "news" that it had been taken. In other words, it recommends to "do what you most want to learn that you will do."[1]: 7

EDT contrasts with causal decision theory (CDT), which prescribes taking the action that will causally produce the best outcome. While these two theories agree in many cases, they give different verdicts in certain philosophical thought experiments. For example, EDT prescribes taking only one box in Newcomb's paradox, while CDT recommends taking both boxes.[1]: 22–26

## Formal description

[edit]

In a 1976 paper, Allan Gibbard and William Harper distinguished between two kinds of expected utility maximization. EDT proposes to maximize the expected utility of actions computed using conditional probabilities, namely

V ( A ) = ∑ j P ( O j | A ) D ( O j ) , {\displaystyle V(A)=\sum \limits _{j}P(O_{j}|A)D(O_{j}),}

where  D ( O j ) {\displaystyle D(O_{j})} is the desirability of outcome  O j {\displaystyle O_{j}} and  P ( O j | A ) {\displaystyle P(O_{j}|A)} is the conditional probability of  O j {\displaystyle O_{j}} given that action  A {\displaystyle A} occurs.[2] This is in contrast to the counterfactual formulation of expected utility used by causal decision theory

U ( A ) = ∑ j P ( A ◻ -> O j ) D ( O j ) , {\displaystyle U(A)=\sum \limits _{j}P(A\mathrel {\Box {\rightarrow }} O_{j})D(O_{j}),}

where the expression  P ( A ◻ -> O j ) {\displaystyle P(A\mathrel {\Box {\rightarrow }} O_{j})} indicates the probability of outcome  O j {\displaystyle O_{j}} in the counterfactual situation in which action  A {\displaystyle A} is performed. Since  P ( A ◻ -> O j ) {\displaystyle P(A\mathrel {\Box {\rightarrow }} O_{j})} and  P ( O j | A ) {\displaystyle P(O_{j}|A)} are not always equal, these formulations of expected utility are not equivalent,[2] leading to differences in actions prescribed by EDT and CDT.

## Thought experiments

[edit]

Different decision theories are often examined in their recommendations for action in different thought experiments.

### Newcomb's paradox

[edit]

Main article: 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:[3]

* 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?

Evidential decision theory recommends taking only box B in this scenario, 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.[1]: 22

Conversely, causal decision theory (CDT) would have recommended that the player takes both boxes, because by that time the predictor has already made a prediction (therefore, the action of the player will not affect the outcome).

Formally, the expected utilities in EDT are

V ( take only B ) = P ( 1M in box B | take only B ) × $ 1 , 000 , 000 + P ( nothing in box B | take only B ) × $ 0 = 0.99 × $ 1 , 000 , 000 + 0.01 × $ 0 = $ 990 , 000 V ( take both boxes ) = P ( 1M in box B | take both boxes ) × $ 1 , 001 , 000 + P ( nothing in box B | take both boxes ) × $ 1 , 000 = 0.01 × $ 1 , 001 , 000 + 0.99 × $ 1 , 000 = $ 11 , 000 {\displaystyle {\begin{aligned}V({\text{take only B}})&=P({\text{1M in box B}}|{\text{take only B}})\times \$1,000,000+P({\text{nothing in box B}}|{\text{take only B}})\times \$0\\\&=0.99\times \$1,000,000+0.01\times \$0=\$990,000\\\V({\text{take both boxes}})&=P({\text{1M in box B}}|{\text{take both boxes}})\times \$1,001,000+P({\text{nothing in box B}}|{\text{take both boxes}})\times \$1,000\\\&=0.01\times \$1,001,000+0.99\times \$1,000=\$11,000\end{aligned}}}

Since  V ( take only B ) > V ( take both boxes ) {\displaystyle V({\text{take only B}})>V({\text{take both boxes}})} , EDT recommends taking only box B.

### Twin prisoner's dilemma

[edit]

See also: Prisoner's dilemma

In this variation on the Prisoner's Dilemma thought experiment, an agent must choose whether to cooperate or defect against her psychological twin, whose reasoning processes are exactly analogous to her own.

Aomame and her psychological twin are put in separate rooms and cannot communicate. If they both cooperate, they each get $5. If they both defect, they each get $1. If one cooperates and the other defects, then one gets $10, and the other gets $0. Assuming Aomame only cares about her individual payout, what should she do?[4]

Evidential decision theory recommends cooperating in this situation, because Aomame's decision to cooperate is strong evidence that her psychological twin will also cooperate, meaning that her expected payoff is $5. On the other hand, if Aomame defects, this would be strong evidence that her twin will also defect, resulting in an expected payoff of $1. Formally, the expected utilities are

V ( Aomame cooperates ) = P ( twin cooperates | Aomame cooperates ) × $ 5 + P ( twin defects | Aomame cooperates ) × $ 0 = 1 × $ 5 + 0 × $ 0 = $ 5 V ( Aomame defects ) = P ( twin cooperates | Aomame defects ) × $ 10 + P ( twin defects | Aomame defects ) × $ 1 = 0 × $ 10 + 1 × $ 1 = $ 1. {\displaystyle {\begin{aligned}V({\text{Aomame cooperates}})&=P({\text{twin cooperates}}|{\text{Aomame cooperates}})\times \$5+P({\text{twin defects}}|{\text{Aomame cooperates}})\times \$0\\\&=1\times \$5+0\times \$0=\$5\\\V({\text{Aomame defects}})&=P({\text{twin cooperates}}|{\text{Aomame defects}})\times \$10+P({\text{twin defects}}|{\text{Aomame defects}})\times \$1\\\&=0\times \$10+1\times \$1=\$1.\end{aligned}}}

Since  V ( Aomame cooperates ) > V ( Aomame defects ) {\displaystyle V({\text{Aomame cooperates}})>V({\text{Aomame defects}})} , EDT recommends cooperating.

### Sleeping beauty problem

[edit]

Main article: Sleeping beauty problem

Evidential decision theory has be applied to the Sleeping Beauty Problem in order to avoid Dutch book arguments. It has been argued that Sleeping Beauty is subject to Dutch books if she assigns a credence of 1/2 of the coin flip being heads, but can avoid them by adopting evidential decision theory. However, Vincent Conitzer argues that halfers are still affected by Dutch books even after adopting evidential decision theory.[5]

## Other supporting arguments

[edit]

Even if one puts less credence on evidential decision theory, it may be reasonable to act as if EDT were true. Namely, because EDT can involve the actions of many correlated decision-makers, its stakes may be higher than causal decision theory and thus take priority.[6]

## Criticism

[edit]

David Lewis has characterized evidential decision theory as promoting "an irrational policy of managing the news".[7] James M. Joyce asserted, "Rational agents choose acts on the basis of their causal efficacy, not their auspiciousness; they act to bring about good results even when doing so might betoken bad news."[8]

## See also

[edit]

* Economics portal
* Philosophy portal

* Causal decision theory
* Decision making
* Expected utility hypothesis
* Game theory
* Newcomb's paradox
* Superrationality

## References

[edit]

1. ^ a b c Ahmed, Arif (2021). Evidential Decision Theory. Cambridge University Press. ISBN 9781108607865.
2. ^ a b Gibbard, A.; Harper, W.L. (1976), Counterfactuals and Two Kinds of Expected Utility (PDF), pp. 7–8
3. ^ Wolpert, D. H.; Benford, G. (June 2013). "The lesson of Newcomb's paradox". Synthese. 190 (9): 1637–1646\. doi:10.1007/s11229-011-9899-3. JSTOR 41931515. S2CID 113227.
4. ^ Greene, P.; Levinstein, B. (2020). "Act Consequentialism without Free Rides". Philosophical Perspectives. 34 (1): 100–101\. doi:10.1111/phpe.12138. S2CID 211161349.
5. ^ Conitzer, Vincent (2015). "A Dutch book against sleeping beauties who are evidential decision theorists". Synthese. 192. Springer Netherlands. arXiv:1705.03560. doi:10.1007/s11229-015-0691-7. Retrieved 4 July 2025.
6. ^ MacAskill, William; Vallinder, Aron; Österheld, Caspar; Shulman, Carl; Treutlein, Johannes (2021), The Evidentialist's Wager (PDF)
7. ^ Lewis, D. (1981), "Causal decision theory" (PDF), Australasian Journal of Philosophy, 59 (1): 5–30, doi:10.1080/00048408112340011, retrieved 2009-05-29
8. ^ Joyce, J.M. (1999), The foundations of causal decision theory, p. 146

## External links

[edit]

* Causal Decision Theory at the Stanford Encyclopedia of Philosophy

* v
* t
* e

Decision theory

Core concepts|

* Ambiguity aversion
* Bounded rationality
* Choice architecture
* Expected utility
* Expected value
* Hyperbolic discounting
* Leximin
* Loss aversion
* Multi-attribute utility
* Path dependence
* Principle of indifference
* Prospect theory
* Rational choice theory
* Risk aversion
* Risk-seeking
* Satisficing
* Strategic dominance
* Subjective expected utility
* Sure-thing
* Utility theorem

Decision models|

* Anscombe-Aumann framework
* Causal decision
* Decision field theory
* Emotional choice
* Evidential decision
* Fuzzy-trace theory
* Intertemporal choice
* Naturalistic decision
* Normative model
* Quantum cognition
* Recognition-primed decision
* Rubicon model
* Savage's subjective expected utility model

Decision analysis tools|

* Analytic hierarchy process
* Analytic network process
* Cost–benefit analysis
* Cost-effectiveness analysis
* Cost–utility analysis
* Decision conferencing
* Decision curve analysis
* Decision rule
* Decision support system
* Decision table
* Decision tree
* Decision matrix
* Decisional balance sheet
* Gittins index
* Influence diagram
* Minimax
* MCDA
* Scoring rule
* Value of information
* perfect
* sample
* uncertainty

Paradoxes and biases|

* Allais paradox
* Certainty effect
* Cognitive bias
* Decoy effect
* Disposition effect
* Ellsberg paradox
* Endowment effect
* Framing effect
* Heuristics
* Newcomb's paradox
* Pseudocertainty effect
* Reference dependence
* Regret
* St. Petersburg paradox
* Status quo bias
* Sunk cost

Uncertainty and risk|

* Deep uncertainty
* Exploration–exploitation
* Info-gap
* Pignistic probability
* Robust decision-making

Related fields|

* Behavioral economics
* Game theory
* Operations research
* Social choice theory
* Utility theory

Key people|

* David Blackwell
* Bruno de Finetti
* Morris H. DeGroot
* Peter C. Fishburn
* Gerd Gigerenzer
* Itzhak Gilboa
* Daniel Kahneman
* R. Duncan Luce
* Oskar Morgenstern
* Howard Raiffa
* Leonard J. Savage
* David Schmeidler
* Herbert Simon
* Amos Tversky
* John von Neumann

Category
*[v]: View this template
*[t]: Discuss this template
*[e]: Edit this template