Usually when people think either of them are a good idea it is because they have been incidentally supplementing and subverting them with a whole lot of their own common sense!

As a person who (right now) thinks that EDT is a good idea, could you help enlighten me?

Wikipedia states that under EDT the action with the maximum value is chosen, where value is determined as V(A) =sum{outcomes O} P(O|A) U(O). The agent can put in knowledge about how the universe works into P(O|A), right?

Now the smoking lesion problem. It can be formally written as something like this,

U(smoking) = 1
U(cancer) = -100000
P(cancer | lesion) > P(cancer | !lesion)
P(smoking | lesion) > P(smoking | !lesion)
P(cancer | lesion&smoking) = P(cancer | lesion&!smoking) = P(cancer | lesion)
P(cancer | !lesion&smoking) = P(cancer | !lesion&!smoking) = P(cancer | !lesion)

I think the tricky part is P(smoking | lesion) > P(smoking | !lesion), because this puts a probability on something that the agent gets to decide. Since probabilities are about uncertainty, and the agent would be certain about its actions, this makes no sense.

Is that the main problem with EDT?

Actually the known fact is more like P(X smoking | X lesion), the probability of any agent with a lesion deciding to smoke. From this the agent will have to derive P(me smoking | me lesion). If the agent is an avarage human being, then they would be equal. But if the agent is special because he uses some specific decision theory or utility function, he should only look at a smaller reference class. I think in this way you get quite close to TDT/UDT.