I occasionally see a question like "what would FDT recommend in ....?" and I am puzzled that there is no formal algorithm to answer it. Instead humans ask other humans, and the answers are often different and subject to interpretation. This is rather disconcerting. For comparison, you don't ask a human what, say, a chessbot would do in a certain situation, you just run the bot. Similarly, it would be nice to have an "FDTbot" one can feed a decision theory problem to. Does something like that exist? If not, what are the obstacles?
Mostly they can't, which is why there are a lot more questions posted about it than people who answer correctly. I can't think of any FDT problem that has been answered correctly where there were more than 3 binary inputs to the decision function, and even some with 2 bits have been controversial.
For the few cases where they can, it's the same way that humans solve any mathematical problem: via an ill defined bunch of heuristics, symmetry arguments, experience with similar problems, and some sort of intuition or insight.