# Risk aversion=Diminishing marginal utility?

From: Nick Bostrom (nick@nickbostrom.com)
Date: Wed Nov 01 2000 - 19:09:52 MST

I would prefer a 100% chance of getting \$1,000,000 to a 50% of getting
2,001,000. This could be explained either by saying that I am risk averse
or by saying that there is a diminishing marginal utility of money for me.
Is there a way of distinguishing these explanations or are they
fundamentally saying the same thing?

We might try to answer this question by considering goods that purportedly
don't have a diminishing marginal utility, such as units of pleasure.
Suppose I prefer a 100% chance of getting 1,000,000 hedons to a 50% of
getting 2,001,000 hedons. Does this then show that I am truly risk averse?
But how do we know that there is not a diminishing utility of hedons? (Not
to mention the difficulty of measuring hedons.)

Maybe we can approach the issue by considering goods that have different
rates of diminishing marginal utility. The marginal utility of hamburgers
decreases very rapidly - after one or two I really don't care to get any
more. The marginal utility of money decreases more slowly - almost any
imaginable sum would still leave me wanting more. Risk aversion, on the
other hand, is not supposed to be relative to goods. So risk aversion would
be what remains when we have factored out the specific diminishing marginal
utility of the good we are considering. The problem is knowing when we have
factored out all the diminishing marginal utility. Maybe we could define
risk aversion as the factor by which our choices deviate from getting the
greatest expected quantity of good x, where x is the good which has the
least diminishing marginal utility. But what would x be? Something like
wish-granting-power? How would that be quantified? Wish-granting power
doesn't come in natural units like kilograms or \$\$. You could say that one
unit of wish-granting power is the power to grant one wish. But how does
one individuate wishes? (One couldn't permit wishes that asks for more
wishes, or wishes that are conjunctions of arbitrarily many "sub-wishes".)

[Wild idea: Could we say that a basic wish is the power to determine the
true answer to a random one-bit question?]

Maybe we'll have to stick to money as the best approximation to such a
"pure good". But then it seems we should forego speaking of diminishing
utility of money. Only stuff like consumption of hamburgers would have a
diminishing marginal utility, and it would be measured by how much less
money we are willing to pay for eating an additional hamburger.

A common intuition is that, other things equal, a more even distribution of
money is better. But rather than grounding this in diminishing utility of
money, one would have to justify it by appealing to risk aversion. Perhaps
one could tell some sort of veil-of-ignorance story to that end.

Alternatively, we could seek to reinterpret all talk of risk aversion as
talk about diminishing utility of money. Is there any reason why this would
not be an attractive option?
Dr. Nick Bostrom
Department of Philosophy
Yale University
Homepage: http://www.nickbostrom.com

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