Yes, framing effects are irrational, I agree. I’m saying that the mere existence of risk aversion with respect to something does not demonstrate the presence of framing effects or any other kind of irrationality (departure from the VNM axioms).
Well, now, hold on. Dawes is not actually saying that (and neither am I)! The claim is not “risk aversion demonstrates that there’s a framing effect going on (which is clearly irrational, and not just in the ‘violates VNM axioms’ sense)”. The point is that risk aversion (at least, risk aversion construed as “preferring less negatively skewed distributions”) constitutes departure from the VNM axioms. The independence axiom strictly precludes such risk aversion.
Whether risk aversion is actually irrational upon consideration — rather than merely irrational by technical definition, i.e. irrational by virtue of VNM axiom violation — is what Dawes is questioning.
The argument Dawes is making is simply not valid. He says …
That is not a good way to characterize Dawes’ argument.
I don’t know if you’ve read Rational Choice in an Uncertain World. Earlier in the same chapter, Dawes, introducing von Neumann and Morgenstern’s work, comments that utilities are intended to represent personal values. This makes sense, as utilities by definition have to track personal values, at least insofar as something with more utility is going to be preferred (by a VNM-satisfying agent) to something with less utility. Given that our notion of personal value is so vague, there’s little else we can expect from a measure that purports to represent personal value (it’s not like we’ve got some intuitive notion of what mathematical operations are appropriate to perform on estimates of personal value, which utilities then might or might not satisfy...). So any VNM utility values, it would seem, will necessarily match up to our intuitive notions of personal value.
So the only real assumption behind those graphs is that this agent’s utility function tracks, in some vague sense, an intuitive notion of personal value — meaning what? Nothing more than that this person places greater value on things he prefers, than on things he doesn’t prefer (relatively speaking). And that (by definition!) will be true of the utility function derived from his preferences.
It seems impossible that we can have a utility function that doesn’t give rise to such preferences over distributions. Whatever your utility function is, we can construct a pair of graphs exactly like the ones pictured (the x-axis is not numerically labeled, after all). But such a preference constitutes independence axiom violation, as mentioned...
The point is that risk aversion (at least, risk aversion construed as “preferring less negatively skewed distributions”) constitutes departure from the VNM axioms.
No, it doesn’t. Not unless it’s literally risk aversion with respect to utility.
So any VNM utility values, it would seem, will necessarily match up to our intuitive notions of personal value.
That seems to me a completely unfounded assumption.
Whatever your utility function is, we can construct a pair of graphs exactly like the ones pictured (the x-axis is not numerically labeled, after all).
The fact that the x-axis is not labeled is exactly why it’s unreasonable to think that just asking your intuition which graph “looks better” is a good way of determining whether you have an actual preference between the graphs. The shape of the graph is meaningless.
Well, now, hold on. Dawes is not actually saying that (and neither am I)! The claim is not “risk aversion demonstrates that there’s a framing effect going on (which is clearly irrational, and not just in the ‘violates VNM axioms’ sense)”. The point is that risk aversion (at least, risk aversion construed as “preferring less negatively skewed distributions”) constitutes departure from the VNM axioms. The independence axiom strictly precludes such risk aversion.
Whether risk aversion is actually irrational upon consideration — rather than merely irrational by technical definition, i.e. irrational by virtue of VNM axiom violation — is what Dawes is questioning.
That is not a good way to characterize Dawes’ argument.
I don’t know if you’ve read Rational Choice in an Uncertain World. Earlier in the same chapter, Dawes, introducing von Neumann and Morgenstern’s work, comments that utilities are intended to represent personal values. This makes sense, as utilities by definition have to track personal values, at least insofar as something with more utility is going to be preferred (by a VNM-satisfying agent) to something with less utility. Given that our notion of personal value is so vague, there’s little else we can expect from a measure that purports to represent personal value (it’s not like we’ve got some intuitive notion of what mathematical operations are appropriate to perform on estimates of personal value, which utilities then might or might not satisfy...). So any VNM utility values, it would seem, will necessarily match up to our intuitive notions of personal value.
So the only real assumption behind those graphs is that this agent’s utility function tracks, in some vague sense, an intuitive notion of personal value — meaning what? Nothing more than that this person places greater value on things he prefers, than on things he doesn’t prefer (relatively speaking). And that (by definition!) will be true of the utility function derived from his preferences.
It seems impossible that we can have a utility function that doesn’t give rise to such preferences over distributions. Whatever your utility function is, we can construct a pair of graphs exactly like the ones pictured (the x-axis is not numerically labeled, after all). But such a preference constitutes independence axiom violation, as mentioned...
No, it doesn’t. Not unless it’s literally risk aversion with respect to utility.
That seems to me a completely unfounded assumption.
The fact that the x-axis is not labeled is exactly why it’s unreasonable to think that just asking your intuition which graph “looks better” is a good way of determining whether you have an actual preference between the graphs. The shape of the graph is meaningless.