A few reasons. First, the VNM framework isn’t about sequential decisions; it’s about one-shot decisions. This doesn’t matter too much in practice because sequential decision problems can be turned into one-shot decision problems either by having the agent pick a policy, or by using what the agent expects it will do in the future in each case to figure out what future outcomes are currently the available options. So if the agent is being supposedly being offered a choice between A and B, but if it picks B, then it will taken an option to switch to C in the future, then it isn’t actually being offered a choice between A and B. The sequential argument doesn’t really make sense in the static VNM context.
But also, the argument from the sequential scenario is much less robust, since as Abram pointed out, it is only one scenario that could happen with intransitive preferences. The fact that every scenario in which an agent gets to act on its intransitive preference also involves unnecessary costs to the agent seems more important. Another way in which the sequential scenario is less robust is that it can be defeated by having a policy of stopping before you get back where you started if offered the opportunity to pay to repeatedly switch outcomes. But of course this tactic does not change the fact that if you pay to go even one step no matter what your starting position was, then you’re paying unnecessary costs.
A few reasons. First, the VNM framework isn’t about sequential decisions; it’s about one-shot decisions. This doesn’t matter too much in practice because sequential decision problems can be turned into one-shot decision problems either by having the agent pick a policy, or by using what the agent expects it will do in the future in each case to figure out what future outcomes are currently the available options. So if the agent is being supposedly being offered a choice between A and B, but if it picks B, then it will taken an option to switch to C in the future, then it isn’t actually being offered a choice between A and B. The sequential argument doesn’t really make sense in the static VNM context.
But also, the argument from the sequential scenario is much less robust, since as Abram pointed out, it is only one scenario that could happen with intransitive preferences. The fact that every scenario in which an agent gets to act on its intransitive preference also involves unnecessary costs to the agent seems more important. Another way in which the sequential scenario is less robust is that it can be defeated by having a policy of stopping before you get back where you started if offered the opportunity to pay to repeatedly switch outcomes. But of course this tactic does not change the fact that if you pay to go even one step no matter what your starting position was, then you’re paying unnecessary costs.