4 Evidential versus causal decision theory

The next two cases come from Elga (2020), in which two decision theorists show a potential donor, Ms Neutra, around their departments.³

Professor Causey, a causal decision theorist, keeps stopping to put his finger in the electrical outlets, and is shocked every time. Asked why, he says it is “to reduce the amount of electrical shocking I experience, of course” (Elga 2020: 212). The outlets are Libet–Ahmed–Newcomb outlets, or LANs. Each contains a brain-scanner, which predicts whether the person approaching is likely to touch it, and runs Programme A if it predicts they will and Programme B if it predicts they won’t.

Touching is better in either column, and the programme was fixed before the decision: “by the time one makes one’s decision, the outlet has irrevocably chosen its programme. So one is guaranteed to do better by touching the outlet” (Elga 2020: 213). So touching strongly statewise dominates not touching, and causal decision theory says touch. The evidential theory says the opposite: touching is strong evidence that the outlet predicted a touch and is running Programme A, so touching makes a shock very likely, and Causey should keep his hands to himself.

The trouble is that Causey is the only one being shocked. Passers-by, cats and first-year students leave the outlets alone and are fine. As Neutra puts it, it is “just shock-avoidance experts such as yourself who stick their fingers in the outlets and receive shocks” (Elga 2020: 214).

In the second scene Neutra visits Professor Evidentia, an evidential decision theorist, who announces that “here at the Evidential Altruism Lab we always choose so as to minimize the expected number of shocks people receive” (Elga 2020: 214) — and then takes out a stun gun and prepares to shock her.

The device on the ceiling is a Decision Prediction Unit. Last week it scanned their brains to predict whether Evidentia would shock Neutra today. “If it predicted that I would shock you, it left you alone last week. But if it predicted that I would refrain, then it ensured that last week you received 20 shocks” (Elga 2020: 215). The shock she is about to administer has no good effects at all; its only causal consequence is the pain.

The crossed-out cells are the ones she is almost certain do not obtain. Shocking is therefore excellent evidence that Neutra was left alone last week, and refraining is excellent evidence that she was shocked twenty times. So the evidential theory says shock. The causal theory says the opposite, and Neutra says why: “there’s nothing to be done now about shocks I may or may not have received last week, so that information is not relevant to your current decision” (Elga 2020: 215).

The two scenes are mirror images. Causey looks ridiculous following causal decision theory, and Evidentia looks ridiculous following evidential decision theory. Elga’s own view (2020: 219–20) is that the two situations are roughly the same, and so whichever way we go, we will need to explain away behaviour that can look ridiculous when framed in a certain way.

One-boxers walk away with a million. Two-boxers walk away with a thousand. This happens over and over, and everybody can see it coming. Doesn’t that settle it? If your theory of rational choice predictably leaves you poorer than the alternative, so the thought goes, so much the worse for your theory.

Here’s a counterargument on the part of the causal decision theorist. People who apply evidential decision theory are being rewarded by the demon before they take their decision, for being the sort of people who One Box. By the lights of causal decision theory, they’re being rewarded for being irrational. But that doesn’t prove that they’re rational.

However, it turns out that the situation is asymmetric: this can happen to the causal decision theorist, but not to the evidential decision theorist.⁴ A causal decision theorist can be put in a case where being “irrational”, by their own lights, is what gets rewarded, and their theory tells them not to do it anyway. An evidential decision theorist cannot be: if being “irrational” is rewarded, and doing the “irrational” thing is evidence that you will get the reward, then evidential decision theory tells you to do the “irrational” thing associated with the reward. So this is a problem that can arise for causal decision theory, and cannot arise for evidential decision theory.

Here is a case with the same structure as Newcomb’s problem, but no demon. Suppose that a gene causes both a desire to smoke and cancer, and that smoking itself causes nothing bad. (This is a stipulation for the sake of the example, and it is false.) Say that getting cancer costs you 10 and smoking is worth 1 to you, so that the outcomes are as in Table 4.

By contrast, the causal theory says smoke. Whether you have the gene, and so whether you get cancer, is causally independent of what you do, so these states are the right ones for the causal theorist, and smoking comes out 1 better in either column: it strongly statewise dominates not smoking.

Many people have the reaction that refraining from smoking, if one is confident that smoking itself causes nothing bad, would be irrational. If so, that would be a problem for evidential decision theory.

To help us understand the structure of the case better, we can look at another causal graph:

The gene causes both cancer and a desire to smoke; and the desire to smoke causes people to smoke; but smoking does not cause cancer. This is the same shape as the Newcomb case in Figure 6: a common cause of the act and the state, and no arrow from the act to the state. So, just as there, smoking is evidence of cancer without being a cause of it.

The evidential theorist’s response is that the causal structure is beside the point. It makes no difference whether smoking causes cancer or merely indicates it. Either way, smoking is bad news.

There is a well-known reply on behalf of the evidential theory, due to Eells (1981: section 4), called the tickle defence.⁵ The gene causes smoking only by causing the desire to smoke. But you know whether you have the desire: you can feel it. So the desire is already your evidence about the gene, and so about cancer, before you do anything. Acting on the desire tells you nothing further. Once the desire is taken into account, then, \Cr(C \mid S) = \Cr(C \mid S^c): smoking is no longer evidence of cancer, the evidential theory no longer tells you to give up, and the case doesn’t arise.