I don’t know how many of the millions of people who’ve bought Daniel Kahneman’s Thinking, Fast and Slow have read it, but I have and I thought it was very interesting. One of things he talks about in chapters 25-26 is risk aversion. Lots of people won’t take a bet to either gain $200 or lose $100 on a coin-toss, and that seems to mean they’re risk averse. They stand to gain more than they stand to lose, and the chances are equal, but they won’t take that chance. Regular readers may remember risk aversion coming up once before when I was talking about Deal or No Deal.
Kahneman says that for a long
time economists used to think that (or at least idealize that) people were risk averse when it came to
money, but not when it came to utility. Your first million makes a bigger
difference to you than your second, and maybe it even makes a bigger difference
than your second and third put together. In view of that, maybe your last $100
makes more of a difference than your next $200. If that’s right, you’re not
rejecting the bet by being risk averse; you’ve just got a proper appreciation
of the diminishing marginal utility of money.
The problem with this line of
thought is that while it can rationalize bets which seem sensible instances
of monetary risk aversion, it can only do so by attributing people utility
functions which also rationalize insane-seeming pieces of (monetary) risk aversion. Matthew
Rabin showed this in a technical paper, and he and Richard Thaler wrote an entertaining paper about it which references Monty Python’s dead parrot sketch. The idea is
that if diminishing marginal value of money is all that is going on, then
someone can’t rationally reject one fairly unattractive bet without rejecting another
very attractive bet. Their first
example is that if someone will always turn down a 50-50 shot at gaining $11 or
losing $10, then there’s no amount of money they could stand to win which would
induce them to take a 50% risk of losing $100. They have several other
examples, including ones which remove the ‘always’ caveat, only demanding that
they would still turn down the first bet even if they were quite a bit richer than they are
now. The basic idea is the utility of money has to tail off surprisingly quickly to rationalize rejecting the small bet, and if it tails off too quickly you'll have to make odd decisions when the stakes are high. They’ve thought of objections and the reasoning is hard (for me) to argue with.
Now, what Thaler and Rabin
reckon is going on is loss aversion. The reason
you won’t take the $100-$200 bet is that you recoil in horror at the thought of
losing $100. There’s plenty of behavioural economics research (I’m told) showing
that people can’t stand losing even if they’re pretty chilled about not gaining,
and that’s why Thaler, Rabin and Kahneman think that’s what’s going on. Thaler
and Rabin say it’s not just loss aversion either, it’s myopic loss aversion. The reason it’s myopic is that you’d take a
bunch of $100-$200 bets if you were offered them at the same time, because overall you’d
probably win big and almost certainly wouldn’t lose. But if that’s your
strategy then you should take the bets when they arise, and in the long run you’ll
probably end up on top.
I agree that people are myopic,
and they don’t always see individual decisions as part of a longterm strategy
where losses today get offset by the same strategy’s gains tomorrow. I think
Thaler and Rabin have missed something when they invoke loss aversion, though.
This is because you can set up the “if you reject this bet then you’ve got to
reject this attractive bet” argument without doing anything with losses.
Suppose I offer people a choice of either $10 or a 50-50 shot at $21. Sure,
some people will gamble, but aren’t lots of people going to take the $10? If
they haven’t already, some behavioural economists should do that experiment,
because if people reject the bet then Rabin’s theorem will kick in just the same
as before and lead to crazy consequences. The difference is that this time you
can’t explain the difference as recoiling in horror at the prospect of losing
$10, because the gamble doesn’t involve losing any money. It just involves not
winning some money, and people are relatively OK with that. (Notice that choosing
not to gamble also involves not winning some money.) If you object that the
non-gamblers want to make sure they get something,
then change the set-up (if your budget stretches that far) to either $20 guaranteed or a 50-50 gamble for $10 or $31.
It still works, and I bet plenty of people will still take the $20.
Now, what I think is going on
is myopic risk aversion. I don’t see that there’s much wrong with risk aversion
in itself. If you could choose either a life containing a million hedons or a
50-50 shot at either a thousand or two million, I’d understand if you took the
million. Only a real daredevil would gamble. And when John Rawls is putting whole-life choices before people in the Original Position, he won’t assume they’re
anything less than maximally risk averse. Maybe Rawls has gone too far the other
way, but I’d definitely want to see a pretty good argument before believing
that the cavalier attitude of the expected-something maximizer is rationally
obligatory.
Now, mostly when we make
decisions they’re small enough and numerous enough that a fairly cavalier strategy has
a very low risk of working out badly overall. Applying original-position
thinking to the minor bets offered by the behavioural economists in the pub is
confused. It feels like you’ve got a 50% chance of getting the bad outcome, but
seen in the context of a more general gambling habit the chances of the bad
outcomes are actually very small even with the cavalier strategy, and since its
potential payoffs are much higher, you’d have to be very risk averse overall to
turn down the gamble. You’re very unlikely to be that risk averse all things
considered, although perhaps Rawls was right that it’s cheeky to make
assumptions.
So that’s what I think’s going
on. Loss aversion is real, but it can’t do the work Thaler and Rabin want,
either in straightforward form or myopic form. I think the real culprit is
myopic risk aversion. Overall risk aversion is rationally permissible, but
myopia isn’t and can result in individual decisions looking more risky than
they really are. Unless the stakes are really high, like on Deal or No Deal.
