the poster “Gray Area” explained why people aren’t being money-pumped, even though they violate independence.
I actually think that (for some examples) it’s actually simpler than that. The Allais paradox assumes that the proposal of the bet itself has no effect on the utility of the proposee. In reality, if I took a 5% chance at $100M, instead of a 100% chance at $4M, there’s a 95% chance I’d be kicking myself every time I opened my wallet for the rest of my life. Thus, taking the bet and losing is significantly worse than never having the bet proposed at all. If this is factored in correctly, EY’s original formulation of the Allais Paradox is no longer functional: I prefer certainty, because losing when certainty was an option carries lower utility than never having bet.
This is more about how you calculate outcomes than it is about independence directly. If losing when you could have had a guaranteed (or nearly-guaranteed) win carries negative utility, and if you can only play once, it does not seem like it contradicts independence.
I actually think that (for some examples) it’s actually simpler than that. The Allais paradox assumes that the proposal of the bet itself has no effect on the utility of the proposee. In reality, if I took a 5% chance at $100M, instead of a 100% chance at $4M, there’s a 95% chance I’d be kicking myself every time I opened my wallet for the rest of my life. Thus, taking the bet and losing is significantly worse than never having the bet proposed at all. If this is factored in correctly, EY’s original formulation of the Allais Paradox is no longer functional: I prefer certainty, because losing when certainty was an option carries lower utility than never having bet.
This is more about how you calculate outcomes than it is about independence directly. If losing when you could have had a guaranteed (or nearly-guaranteed) win carries negative utility, and if you can only play once, it does not seem like it contradicts independence.