Unfortunately the better parts of my post were lost—or rather more of the main point.
I posit that the utility valuation is an impossibility currently. I was not really challenging whether your function was exponential or logarithmic—but questioning how you came to the conclusion; how you decide, for instance where exactly the function changes especially having not experienced the second state. The “logarithmic” point I was making was designed to demonstrate that true utility may differ significantly from expected utility once you are actually at point 2 and thus may not be truly representative.
Mainly I am curious as to what value you place on “intuition” and why.
If you wanted to, we could assess at least a part of your u-curve. That might show you why it isn’t an impossibility, and show what it means to test it by intuitions.
Would you, right now, accept a deal with a 50-50 chance of winning $100 versus losing $50?
If you answer yes, then we know something about your u-curve. For example, over a range at least as large as (100, −50), it can be approximated by an exponential curve with a risk tolerance parameter of greater than 100 (if it were less that 100, then you wouldn’t accept the above deal).
Here, I have assessed something about your u-curve by asking you a question that it seems fairly easy to answer. That’s all I mean by “testing against intuitions.” By asking a series of similar questions I can assess your u-curve over whatever range you would like.
You also might want to do calculations: for example, $10K per year forever is worth around $300K or so. Thinking about losing or gaining $10K per year for the rest of your life might be easier than thinking about gaining or losing $200-300K.
I think this greatly oversimplifies the issue. Whatever my response to the query is, it is only an estimation as to my preferences. It also assumes that my predicted risk will, upon the enactment of an actual deal, stay the same; if only for the life of the deal.
A model like this, even if correct for right now, could be significantly different tomorrow or the next day. It could be argued that some risk measurements do not change at intervals so fast as would technically prohibit recalculation. Giving a fixed metric puts absolutes on behaviors which are not fixed, or which unpredictably change. Today, because I have lots of money in my account, I might agree to your deal. Tomorrow I may not. This is what I mean by intuitions—I may think I want the deal but I may in reality be significantly underestimating the chance of −50 or any other number of factors which may skew my perception.
I know of quite a few examples of people getting stuck in high load mutual funds or other investments because their risk preferences significantly changed over a much shorter time period than they expected because they really didn’t want to take that much risk in their portfolio but could not cognitively comprehend the probability as most people cannot.
This in no way advocates going further to correcting for these mistakes after the fact—however the tendencies for economists and policy makers is to suggest modeling such as this. In fact most consequentialists make the case that modeling this way is accurate however I have yet to see a true epistemic study of a model which reliably demonstrates accurate “utility” or valuation. The closest to accurate models I have seen take stated and reveled preferences together and work towards a micro estimation which still has moderate error variability where not observed (http://ideas.repec.org/a/wly/hlthec/v13y2004i6p563-573.html). Even with observed behavior applied it is still terribly difficult and unreliable to apply broadly—even to an individual.
Unfortunately the better parts of my post were lost—or rather more of the main point.
I posit that the utility valuation is an impossibility currently. I was not really challenging whether your function was exponential or logarithmic—but questioning how you came to the conclusion; how you decide, for instance where exactly the function changes especially having not experienced the second state. The “logarithmic” point I was making was designed to demonstrate that true utility may differ significantly from expected utility once you are actually at point 2 and thus may not be truly representative.
Mainly I am curious as to what value you place on “intuition” and why.
If you wanted to, we could assess at least a part of your u-curve. That might show you why it isn’t an impossibility, and show what it means to test it by intuitions.
Would you, right now, accept a deal with a 50-50 chance of winning $100 versus losing $50?
If you answer yes, then we know something about your u-curve. For example, over a range at least as large as (100, −50), it can be approximated by an exponential curve with a risk tolerance parameter of greater than 100 (if it were less that 100, then you wouldn’t accept the above deal).
Here, I have assessed something about your u-curve by asking you a question that it seems fairly easy to answer. That’s all I mean by “testing against intuitions.” By asking a series of similar questions I can assess your u-curve over whatever range you would like.
You also might want to do calculations: for example, $10K per year forever is worth around $300K or so. Thinking about losing or gaining $10K per year for the rest of your life might be easier than thinking about gaining or losing $200-300K.
I think this greatly oversimplifies the issue. Whatever my response to the query is, it is only an estimation as to my preferences. It also assumes that my predicted risk will, upon the enactment of an actual deal, stay the same; if only for the life of the deal.
A model like this, even if correct for right now, could be significantly different tomorrow or the next day. It could be argued that some risk measurements do not change at intervals so fast as would technically prohibit recalculation. Giving a fixed metric puts absolutes on behaviors which are not fixed, or which unpredictably change. Today, because I have lots of money in my account, I might agree to your deal. Tomorrow I may not. This is what I mean by intuitions—I may think I want the deal but I may in reality be significantly underestimating the chance of −50 or any other number of factors which may skew my perception.
I know of quite a few examples of people getting stuck in high load mutual funds or other investments because their risk preferences significantly changed over a much shorter time period than they expected because they really didn’t want to take that much risk in their portfolio but could not cognitively comprehend the probability as most people cannot.
This in no way advocates going further to correcting for these mistakes after the fact—however the tendencies for economists and policy makers is to suggest modeling such as this. In fact most consequentialists make the case that modeling this way is accurate however I have yet to see a true epistemic study of a model which reliably demonstrates accurate “utility” or valuation. The closest to accurate models I have seen take stated and reveled preferences together and work towards a micro estimation which still has moderate error variability where not observed (http://ideas.repec.org/a/wly/hlthec/v13y2004i6p563-573.html). Even with observed behavior applied it is still terribly difficult and unreliable to apply broadly—even to an individual.