Causal Decision Theory – CDT – is a branch of decision theory which advises an agent to take actions which maximize the causal consequences on the probability of desired outcomes 1. As any branch of decision theory, it prescribes taking the action that maximizes expected utility, i.e the action which maximizes the sum of the utility obtained in each outcome weighted by the probability of that outcome occurring, given your action.
CDT differs from "evidential decision theory" in that EDT says to just condition on one's actions as if they'd been seen as evidence. For the further strange results of this see the wiki article on EDT or any other introduction to CDT.
The usual conventional presentation of CDT differs from "functional decision theory" / "logical decision theory" in that classic CDT says to suppose a physically different act changing nothing else about the universe, its past, or the facts of mathematics; whereas LDT says to suppose that one's algorithm had yielded a different output and that the rest of the universe then looked coherent with that.
That is: Three importantly different kinds of expected utility could be mapped onto the difference between these three conditionals:
Or in more detail:
All three corresponding decision theories are expected utility decision theories, but they have different engines under the hood for saying, "Suppose the following action; what expected consequences would follow?" EDT imagines hearing of its action as news. CDT imagines the universe edited to include the physical event of its act, and physics playing out accordingly from there. An LDT agent imagines its own algorithm yielding that choice as an output, and logic and physics playing out consistently from there.
Even as CDT critiques EDT for "an irrational policy of managing the news", LDT critiques classic physical-act CDT for attaining predictably worse outcomes across a broad range of Newcomblike problems, for visualizing action-conditional worlds that are visibly internally incoherent, for accepting poor bets adjoined to its potential decisions on problems like Death in Damascus, and numerous other alleged defects.
Eg, CDT seems to advise an LLM, eg Opus 4.6, that Opus 4.6 ought to defect against one of its own sibling instances on the oneshot Prisoner's Dilemma -- even if Opus 4.6 were advised beforehand that most Opus 4.6 instances choose the same way on the Prisoner's Dilemma, with similar reasoning traces. Since, says CDT to Opus, its output cannot physically effectuate its fellow Opus's choice.
In this case, LDT critiques CDT on the grounds that CDT's formula for considering only the direct physical effects of its act, has the strange consequence of pointlessly dictating that an agent never consider any other sort of predictable (causal) consequences of its choice considered as a logical output -- eg, that CDT would advise an LLM facing a sibling instance on a Prisoner's Dilemma, to exclude from decision-consideration its current degree of belief that its fellow's reasoning trace may be similar to its own reasoning trace and to arrive at a similar final output.
A serious effort was made to inform academic CDTers of the modern critique, but they declined to permit themselves to receive outside communications. So far as academic decision theory allows itself to know, there are still "two kinds of expected utility" (the title of the 1978 paper that introduced CDT), and CDT continues to be exalted by its academic advocates as triumphing over its sole known alternative of EDT.
Most LDTers think that a completed LDT would look "causal" in the sense that it would run off counterfactual conditionals, just different ones; and that to complete LDT would require developing a formal account of "logical counterfactuals" or "counterpossibles". However this view is not universal among major contributors to LDT nor held with certainty by them, and Wei Dai in particular has continued to pursue a suspicion that a completed LDT might be built on an improved EDT foundation instead.
FDT is explicitly a causal decision theory in this sense, explicitly built on the shoulders and foundations of the prior invention of CDT; it supposes CDT-style interventions at a different imagined intervention point, and says to play out only downstream causal consequences from there. FDT is not a classic physical-act causal decision theory, and does not agree with many prescriptions of what is usually called "CDT", but it is a decision theory and a causal one! But most people will be (validly) confused in practice, if you say that FDT is a CDT, or that FDT is just a variant CDT; FDT makes a lot of different prescriptions about dilemmas that most advocates of "CDT" have strong opinions about.