As far as I can tell we’re not actually dividing the space of W’s by a plane, we’re dividing the space of E(W|π)’s by a plane. We don’t know for certain that U-V is negative, we merely think so in expectation. This leads to the Bayesian correction for the Optimizer’s curse, which lets us do better when presented with lots of options with different uncertainties, but if the uncertainty is fixed it won’t let us pick a strategy that does better than the one that maximizes the proxy.
As far as I can tell we’re not actually dividing the space of W’s by a plane, we’re dividing the space of E(W|π)’s by a plane. We don’t know for certain that U-V is negative, we merely think so in expectation. This leads to the Bayesian correction for the Optimizer’s curse, which lets us do better when presented with lots of options with different uncertainties, but if the uncertainty is fixed it won’t let us pick a strategy that does better than the one that maximizes the proxy.
Because expectation is affine with respect to utility functions, this does divide the space by a plane.
Yes, there is a connection with the optimizer’s curse style of reasoning.