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As far as I can reconstruct EDT's algorithm, it goes something like this:
1) I know that smoking is correlated with lung cancer.
2) I've read in a medical journal that smoking and lung cancer have a common cause, some kind of genetic lesion. I don't know if I have that lesion.
3) I'd like to smoke now, but I'm not sure if that's the best decision.
4) My friend, a causal decision theorist, told me that smoking or not smoking cannot affect the lesion that I already have or don't. But I don't completely buy that reasoning. I prefer to use something else, which I will call "evidential decision theory".
5) To figure out the best action to take, first I will counterfactually imagine myself as an automaton whose actions are chosen randomly, taking into account the lesion that I have or don't, using the frequencies observed in the world. So an automaton with the lesion will have a higher probability of smoking and a higher probability of cancer.
6) Next, I will figure out what the automaton's actions say about its utility, using ordinary conditional probabilities and expected values. It looks like the utility of automatons that smoke is lower than the utility of those that don't, because the former ones are more likely to get cancer.
7) Now I will remember that I'm not an automaton, and choose to avoid smoking based on the above reasoning!
Does that make sense?
The problem with this line of reasoning is that the desire to smoke is correlated with smoking, and therefore with the genetic lesion. Since and EDT agent is assumed to perform Bayesian updates, it should update its probability of having the lesion upon the observation that it has a desire to smoke.
How much it should update depends on its prior.
If, according to its prior, the desire to smoke largely screens off the correlation between the lesion and smoking, then the agent will choose to smoke.
Sorry, are you saying that EDT is wrong, or that my explanation of EDT is wrong? If it's the former, I agree. If it's the latter, can you give a different explanation? Note that most of the literature agrees that EDT doesn't smoke in the smoking lesion problem, so any alternative explanation should probably give the same result.
The latter. The objection that I described is known as "tickle defense of EDT".
Keep in mind that EDT is defined formally, and informal scenarios typically have implicit assumptions of probabilistic conditional independence which affect the result.
By making these assumption explicit, it is possible to have EDT smoke or not smoke in the smoking lesion problem, and two-box or one-box in Newcomb's problem.
In fact the smoking lesion problem and Newcomb's problem are two instances of the same type of decision problem, but their presentations may yield different implicit assumptions: in the smoking lesion problem virtually anybody makes assumptions such that smoking is intuitively the optimal choice, in Newcomb's problem there is no consensus over the optimal choice.
OK, thanks. Though if that's indeed the "proper" version of EDT, then I no longer understand the conflict between EDT and CDT. Do you know any problem where EDT+tickle disagrees with CDT?
CDT essentially always chooses two-box/smoke in Newcomb-like problems, in EDT, the choice depends on the specific formalization of the problem.