Determining a Person's Utility of $$

[KUJustin]

This question presented itself to me during an episode of Deal or No Deal that my family was watching.

It seems to me that if we can develop a complete scale of a person's utility of money from a few dollars up to a million we can couple that with an estimate of bank offers for a variety of situations in order to give a correct decision quickly and easily while accounting for the risk-aversiveness of the individual.

So the question is, how would you go about determining a person's individual utility of money? I'm talking practically speaking, what exactly would you do?

Keep in mind that (I'm guessing) the person will likely struggle to accurately answer any preference questions you give them.

I haven't really sat and thought about this but my thoughts up to this point:
1. With enough redundancy of simple preference questions (e.g. would you prefer $50,000 or a 50/50 chance at $200,000) we should be able to overcome much of their inability to accurately compare sums of money.
2. It may benefit us to establish a range of probabilities that we're working with in addition to the built-in range of values (the few dollars to a million dollars). Their preferences on a 1 in 1,000 wager are of little consequence.
3. Using their income, net worth, etc as a factor is a possibility, but it's one that I'm not really comfortable with. Individual personalities are just too strong for this to provide enough valuable data, plus it just seems inelegant.
4. Obviously we would hope to find a utility line that will give us a full scale and also (hopefully) be more accurate than any of the individual situational preferences the person tried to state.

Anyway, if someone really wants to sit down and crunch their head about this I'd be interested in how you'd go about it (EXACTLY what data would you collect, EXACTLY how, EXACTLY what would you do with it?)

[arahant]

Well, any set of rules you came up with wouldn't be executable by the people on the show. I would say most of them would take a good 10 minutes just to figure out the average of the remaining amounts, and then they'd probably get it wrong.

Even if you came up with a utility curve, it might be easy to apply it to the bank offer, but weighting all the remaining outcome possibilities would be damn near impossible.

But if you wanted to do the exercise just in theory, I would think that the game itself would provide an excellent data set. Just have the individual play it 100 times and build the curve off of that. I doubt there is a better way to do it, but I guess it depends on your outcome measure.

[KUJustin]

Shouldn't we assume the player is making decisions that are sub-optimal given their utility curve based on what you said in the first paragraph?

[hmkpoker]

There is no objective way to do it.

Let's say I offered you a choice between a guaranteed $10, or a gamble which requires you to pay $10 for a 9:1 shot at winning $250. I'm sure almost everyone here would take the gamble, since it's +EV (return of EV=$15 instead of $10). Ok, but what if the stakes were your life savings? Suddenly you might think differently, even though the raw numbers tell us it would be "irrational" not to put all the money we have on a 9:1 shot. Just how much money has to be at stake for you to take the straight offer instead of the gamble? Depends entirely on the person.

[KUJustin]

hmk, reread the OP perhaps.

[arahant]

[ QUOTE ]
Shouldn't we assume the player is making decisions that are sub-optimal given their utility curve based on what you said in the first paragraph?

[/ QUOTE ]

Hmm. Fair point. I guess I was sort of working off the utility of the decision, which I think involves more than the money and risk...
Maybe the question is, 'how do you measure risk aversion when an individual can't assess risk'...

Hmm...I'll ponder and maybe return later. I have a vague feeling that the exercise is really inappropriate for some reason, and that the best measure of a persons 'utility' in a choice is the choice itself.