Here’s fundamental impossibility result for modeling risk aversion in expected utility framework.
I’m not sure we’re reading the same paper. Rabin argues that people are (should be) roughly risk-neutral when stakes are small, as massively concave utility functions get ridiculous- which is what I argue:
Local risk neutrality, though, is the norm- zoom in on any utility function close enough and it’ll be roughly flat.
The meat of the paper also rests on a very strong assumption: that the person rejects the gamble at any wealth level. He discusses a narrower case (what I would call my “lunch” case) where you know they reject the value at anything below a certain point, but nothing about their risk attitude above that point. In my example, that would be choosing not to gamble (for a small yield) if it puts you under $3. For his example, the threshold is rather high: $350k. He calculates that someone who turns down a gamble that replaces their wealth of {1 340,000} with {.5 339,900, .5 340,105} is insanely cautious. I agree- I don’t expect a sane person to behave that way. That’s not an indictment of expected utility theory, that’s an indictment of the parameters chosen.
When I help someone pick out a function to model their preferences, I don’t elicit it the way he does. We pick some gambles that are easy to wrap their head around, find indifference values, fit it to a function like log or exponential, and then sanity check the output. If we got values like the ones he’s getting from a fitted function, I would suspect they miscalculated their indifference values and we would play around some more, possibly adding thresholds and making it a piecewise function. It’s not so much a “fundamental impossibility result” as it is “if things look like this, you’re not doing anything useful.”
(There’s a separate, descriptive question- “is a EU calculation with a consistent utility function why people refuse modest gambles?”- which I think is secondary. They might refuse a gamble because they’re bad at math, or they have a massive case of status quo bias, or so on. I don’t think we should care much about predicting that sort of behavior compared to prescribing carefully planned behavior.)
Utility functions are a wrong abstraction, and you’ll be better off if you abandon them.
I’m not sure what you mean here, so I’ll state my reaction to some possible meanings. I affirm that utility functions are a calculation method useful for capturing risk attitudes but shouldn’t be given philosophical importance. I deny that utility functions cannot be a useful calculation method.
Here’s fundamental impossibility result for modeling risk aversion in expected utility framework.
Utility functions are a wrong abstraction, and you’ll be better off if you abandon them.
I’m not sure we’re reading the same paper. Rabin argues that people are (should be) roughly risk-neutral when stakes are small, as massively concave utility functions get ridiculous- which is what I argue:
The meat of the paper also rests on a very strong assumption: that the person rejects the gamble at any wealth level. He discusses a narrower case (what I would call my “lunch” case) where you know they reject the value at anything below a certain point, but nothing about their risk attitude above that point. In my example, that would be choosing not to gamble (for a small yield) if it puts you under $3. For his example, the threshold is rather high: $350k. He calculates that someone who turns down a gamble that replaces their wealth of {1 340,000} with {.5 339,900, .5 340,105} is insanely cautious. I agree- I don’t expect a sane person to behave that way. That’s not an indictment of expected utility theory, that’s an indictment of the parameters chosen.
When I help someone pick out a function to model their preferences, I don’t elicit it the way he does. We pick some gambles that are easy to wrap their head around, find indifference values, fit it to a function like log or exponential, and then sanity check the output. If we got values like the ones he’s getting from a fitted function, I would suspect they miscalculated their indifference values and we would play around some more, possibly adding thresholds and making it a piecewise function. It’s not so much a “fundamental impossibility result” as it is “if things look like this, you’re not doing anything useful.”
(There’s a separate, descriptive question- “is a EU calculation with a consistent utility function why people refuse modest gambles?”- which I think is secondary. They might refuse a gamble because they’re bad at math, or they have a massive case of status quo bias, or so on. I don’t think we should care much about predicting that sort of behavior compared to prescribing carefully planned behavior.)
I’m not sure what you mean here, so I’ll state my reaction to some possible meanings. I affirm that utility functions are a calculation method useful for capturing risk attitudes but shouldn’t be given philosophical importance. I deny that utility functions cannot be a useful calculation method.