We will consider a special version of the Smoking Lesion where there is 100% correlation between smoking and cancer - ie. if you have the lesion, then you smoke and have cancer, if you don't have the lesion, then you don't smoke and don't have cancer. We'll also assume the predictor is perfect in the version of Newcomb's we are considering. Further, we'll assume that the Lesion is outside of the "core" part of your brain, which we'll just refer to as the brain and assume that it affects this by sending hormones to it.

Causality

Notice how similar the problems are. Getting the $1000 or to smoke a cigarette is a Small Gain. Getting cancer or missing out on the $1 million is a Big Loss. Anyone who Smokes or Two-Boxes gets a Small Gain and a Big Loss. Anyone who Doesn't Smoke or One-boxes gets neither.

So while from one perspective these problems might seem the same, they seem different when we try to think about it casually.

For Newcomb's:

• Imagine a One-Boxer counterfactually Two-Boxers
• Then their brain my be that of a Two-Boxer, so they are predicted to Two-Box, so they miss out on the million

For Smoking Lesion:

• Imagine that a Non-Smoker counterfactually Smokes
• Then we don't imagine this giving them the Lesion, so they still don't get cancer

Or at least these are the standard interpretations of these problems. The key question two ask here is why does it seem reasonable to imagine the predictor changing its prediction if you counterfactually Two-Box, but the lesion remaining the same if you counterfactually smoke?

Linkages

The mystery deepens when we realise that in Smoking Lesion, the Lesion is taken to cause both Smoking and Cancer, while in Newcomb's, your Brain causes both your Decision and the Prediction. For some reason, we seem more inclined to cut the link between Smoking and the Lesion than between your Decision and your Brain.

How do we explain this? One possibility is that for there Lesion there is simply more indirection - the link is Lesion -> Brain -> Decision - and that this pushes us to see it as easier to cut. However, I think it's worthwhile paying attention to the specific links. The link between your Brain and your Decision is a very tightly coupled link. It's hard to imagine a mismatch here without the situation becoming inconsistent. We could imagine a situation where the output of your brain goes to a chip which makes the final decision, but then we've added an entirely new element into the problem and so we hardly seem to be talking about the same problem.

On the other hand, this is much easier to do with the link between the Lesion and Brain - you just imagine the hormones never arriving. That would contradict the problem statement, but it isn't inconsistent physically. But why do we accept this as the same problem?

Some objects in problems "have a purpose" in that if they don't perform a particular function, we'll feel like the problem "doesn't match the description". For example, the "purpose" of your brain is to make decisions and the "purpose" of a predictor is to predict your decisions. If we intervene to break either the Brain-Decision linkage or the Brain-Predictor linkage, then it'll feel like we've "broken the problem".

In contrast, the Lesion has two purposes - to affect your behaviour and whether you have cancer. If we strip it of one, then it still has the other, so the problem doesn't feel broken. In other words, in order to justify breaking a linkage, it's not enough that it just be a past linkage, but we also have to be able to justify that we're still considering the same problem.

Reflections

It's interesting to compare my analysis of Smoking Lesion to CDT. In this particular instance, we intervene at a point in time and only casually flow the effects forward in the same way that CDT has. However, we haven't completely ignored the inconsistency issue since we can imagine whatever hormones the lesion releases not actually reaching the brain. This involves ignoring one aspect of the problem, but prevents the physical inconsistency. And the reason why we can do this for the Smoking Lesion, but not Newcomb's Problem is that the coupling from Brain to Lesion is not as tight as that from Decision to Brain.

The counterfactuals ended up depending on both the physical situation and the socio-linguistic conventions. How tightly various aspects of the situation were bound determined the amount of intervention that would be required to break the linkage without introducing an inconsistency, while the socio-linguistic conventions determined whether the counterfactual was accepted as still being the same problem.

Related:

• Alien implant: Newcomb's Smoking Lesion - Less Wrong Discussion
• Ambijectivity - Scott Alexander argues that when we say that an artwork is "better" than another, we are imagining repeatedly breaking down questions until we end up with 100s or 1000s of objective questions which are then given different weightings. An artwork will seem clearly better than another if it rates higher on almost all the questions, particularly those that are typically assigned higher weights. Similarly, we could imagine dozens of factors affecting what counts as a valid counterfactual, with each factor being accorded a different weight.