Vladimir_Nesov comments on Can anyone explain to me why CDT two-boxes? - Less Wrong Discussion
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What you actually choose is one particular option (you may even strongly suspect in advance which one; and someone else might know it even better). "Choice" doesn't imply lack of determinism. If what you choose is something definite, it could as well be engraved on a stone tablet in advance, if it was possible to figure out what the future choice turns out to be. See Free will (and solution).