The VNM axioms are about preferences over lotteries over commodity bundles, not about preferences over lotteries over world histories. A commodity bundle is some ill-specified, immiscible utility fluid. If you want to change that model by adding an extended timeline of causal repercussions, so that there is enough room in your theory to indirectly account for instrumental preferences, then it seems to me you either have to explain what you mean by world-history bundles (UDT with its program execution histories might be thought of as having preferences over multiple world histories at once), or you should admit that you’re throwing out additivity of commodities. Additivity formalized the intuition that more goodness is better, i.e. that preferences scale with quantities of resources or intensities of emotion or frequencies of experience or whatever. That can be offloaded to the specifics of the utility function, and probably should be, but I’ve never seen anyone state that’s how they’re thinking.
There is a second, less general way some people alter VNM, by talking about preferences over lotteries over individual events within a timeline. This third form of VNM does not have space enough to account for instrumental utility unless you artificially group together causally related events, like having preferences over lotteries for “1 hour pre-travel preparation time and getting to go to Ecuador”. It’s still kind of useful for discussion because it exposes that way human preferences are similar for repeatable events, states, and experiences.
The VNM axioms are about preferences over lotteries over commodity bundles, not about preferences over lotteries over world histories. A commodity bundle is some ill-specified, immiscible utility fluid. If you want to change that model by adding an extended timeline of causal repercussions, so that there is enough room in your theory to indirectly account for instrumental preferences, then it seems to me you either have to explain what you mean by world-history bundles (UDT with its program execution histories might be thought of as having preferences over multiple world histories at once), or you should admit that you’re throwing out additivity of commodities. Additivity formalized the intuition that more goodness is better, i.e. that preferences scale with quantities of resources or intensities of emotion or frequencies of experience or whatever. That can be offloaded to the specifics of the utility function, and probably should be, but I’ve never seen anyone state that’s how they’re thinking.
There is a second, less general way some people alter VNM, by talking about preferences over lotteries over individual events within a timeline. This third form of VNM does not have space enough to account for instrumental utility unless you artificially group together causally related events, like having preferences over lotteries for “1 hour pre-travel preparation time and getting to go to Ecuador”. It’s still kind of useful for discussion because it exposes that way human preferences are similar for repeatable events, states, and experiences.