Excellent response. Thank you. :) I’ll start with some basic responses, and will respond later to other points when I have more time.
I think you intend ‘sensitive to unused alternatives’ to refer to the Independence axiom of the VNM theorem, but VNM Independence isn’t about unused alternatives. It’s about lotteries that share a sublottery. It’s Option-Set Independence (sometimes called ‘Independence of Irrelevant Alternatives’) that’s about unused alternatives.
I was speaking casually here, and I now regret it. You are absolutely correct that Option-Set independence is not the Independence axiom. My best guess about what I meant was that VNM assumes that the agent has preferences over lotteries in isolation, rather than, for example, a way of picking preferences out of a set of lotteries. For instance, a VNM agent must have a fixed opinion about lottery A compared to lottery B, regardless of whether that agent has access to lottery C.
> agents with intransitive preferences can be straightforwardly money-pumped
You are correct. My “straightforward” mechanism for money-pumping an agent with preferences A > B, B > C, but which does not prefer A to C does indeed depend on being able to force the agent to pick either A or C in a way that doesn’t reliably pick A.
Excellent response. Thank you. :) I’ll start with some basic responses, and will respond later to other points when I have more time.
I was speaking casually here, and I now regret it. You are absolutely correct that Option-Set independence is not the Independence axiom. My best guess about what I meant was that VNM assumes that the agent has preferences over lotteries in isolation, rather than, for example, a way of picking preferences out of a set of lotteries. For instance, a VNM agent must have a fixed opinion about lottery A compared to lottery B, regardless of whether that agent has access to lottery C.
You are correct. My “straightforward” mechanism for money-pumping an agent with preferences A > B, B > C, but which does not prefer A to C does indeed depend on being able to force the agent to pick either A or C in a way that doesn’t reliably pick A.