If you accept both properties and you violate independence, you can be money-pumped. Here is how it works, concretely. Suppose your preference between gambles A and B depends on what the common component C is (as the independence axiom says it shouldn’t). Before the uncertainty resolves, you evaluate the compound lottery holistically and prefer the plan involving B (because, in combination with the C branch, B produces a better overall distribution). But then the coin comes up heads, the C branch is now off the table, and you find yourself choosing between A and B in isolation. Consequentialism says you should evaluate based on what’s still possible. And in isolation, you prefer A. So you switch from your plan (B) to your current preference (A). You are dynamically inconsistent.
Can someone clarify this passage to me? I find myself increasingly confused. Earlier, we assume agent can form a plan: “if the coin comes up heads (no C), I will choose A, if coin comes up tails, I will choose B (with C)”. How can I be money pumped? I don’t violate dynamic consistency nor do I violate consequentialism. Yet I violate independence, and can’t be money pumped. I can’t be convinced to pre-commit to either B or A, since there are no predictors involved, and I can just postpone my actual choice.
Edit: Actually, I don’t violate independence either, these are simply different outcomes. So I don’t understand this argument at all.
Can someone clarify this passage to me? I find myself increasingly confused. Earlier, we assume agent can form a plan: “if the coin comes up heads (no C), I will choose A, if coin comes up tails, I will choose B (with C)”. How can I be money pumped? I don’t violate dynamic consistency nor do I violate consequentialism. Yet I violate independence, and can’t be money pumped. I can’t be convinced to pre-commit to either B or A, since there are no predictors involved, and I can just postpone my actual choice.
Edit: Actually, I don’t violate independence either, these are simply different outcomes. So I don’t understand this argument at all.