Deliberating agents should take their choice to be between worlds that differ over the past as well as over the future. In particular, they differ over the effects of the present choice but also over its unknown causes. Typically these past differences will be microphysical differences that don’t matter to anyone. But in Betting on the Past they matter to Alice.
. . .
On this new picture, which arises naturally from [evidential decision theory]. . ., it is misleading to think of decisions as forks in a road. Rather, we should think of them as choices between roads that were separate all along. For instance, in Betting on the Past, Alice should take herself to be choosing between actualizing a world at which P was all along true and one at which it was all along false.
From Arif Ahmed’s Evidence, Decision and Causality (ch. 5.4, p. 142-143; links mine):
. . .