
Expected Utility - rayalez
http://orangemind.io/post/expected-utility
======
tedmiston
> This is a very useful concept, because when you think like that about every
> action you take, you end up making much better decisions. You don’t take
> dumb risks, and you don’t miss great opportunities.

> In life, we need to make decisions under uncertainty. When you know your
> values, and take actions with maximum expected utility, you can take the
> optimal way towards achieving your goals.

Like all things statistics, it's true _in the long run_ , _over many trials_.

But in many real life circumstances we don't get many trials.

Sometimes a better strategy is to disregard statistics because our sample size
is small. Decision making is different when you can only make a small amount
of spins.

I also think about the cost to reverse a decision that doesn't end well. As
Jeff Bezos famously said (paraphrasing), it's not about the mistakes you make,
but how you recover.

Some other aspects to consider are opportunity cost and diminishing marginal
utility.

~~~
wyager
>Decision making is different when you can only make a small amount of spins.

You should still be maximizing expected utility. For e.g. recreational
gambling, factors in your utility function such as entertainment come into
play, which explains why gambling recreationally can be rational behaviour.

~~~
soVeryTired
I broadly agree with what you said about gambling, but if you take that type
of reasoning too far it can lead to some dubious conclusions.

If I'm free to add fudge factors to a utility function in order to explain an
agent's behaviour, the assertion that the agent is rational (i.e. maximises
utility) becomes meaningless. I can always add more fudge factors to explain
deviation from rationality.

Much better to specify a utility function in advance and test how well the
agent's behaviour fits your theory. IMO that's a trick economics often misses.

------
carsongross
Myth: you have any idea what the probabilities are of most outcomes in real
life.

Reality: you make a wild-ass guess, try your best, and try not to die if shit
doesn't go your way.

Read up on absorbing conditions per Nassim Taleb. People should be be aiming
for anti-fragility, not maximizing impossible-to-calculate utility functions.

------
mrdmnd
I'd add a nit - this is the _expected value_ of the game. I might have a
utility preference curve that is non-linear in dollars - for instance, the
classic U(v) = log(v).

------
Houshalter
Expected utility has a lot of nice properties and is the simplest decision
system that's completely consistent. Other decision systems tend to have flaws
that can be exploited to take all their money, if you are allowed to make bets
with them.

However expected utility has really weird edge cases. Like Pascal's Mugging -
events with essentially infinite utility and infinitesimal probability. These
don't occur very often in everyday life. But programming an AI to follow
expected utility to the letter, might have some weird consequences.

If you allow slightly more complexity, you can get decision systems a bit more
complicated that avoid this problem, and are still consistent. E.g. "median
utility". This itself has problems, like ignoring slightly unlikely outcomes
that are really bad or really good. But you can fix that too by adding a bit
more complexity. I wrote about how to do this here:
[http://houshalter.tumblr.com/post/129690629075/against-
expec...](http://houshalter.tumblr.com/post/129690629075/against-expected-
utility)

This system might be preferable to expected utility. E.g. if you were to play
a lottery that had a jackpot so large the expected utility was positive (even
after adjusting for the logarithmic utility of money.) It still might be
preferable to not buy just to buy _just one_ ticket, because you will still
almost certainly lose. But if you had the option to buy many tickets, the odds
of winning might increase enough to be worth it.

------
tootie
Exepcted utility has been thoroughly replaced by Prospect Theory.

[https://en.wikipedia.org/wiki/Prospect_theory](https://en.wikipedia.org/wiki/Prospect_theory)

~~~
zevyoura
> The [Prospect Theory] model is descriptive: it tries to model real-life
> choices, rather than optimal decisions, as normative models do.

Expected utility is normative.

------
nitwit005
After a long series of small losses, our wheel spinner sinks into alcohol,
despair, and eventually suicide.

------
draw_down
It's an interesting way to think but I disagree that it's very useful because
the whole problem is correctly calculating the expected value in the first
place for real-life events. In a situation where that calculation is trivial,
as with the wheel, you should certainly use it.

------
hammock
_> This is the kind of problem you are solving every time you are trying to
decide whether or not to take any risky action._

Citation needed. I believe most of the time we are using other heuristics
rather than actually calculating some form of expected utility via
probabilities.

~~~
zfnsgmdydmy
But that's what a heuristic is.

------
protomyth
...and if you only have $20, you cannot spin the wheel at all.

Quite a lot of decisions in life are barred by the severity of the penalty
independent of the possible reward.

