The UDT solution says: “instead of drawing a graph containing , draw one that contains and you will see that the independence between beliefs and decisions is restored!”
Can you try to come up with a situation where that independence is not restored? If we follow the analogy with correlations, it’s always possible to find a linear map that decorrelates variables...
Ha, indeed. I should have made the analogy with finding a linear change of variables such that the result is decomposable into a product of independent distributions—ie if (x,y) is distributed on a narrow band about the unit circle in R^2 then there is no linear change of variables that renders this distribution independent, yet a (nonlinear) change to polar coordinates does give independence.
Perhaps the way to construct a counterexample to UDT is to try to create causal links between and of the same nature as the links between and the in e.g. Newcomb’s problem. I haven’t thought this through any further.
Can you try to come up with a situation where that independence is not restored? If we follow the analogy with correlations, it’s always possible to find a linear map that decorrelates variables...
Ha, indeed. I should have made the analogy with finding a linear change of variables such that the result is decomposable into a product of independent distributions—ie if (x,y) is distributed on a narrow band about the unit circle in R^2 then there is no linear change of variables that renders this distribution independent, yet a (nonlinear) change to polar coordinates does give independence.
Perhaps the way to construct a counterexample to UDT is to try to create causal links between and of the same nature as the links between and the in e.g. Newcomb’s problem. I haven’t thought this through any further.