I like the idea from Pretentious Penguin that, IIA might not be satisfied in general, but if you first get the agent to read A, B, C, and then offer {A,B} as options and {A,B,C} as options, (a specific instance of) IIA could be satisfied in that context.
You can gain info by being presented with more options, but once you have gained info, you could just be invariant to being presented with the same info again.
so you would get IIA*: “whether you prefer option A or B is independent of whether I offer you an irrelevant option C, provided that you had already processed {A,B,C} beforehand”
You can’t have processed all possible information at a finite time, so above is limited relative to the original IIA.
I also didn’t check whether you get additional problems with IIA*.
I like the idea from Pretentious Penguin that, IIA might not be satisfied in general, but if you first get the agent to read A, B, C, and then offer {A,B} as options and {A,B,C} as options, (a specific instance of) IIA could be satisfied in that context.
You can gain info by being presented with more options, but once you have gained info, you could just be invariant to being presented with the same info again.
so you would get IIA*: “whether you prefer option A or B is independent of whether I offer you an irrelevant option C, provided that you had already processed {A,B,C} beforehand”
You can’t have processed all possible information at a finite time, so above is limited relative to the original IIA.
I also didn’t check whether you get additional problems with IIA*.