When I read about the Allais paradox (in lukeprog’s post, after he fixed your objection), my first thought was that this violation would occur when the cat was actually something very like an orange, such as a grapefruit. For example, suppose that the cat actually is an orange. So you prefer an apple to an orange, but you prefer an orange to a gamble which is 70% apple and 30% orange. And the neoclassical utility theorist would explain this by saying that you prefer certainty to uncertainty, so adding a term for certainty to the utility function. And then, if the choice is really between 70% apple and 30% grapefruit versus 70% orange and 30% grapefruit, the latter is still more certain than the former (although not completely certain), so might well be preferred.
This sounds like I’m trying to come up with a way to save utility theory, but actually that’s not how it went. My immediate intuitive reaction to reading lukeprog’s paraphrase of your example was ‹I’ll bet that this happens when the cat is similar to the orange.›, without any conscious reasoning behind it, and it was only after thinking about this hypothesis that I realised that it suggested a way to save utility theory. So I’m quite curious: Does the Allais paradox appear only when the cat is similar to an orange, or does it also appear when the cat is (as the terms ‘apple’, ‘orange’, and ‘cat’ imply) really quite different?
When I read about the Allais paradox (in lukeprog’s post, after he fixed your objection), my first thought was that this violation would occur when the cat was actually something very like an orange, such as a grapefruit. For example, suppose that the cat actually is an orange. So you prefer an apple to an orange, but you prefer an orange to a gamble which is 70% apple and 30% orange. And the neoclassical utility theorist would explain this by saying that you prefer certainty to uncertainty, so adding a term for certainty to the utility function. And then, if the choice is really between 70% apple and 30% grapefruit versus 70% orange and 30% grapefruit, the latter is still more certain than the former (although not completely certain), so might well be preferred.
This sounds like I’m trying to come up with a way to save utility theory, but actually that’s not how it went. My immediate intuitive reaction to reading lukeprog’s paraphrase of your example was ‹I’ll bet that this happens when the cat is similar to the orange.›, without any conscious reasoning behind it, and it was only after thinking about this hypothesis that I realised that it suggested a way to save utility theory. So I’m quite curious: Does the Allais paradox appear only when the cat is similar to an orange, or does it also appear when the cat is (as the terms ‘apple’, ‘orange’, and ‘cat’ imply) really quite different?