Hm I don't follow.
Could you please define "expected value in money terms" vs "expected value in utility of money terms"
https://moneyterms.co.uk/utility/
The expected value is the amount multiplied by the chance of getting it. SO if you have a 50% chance of getting £1,000 the expected value is £500.
That GP comment is saying is that in the case of insurance the small risk of being wiped out financially vs the certain cost of premiums the expected value is negative (for insurers to be profitable) BUT because the effect on utility of losing a huge amount of money is so bad, the expected value of the utility is positive.
It's a highly unscientific concept.
The point is that it matters how much certain amount of money or wealth is worth for you not how much wealth you have. It's an important point as it explains why calculations purely in money terms are useless for making financial decisions (as seen in example of insurance)
Precisely. Like when a priest says that "love" is "god" and "god" is "love".
Plenty of our language is deeply unscientific.
It’s analogous to “holes” in semiconductors or virtual particles. You can’t directly observe it. But it’s an intuitive notion that makes many calculations easier.
Critically, there are several valid definitions of utility, e.g. the von Neumann–Morgenstern (VNM) utility theorem [1] and revealed preference [2]. Each has its own axioms, defined with varying rigour, that can be theoretically extended and practically applied.
> a highly unscientific concept
Sure, it’s unscientific in the way mathematics are unscientific: it starts with a set of axioms and extends from that. Determining whether the chosen axioms fit a particular situation is a separate, more scientific question.
That said, similar criticisms have been raised about e.g. auction theory and quantum physics, both of which (like utility-based models) make testable predictions.
[1] https://en.m.wikipedia.org/wiki/Von_Neumann%E2%80%93Morgenst...
"In economics, a utility representation theorem asserts that, under certain conditions, a preference ordering can be represented by a real-valued utility function, such that option A is preferred to option B if and only if the utility of A is larger than that of B."
You may challenge the assumptions but otherwise it's mathematics.
> It's "vibes" dressed up in sciency sounding language
This is pop economics. (And again, as mentioned, it’s not science-y. It’s applied mathematics. It’s only when you use the model to make predictions that it becomes science-y.)
Of course, if you’ve refuted von Neumann and Morgenstern, by all means, publish. Otherwise this is the “series of tubes” equivalent for economics.
It’s foundational to one branch. Almost all of finance, for instance, doesn’t bother with utility functions.
One can similarly complain that mathematicians have different rules for parallel lines depending on geometry. Like, sure. But if you’re in the field it makes perfect sense why parallel lines don’t intersect in a Euclidean space but do in a curved one. Given utility functions are literally ordered sets of preferences, it strikes me as trivial that there would be a multitude of them. (If this bothers you, don’t look up Gödel.)
The economists who deal with utility functions are more or less applied game theoreticians. Some people have a problem with game theory and statistics because they’re unpure. Like, sure. Fine. I also have a small stable of useless opinions, e.g. raisins are trash fruit. That doesn’t mean raisins are themselves useless; it’s just my opinion that’s adding zero value in a world where raisins do.
You need the concept of utility and some (reasonable) assumptions about the shape of the utility curve to derive CAPM - at least the way I was taught it and there may be an alternative I do not know of?
I do not think there being a multitude of utility curves is a problem. It seems to be there is a lack of a clear concept.
I do not think that your analogy with maths works. Maths is is more abstract and should change with different sets of axioms. Economics is supposed to be based on observations of the real world.
But the relationship between utility and money isn't linear. If for you, $10 is worth 10u and $91 is worth only 89u, this deal has expected value of +0.1u.
Why and how isn't it linear? It's a hard problem that can't be answered easily. However we know it's true for most big institutions in stock and bond markets. A financial product will need to provide extra expected value in term of money to compensate the risk, otherwise no one buys it.
That's why you should only engage in negative bets, aka insurance. There you are trading a next dollar (worth less) for a previous dollar (worth more).
I think a great illustration is an extreme case. If I have a house and just enough income to cover all my needs and wants (including retirement savings), then depending on my attitude an extra $1000 per year might have no effect at all - I have nothing I want to spend it on and nothing to save for.
But losing my home would still be devastating. So the utility value of the $1000 per year for the rest of my life is low or none, but the utility value of the previously earned money I would lose from losing my house is high.
A million dollars is a million dollars, or it's a house. I don't need a million dollars but I do need a house or I freeze to death. I can't eat a million dollars worth of food but I need to eat food every day or I die.
Gambling is seen as immoral because it's about extending your exchange value capabilities, although most people who gamble are poor as dirt and a winning bet is often about paying your utility bills and having a day out over being able to do neither (while losing bets contribute to being unable to do either).
Insurance is seen as prudent because it acts as a fail safe over your use values, be it your health, housing, employment, etc. Social security is basically a system of spreading the odds over the population, forcing everyone to do the small bets to contain the catastrophic outlier probabilities - in theory.
>>Gambling is seen as immoral because it's about extending your exchange value capabilities
Why would extending your exchange value capabilities would be seen as immoral? It sounds good to me. I think you are missing the point.
In the context of money variance is usually synonymous with instability and unpredictability. Those things are bad and it’s worth paying a fairly priced premium to avoid them.
In simple math terms gambling is essentially the opposite dynamic. Of course things that are unpredictable can be entertaining, which is why gambling is correctly viewed as a form of entertainment.
Think of it in terms of life. Once you are dead you’re dead, it’s the end. If the variance in your life outcomes “crosses the zero line” then the game ends, even if it’s just for an hour.
You could bend your argument to cover that by arguing that the utility of that last little fraction tends to infinity. Like what would you exchange for the drink of water that would save your life if you were minutes from death?
But it’s a bit strained, especially as a way to explain it to someone for whom utility is not already intuitive.
I think it’s pretty easy to understand that excessive variance leads to death or very negative outcomes.
All you need to demonstrate it is a houseplant and a supply of water, air, and sunshine. If you increase the variance of any of those three things sufficiently you quickly don’t have a houseplant any more, regardless of the average total supply.
You gamble every paycheck knowing eventually you will get a big payout. You quickly pay for the waterline and now you don't have to walk 300 ft to the well everyday.
In the Philippines they even have a pooling system 'paluwagan' like this to make it possible for people to buy big things without a bank account or having to store large sums for large period of time which can be risky there.
If you've been in the position where every dollar you make gets somehow taken from you without warning for years you'd act differently. Goes from things like avoiding banks due to various fees or garnishments, up to practices of wearing expensive jewelry because it's a fairly efficient way to carry value on your person, and because you often get to keep it even when you get arrested, unlike the cash in your pocket.
That's why I mentioned that "avoiding variance" in itself is not a good argument. You avoid it for a reason and that reason is that (u(x - a) + (u + a)) / 2 < u(x) for vast majority of life scenarios.
Imagine you have $10k to your name and flip a coin for $1k. Your expected value in money terms is $9k * 0.5 + $11k * 0.5. Your expected value in utility terms is: u($9k) * 0.5 + u($11k) * 0.5 where u is a function that tells you how much worth you get from money. See wikipedia link for some explanation (although I think the articles are over-complicated and don't convey the point in clear way):
https://en.wikipedia.org/wiki/Utility
https://en.wikipedia.org/wiki/Marginal_utility#Law_of_Dimini...
The key point is that utility is concave (a coin flip for any amount has negative utility) which is obvious when you think about it (better to be a millionaire than flip a coin to be busted or have 2 million net worth) but maybe not something most people think when making everyday decisions.