Expected Utility | Hacker News Reader

Expected Utility

orangemind.io

19 pointsrayalez14 comments

> 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.

>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.

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.

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.

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).

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...

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.

Exepcted utility has been thoroughly replaced by Prospect Theory.

https://en.wikipedia.org/wiki/Prospect_theory

> 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.

Yep.

tl;dr - people over value loses, and undervalue gains.

If we have a coin toss game where head=5$ for me and tails=5$ for you, you will only play if the game is something like 70 / 30 in your favor.

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

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.

>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.

But that's what a heuristic is.

...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.

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