Abstract
Andy Egan has presented a dilemma for decision theory. As is well known, Newcomb cases appear to undermine the case for evidential decision theory (EDT). However, Egan has come up with a new scenario which poses difficulties for causal decision theory. I offer a simple solution to this dilemma in terms of a modified EDT. I propose an epistemological test: take some feature which is (i) relevant to your evaluation of the scenarios under consideration, (ii) evidentially correlated with the actions under consideration albeit, (iii) causally independent of them. Hold this feature fixed as a hypothesis. The test shows that, in Newcomb cases, EDT would mislead the agent. Where the test shows EDT to be misleading, I propose to use fictive conditional credences in the EDT-formula under the constraint that they are set to equal values. I then discuss Huw Price’s defence of EDT as an alternative to my diagnosis. I argue that my solution also applies if one accepts the main premisses of Price’s argument. I close with applying my solution to Nozick’s original Newcomb problem.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Notes
A dependency hypothesis is “... a maximally specific proposition about matters outside the agent’s influence and relevant to features of the outcome that the agent cares about” (Lewis 1981, p. 19). With respect to chancy outcomes, “... dependency hypotheses are exactly the conjunction of probabilistic full patterns” (Lewis 1981, p. 27).
There are several uncertainties about the original case (Ledwig 2000). The verdict may not be stable if one varies the several aspects of the example: one’s confidence in the predictor, what grounds this confidence, the pay-offs, issues of risk aversion, repeated and one-shot cases, and so on. There are reasons why one’s intuitive verdict on the case may go astray. I shall largely ignore these issues.
I replace Egan’s example The Smoking Lesion (2007, p. 94) with Price’s to facilitate incorporating Price’s treatment.
It is natural to understand Egan’s description as follows: Paul’s present credence that he is a psychopath is low and won’t change until he learns that he actually pushed the button. One may feel reservations how Paul can seriously consider doing a thing like killing all psychopaths without thereby having a reason to revise his low initial credence. However, it should be possible to build a plausible example which exhibits the features intended by Egan, unless one principally denies a plausible claim: there are possible cases where the agent does not get any new evidence about her causal structure before she really performs an action. As Lewis puts this claim: ‘(How can I tell what I think till I see what I say?—E. M. Forster) For the dithery and the self-deceptive, no amount of Gedankenexperimente in decision can provide as much selfknowledge as the real thing.’(Lewis 1986, p. 312) I see no reason to deny Lewis’s claim. If one feels too concerned about the plausibility of Egan’s case, I propose to replace it by a case which more convincingly represents the structure intended by Egan.
The evidence might be just the low overall proportion of PMS in the population.
The causal relationship is stipulated such that E is positive evidence for F and \(\lnot \)E is positive evidence for \(\lnot \)F. The case where \(\lnot \)E just leaves your credence in F unaltered can be treated as a special instance of this structure.
I do not deny that the causal link must have a certain modal stability. What I deny is that this modal stability is defined with respect to the situations as presented by EDT.
Deliberation and causal structure might conflict. If F is the case, and F reliably causes you to choose A, you can follow EDT only if it recommends A. For instance, if Coco is in PMS and PMS reliably causes one to eat chocolate, he cannot follow the erroneous recommendation to refrain. But this does not make a difference to my argument that EDT will mislead the agent’s expectations in such cases. The agents are just unable to follow where EDT leads them.
Isn’t it already worrisome that EDT will distort Paul’s decision if he is no psychopath? It is. But probably we cannot expect that a decision theory should give good advice for any coherent constellation of evidence and a hypothesis about how the world is.
This constraint excludes solutions such as weighing one’s conditional credences \(\hbox {C}(\hbox {F/A}_{1}), {\ldots } \hbox {C}(\hbox {F/A}_{\mathrm{n}})\) by one’s prior unconditional credences in one’s options \(\hbox {C}(\hbox {A}_{1}),{\ldots } \hbox {C}(\hbox {A}_{\mathrm{n}})\).
See Appendix.
See Appendix.
Correlation in the loose sense that is compatible with \(\lnot \)A just telling you nothing new about whether you are in F.
I distinguish this reading from a variant where Newcomb’s problem is interpreted as a two-person game. The game imposes constraints on how the prediction mechanism works. The predictor is reliable just because he knows your dominant strategy. I surmise that in this variant, your knowledge of the dominant option allows you to decide which conditional credence is not misleading.
Price’s diagnosis does not apply to the original Newcomb problem. According to Price, upon choosing not to consume Coco would fall into a relevant subclass of those not consuming. The class of those not consuming is formed partly of those who are not inclined to chocolate in the first place and partly of those who share Coco’s motives. The EDT-rational option that corresponds to Coco’s choosing not to eat chocolate would be to choose one box. But there is no comparable division among the one-boxers according to their motives to be expected. The motive to be expected from any one-boxer is to get the good news coming with one-boxing and to avoid the bad news coming with two-boxing.
If intuitions vary with different pay-offs, then this proposal might be partially revisionary, although there is the built-in flexibility for issues of risk.
Proposals which face this problem include Meek and Glymour’s (1994) distinction between two different perspectives on the Newcomb problem, depending on whether one’s action is seen as an intervention or not, and Nozick’s (1993) combination of EDT and CDT. Each encounters difficulties to the degree that it integrates elements of EDT.
For instance, CDT and Ledwig’s (2000) proposal to conceive Nozick’s original problem as a game against nature do not have this flaw. One could support my proposed test by interpreting the Newcomb case as a game against nature, but I do not commit myself to such an interpretation.
References
Ahmed, A., & Price, H. (2012). Arntzenius on ‘Why Ain’cha Rich?’. Erkenntnis, 77, 15–30.
Ahmed, A. (2012). Push the button. Philosophy of Science, 79, 386–395.
Arntzenius, F. (2008). No regrets, or: Edith Piaf revamps decision theory. Erkenntnis, 68, 277–297.
Cantwell, J. (2010). On an alleged counter-example to causal decision theory. Synthese, 173, 127–152.
Edgington, D. (2011). Conditionals, causation, and decision. Analytic Philosophy, 52, 75–87.
Egan, A. (2007). Some counterexamples to causal decision theory. Philosophical Review, 116, 93–114.
Fisher, J. C. Disposition-based decision theory. Unpublished manuscript.
Gustafsson, J. (2011). A note in defence of ratificationism. Erkenntnis, 75, 147–150.
Kyburg, H. (1988). Powers. In W. L. Harper & B. Skyrms (Eds.), Causation in decision, belief change, and statistics (Vol. II, pp. 71–82). Dordrecht: Kluwer.
Ledwig, M. (2000). Newcomb’s problem. PhD Dissertation, Universität Konstanz. http://kops.ub.uni-konstanz.de/bitstream/handle/urn:nbn:de:bsz:352-opus-5241/ledwig.pdf?sequence=1.
Lewis, D. (1981). Causal decision theory. Australasian Journal of Philosophy, 59, 5–30.
Lewis, D. (1986). Part 7: Dependence and decision. In Philosophical Papers (Vol. II, pp. 271–343). Oxford: Oxford University Press.
Meek, C., & Glymour, C. (1994). Conditioning and intervening. British Journal for the Philosophy of Science, 45, 1001–1021.
Nozick, R. (1993). The nature of rationality. Princeton: Princeton University Press.
Nozick, R. (1998). Newcomb’s problem and two principles of choice. In Socratic puzzles (pp. 45–74). Cambridge, MA: Harvard University Press (originally 1969).
Price, H. (1986). Against causal decision theory. Synthese, 67, 195–212.
Price, H. (1991). Agency and probabilistic causality. The British Journal for the Philosophy of Science, 42, 157–176.
Schwartz, B., Ben-Haim, Y., & Dacso, C. (2010). What makes a good decision? Robust satisficing as a normative standard of rational decision making. Journal for the Theory of Social Behaviour, 41, 209–227.
Wedgwood, R. (2013). Gandalf’s solution to the Newcomb problem. Synthese, 190, 2643–2675.
Weirich, P. (2008). Causal decision theory. In E. N. Zalta (Ed.), The Stanford encyclopedia of philosophy (Winter 2008 ed.). http://plato.stanford.edu/archives/win2008/entries/decision-causal/.
Author information
Authors and Affiliations
Corresponding author
Appendix
Appendix
Here is the full elaboration of the numeric examples:
The formulas for calculating Coco’s original EDT-value are as follows:
Inserting the numbers:
The formulas for calculating Paul’s original EDT-values are as follows:
Inserting the numbers yields:
Rights and permissions
About this article
Cite this article
Dohrn, D. Egan and agents: How evidential decision theory can deal with Egan’s dilemma. Synthese 192, 1883–1908 (2015). https://doi.org/10.1007/s11229-015-0661-0
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11229-015-0661-0