The Allais paradox (both Eliezer version and the Wikipedia article) seems to not specify at all if the reward is instantaneous or delayed, so I wouldn’t say the risk aversion isn’t justified—if offered the paradox with no precision, I would say there is a chance for the reward to be instant, a chance for it to be delayed, so the risk aversion should be partially considered. It’s a bit of nitpicking, but not that much. There is no mention of time/delay in either of the paradox nor the axiom, and that seems to be a weakness to me.
And even without time, information can still have some value. If you chose 1B in the Allais paradox and lose, you can regret your choice (leading to, in fact, a <0 outcome) more than in you chose 2B and lose. Because of the information that it’s purely because of your choice you lose money. Or people can have a lower opinion of you (which may have negative consequences on your life) if they have the information too. Regretting what was a rational decision can be considered irrational, so I don’t see a problem with it being incompatible with VNM axioms. But the reaction of other people being irrational is not something you can discard the same way—if a VNM rational agent is unable to deal with human beings who aren’t perfectly rational, then there is a problem.
In short : the value of information is more important when it creates uncertainty—when the results of the lottery are delayed. But even when the results are instantaneous, information still have some value (positive or negative) that can make choosing 1A over 1B and 2B over 2A the rational choice to do in some situations.
The Allais paradox (both Eliezer version and the Wikipedia article) seems to not specify at all if the reward is instantaneous or delayed, so I wouldn’t say the risk aversion isn’t justified—if offered the paradox with no precision, I would say there is a chance for the reward to be instant, a chance for it to be delayed, so the risk aversion should be partially considered. It’s a bit of nitpicking, but not that much. There is no mention of time/delay in either of the paradox nor the axiom, and that seems to be a weakness to me.
And even without time, information can still have some value. If you chose 1B in the Allais paradox and lose, you can regret your choice (leading to, in fact, a <0 outcome) more than in you chose 2B and lose. Because of the information that it’s purely because of your choice you lose money. Or people can have a lower opinion of you (which may have negative consequences on your life) if they have the information too. Regretting what was a rational decision can be considered irrational, so I don’t see a problem with it being incompatible with VNM axioms. But the reaction of other people being irrational is not something you can discard the same way—if a VNM rational agent is unable to deal with human beings who aren’t perfectly rational, then there is a problem.
In short : the value of information is more important when it creates uncertainty—when the results of the lottery are delayed. But even when the results are instantaneous, information still have some value (positive or negative) that can make choosing 1A over 1B and 2B over 2A the rational choice to do in some situations.