A clever adversary who knows your preferences can now exploit this. They offer you a sequence of trades: pay a small amount to switch from plan-A to plan-B before the coin flip (because ex ante you prefer B in context), then after the coin lands heads, pay a small amount to switch from B to A (because ex post you prefer A in isolation). You have paid twice and ended up exactly where you started.
OK, I see you’ve confused Independence of Irrelevant Alternatives with VNM-Independence here. I don’t want to be too harsh here, because this is probably my fault, but this basically completely undermines your core argument since you haven’t actually refuted the Dutch Book for VNM independence. In short, c. 2022:
I made an edit describing VNM-independence as a probabilistic version of IIA in the Wikipedia article on the VNM theorem. By this I meant they share a common structure in that both are about ignoring details that obviously shouldn’t affect the outcome, but which several people misunderstood as saying VNM-independence encompasses IIA (it doesn’t).
In this StackExchange comment, I answered the question in the OP’s title without explaining they were confusing the two axioms in the body.
I’ve since fixed both of these, but for a while these were two of the first things that showed up when you Googled the topic, so chances are you read them.
There’s several other major misunderstandings in this post that trace back to Wikipedia articles that I, unfortunately, haven’t had time to correct. In general: Wikipedia articles and online resources on rational choice or decision theory are not reliable. I do not recommend reading them. They consistently make several basic errors along that show up in this post, like conflating descriptive and prescriptive validity, confusing expected value with expected utility, and citing confused philosophers as if they represent substantial viewpoints (when they contain mathematical errors that have been repeatedly pointed out by experts).
I recommend plugging this into Gemini and asking it to explain all the mistakes in this post, which it should be able to do; it did a good job explaining the difference between IIA and VNM-independence when I tried it out.
OK, I see you’ve confused Independence of Irrelevant Alternatives with VNM-Independence here. I don’t want to be too harsh here, because this is probably my fault, but this basically completely undermines your core argument since you haven’t actually refuted the Dutch Book for VNM independence. In short, c. 2022:
I made an edit describing VNM-independence as a probabilistic version of IIA in the Wikipedia article on the VNM theorem. By this I meant they share a common structure in that both are about ignoring details that obviously shouldn’t affect the outcome, but which several people misunderstood as saying VNM-independence encompasses IIA (it doesn’t).
In this StackExchange comment, I answered the question in the OP’s title without explaining they were confusing the two axioms in the body.
I’ve since fixed both of these, but for a while these were two of the first things that showed up when you Googled the topic, so chances are you read them.
There’s several other major misunderstandings in this post that trace back to Wikipedia articles that I, unfortunately, haven’t had time to correct. In general: Wikipedia articles and online resources on rational choice or decision theory are not reliable. I do not recommend reading them. They consistently make several basic errors along that show up in this post, like conflating descriptive and prescriptive validity, confusing expected value with expected utility, and citing confused philosophers as if they represent substantial viewpoints (when they contain mathematical errors that have been repeatedly pointed out by experts).
I recommend plugging this into Gemini and asking it to explain all the mistakes in this post, which it should be able to do; it did a good job explaining the difference between IIA and VNM-independence when I tried it out.