What about the physical process of offering somebody a menu of lotteries consisting only of options that they have seen before? Or a 2-step physical process where first one tells somebody about some set of options, and then presents a menu of lotteries taken only from that set? I can’t think of any example where a rational-seeming preference function doesn’t obey IIA in one of these information-leakage-free physical processes.
What about the physical process of offering somebody a menu of lotteries consisting only of options that they have seen before? Or a 2-step physical process where first one tells somebody about some set of options, and then presents a menu of lotteries taken only from that set? I can’t think of any example where a rational-seeming preference function doesn’t obey IIA in one of these information-leakage-free physical processes.