Dynamic consistency + Consequentialism → Independence
This really helped me understand the problem with independence. So imagine a consequentialist agent in a Parfit’s hitchhiker situation. Given the option to become non consequentialist (and thus able to carry through on a commitment to pay for a ride) it would do so, since that is the consequentialist thing to do (looking forward it’s the best option). So consequentialism is not actually a stable state of being.
Which of dynamic consistency and consequentialism is not obeyed in EE situations like the one you suggested and how?
My intuition is that
Both are obeyed, and EE can in fact be expressed as a vnm utility function (prove me wrong by answering the above question! It’s an intuition because i haven’t yet been able to pin down how to express EE as a vnm utility function, more below)
Utility theory axioms imply that some utility function exists, not its form.
Said utility function depends on your preferences. If i have a buck and you offer me repeated 50-50 odds of winning 50% of everything or losing 40% of everything its a bad bet—unless this is the only way for me to make money and i want to buy something for two bucks. In this case, a chance is better than nothing.
More generally, EE is specifying a certain set of preferences where having a higher expected wealth is less important than ensuring the growth is measure 1. This is a useful set of preferences in the real world, but neither necessitated nor argued against by the axioms of utility theory.
I expect that if my preferences are about what will happen in the limit of the game, and i care about what happens most of the time, that the utility function will converge to the EE solution, regardless of the specific dynamics. (Is that defining dynamics as outcomes?)