Direction of causality, or even causality itself, is irrelevant to FDT. Subjunctive dependence is simply a statement that two variables are not independent across the possible worlds conditional on parameters of interest. It doesn’t say that one causes the other or that they have a common cause.
In the calculator example, the variables are the outputs of the two calculators, and the parameters of interest are inputs common to both calculators. In this case the dependence is extremely strong: there is a 1:1 relation between the outputs for any given input in all possible worlds where both calculators are functioning correctly.
For the purposes of FDT, the relevant subjunctive dependence is that between the decision process outputs and the outcomes, and the variables of interest are the inputs to the decision process. In carefully constructed scenarios such as Newcombe’s problem, the subjunctive dependence is total: Omega is a perfect predictor. When the dependence is weaker, the details matter more—but still causality is irrelevant.
In the case of weaker dependence you can get something like a direction of dependence, in that perhaps each value of variable A corresponds to a single value of variable B across possible worlds, but not vice versa. This still doesn’t indicate causality.
FDT can require that P come augmented with
information about the logical, mathematical, computational, causal, etc. structure
of the world more broadly. Given a graph G that tells us how changing a logical variable affects all other variables, we can re-use Pearl’s do operator to give a
decision procedure for FDT
FDT seems to rely heavily on this sort of assumption, but also seems to lack any sort of formalization of how the logical graphs work.
Direction of causality, or even causality itself, is irrelevant to FDT. Subjunctive dependence is simply a statement that two variables are not independent across the possible worlds conditional on parameters of interest. It doesn’t say that one causes the other or that they have a common cause.
In the calculator example, the variables are the outputs of the two calculators, and the parameters of interest are inputs common to both calculators. In this case the dependence is extremely strong: there is a 1:1 relation between the outputs for any given input in all possible worlds where both calculators are functioning correctly.
For the purposes of FDT, the relevant subjunctive dependence is that between the decision process outputs and the outcomes, and the variables of interest are the inputs to the decision process. In carefully constructed scenarios such as Newcombe’s problem, the subjunctive dependence is total: Omega is a perfect predictor. When the dependence is weaker, the details matter more—but still causality is irrelevant.
In the case of weaker dependence you can get something like a direction of dependence, in that perhaps each value of variable A corresponds to a single value of variable B across possible worlds, but not vice versa. This still doesn’t indicate causality.
What I have in mind is stuff like this:
FDT seems to rely heavily on this sort of assumption, but also seems to lack any sort of formalization of how the logical graphs work.