The collision I’m seeing is that between formal, mathematical axioms, and English language usage. Its clear that Benelliot is thinking of the axiom in mathematical terms: dry, inarguable, much like the independence axioms of probability: some statements about abstract sets. This is correct—the proper formulation of VNM is abstract, mathematical.
Kilobug is right in noting that information has value, ignorance has cost. But that doesn’t subvert the axiom, as the axioms are mathematically, by definition, correct; the way they were mapped to the example was incorrect: the choices aren’t truly independent.
Its also become clear that risk-aversion is essentially the same idea as “information has value”: people who are risk-averse are people who value certainty. This observation alone may well be enough to ‘explain’ the Allais paradox: the certainty of the ‘sure thing’ is worth something. All that the Allais experiment does is measure the value of certainty.
The collision I’m seeing is that between formal, mathematical axioms, and English language usage. Its clear that Benelliot is thinking of the axiom in mathematical terms: dry, inarguable, much like the independence axioms of probability: some statements about abstract sets. This is correct—the proper formulation of VNM is abstract, mathematical.
Kilobug is right in noting that information has value, ignorance has cost. But that doesn’t subvert the axiom, as the axioms are mathematically, by definition, correct; the way they were mapped to the example was incorrect: the choices aren’t truly independent.
Its also become clear that risk-aversion is essentially the same idea as “information has value”: people who are risk-averse are people who value certainty. This observation alone may well be enough to ‘explain’ the Allais paradox: the certainty of the ‘sure thing’ is worth something. All that the Allais experiment does is measure the value of certainty.