An option that dominates in finite cases will always provably be part of the maximal option in finite problems; but in infinite problems, where there is no maximal option, the dominance of the option for the infinite case does not follow from its dominance in all finite cases.
If you allow a discontinuity where the utility of the infinite case is not the same as the limit of the utilities of the finite cases, then you have to allow a corresponding discontinuity in planning where the rational infinite plan is not the limit of the rational finite plans.
Bayesianism, Infinite Decisions, and Binding replies to Vann McGee’s “An airtight dutch book”, defending the permissibility of an unbounded utility function.
An option that dominates in finite cases will always provably be part of the maximal option in finite problems; but in infinite problems, where there is no maximal option, the dominance of the option for the infinite case does not follow from its dominance in all finite cases.
If you allow a discontinuity where the utility of the infinite case is not the same as the limit of the utilities of the finite cases, then you have to allow a corresponding discontinuity in planning where the rational infinite plan is not the limit of the rational finite plans.