<more needed>
<In response to some of Eliezer's writing on TDT, Wei Dai came up with Updateless Decision Theory (UDT). UDT is clearly superior to TDT in cases such as counterfactual mugging. TDT gets these problems wrong as a result of updating on its observations before calculating expected utility; even though it is considering the consequences of its policies in the abstract, it is doing so only in the "current branch" (ie, updatefully), and so it misses the positive consequences of its policy on other branches.
Functional decision theory (FDT) was an attempt to write up the general motivation behind both TDT and UDT in a more needed>general way, which would have ideally created an umbrella term for decision theories sharing a flavor with UDT and TDT. To this end, the coathors of the FDT paper attempted to include Wei Dai as a coathor and get his approval of the general write-up as representing the spirit of UDT. However, the direction of the paper ended up heavily incorporating intuitions from causal decision theory (CDT), describing FDT as a shift from physical causality to logical causality, so that abstract mathematical nodes such as (critically) the output of the decision procedure could be included in the causal picture, and understood as exercising causal influence, even over physical circumstances.
Wei Dai intended UDT to be much closer to evidential decision theory (EDT) and further from CDT in spirit, and as such, declined to co-author the paper.
The FDT paper thus describes a general framework which remains agnostic about an updateless approach (like UDT) vs an updateful one (like TDT), but which sticks close to the logical-causality approach introduced by TDT. As such, it can be regarded as a successor to TDT (because it backs off from the fundamental mistake of TDT, namely, its updatefulness, while sticking to the core logical-causality intuition of TDT).
TDT will endorse one-boxing in this scenario and hence endorses the winning decision. When Omega predicts your behavior, it carries out the same abstract computation as you do when you decide whether to one-box or two-box. To make this point clear, we can imagine that Omega makes this prediction by creating a simulation of you and observing its behavior in Newcomb's problem. This simulation will clearly decide according to the same abstract computation as you do as both you and it decide in the same manner. NowNow, given that TDT says to act as if deciding the output of this computation, it tells you to act as if your decision to one-box can determine the behavior of the simulation (or, more generally, Omega's prediction) and hence the filling of the boxes. So TDT correctly endorses one-boxing in Newcomb's problem as it tells the agent to act as if doing so will lead them to get $1,000,000 instead of $1,000.
Timeless decision theory (TDT) is a decision theory, developed by Eliezer Yudkowsky which, in slogan form, says that agents should decide as if they are determining the output of the abstract computation that they implement. This theory was developed in response to the view that rationality should be about winning (that is, about agents achieving their desired ends) rather than about behaving in a manner that we would intuitively label as rational. Prominent existing decision theories (including causal decision theory, or CDT) fail to choose the winning decision in some scenarios and so there is a need to develop a more successful theory.