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> With this in mind insurance is a service worth paying for as long as the fee is lower than utility you gain from it.

Why even consider the insurance as investment (money increasing tool)? A stock market would get you higher gains at more controlled risk.

The 3rd best financial advice I got is about insurances: "Pay the insurance only if the negative outcome would cause you a significant financial loss" (and is of relatively high probability)

So, insuring a house from fire etc. makes sense. But, my $2k bike is not worth covering (from my PoV). Or, if we go to extreme, my (unnecessary) motorbike/boat/jet ski as if they are destroyed, I can continue living without them (a bit of exaggerated example, but I hope you get my point). Same for insuring a house from unlikely events.

> Why even consider the insurance as investment (money increasing tool)?

Most people wouldn't consider it in that way - unless the risk they're insuring is terribly mispriced or they plan to do some insurance fraud.

Disagree on the probability bit. The important part is the severity of the negative outcome.

And if you can't afford to lose the toy you couldn't afford to buy it in the first place. Thus toys should never be insured.

(That is, of course, assuming they aren't mispricing it. I've seen a situation like that where I considered it: There are companies that offer small-appliance warranties at approximately an x% of price model--reliability doesn't enter into it. If you know that with your use case the product is likely to fail within the warranty... But some searching shows the real business model is to make it nearly impossible to actually make your claim.)

> And if you can't afford to lose the toy you couldn't afford to buy it in the first place. Thus toys should never be insured.

You’re getting this wrong.

Being unable to afford to lose a toy doesn’t mean you weren’t able to afford it, it means you weren’t able to afford buying it twice.

It works the same way with home insurance. I can afford the house. I can’t afford two houses if my current house burns down and I need to buy another one.

> insurance is a service worth paying for as long as the fee is lower than utility you gain from it

Critically, the variable that makes gambling rational is the hedonistic pleasure one derives from it.

Insurance versus gambling seems like a penetrating question, but as you describe, it really is not. The more-germane one is gambling versus drinking or theme parks or mindless television.

> This decreases combined utility of you and your counter-party.

The counterparty tends to have an edge. Roulettes have zeros, bookies get a cut, etc. I guess on a poker table everyone thinks that they have an edge but they can't all be right.

Also casinos typically take rakes in poker

index funds also take a fee

Effect of rake makes it such that only about 5% of players show profit in the long run.

The edge you have from selling insurance is selling psychological safety, people pay to not feel negative. Maybe some gamblers can recognise moments they've been irritated where some rule requires insurance, "let me embrace the risk on my own dammit"

The edge they have is providing more utility for you dollar, as OP said.

That kind of edge is just having a good or service someone would pay for.

You haven't demonstrated most of these assertions. For example, if everyone gambled against everyone else every second, then that system has a pretty good chance of staying close to equilibrium for a long time, whereas your model indicates that the total utility would be depleted almost immediately. Whereas if everyone was fully insured for absolutely every risk in their life and immediately received a replacement of the exact same value on any loss, then the overall system would just steadily trend to all the money ending at the insurer, which doesn't seem like increased total utility

>>You haven't demonstrated most of these assertions. For example, if everyone gambled against everyone else every second, then that system has a pretty good chance of staying close to equilibrium for a long time

>>whereas your model indicates that the total utility would be depleted almost i

Can you describe specific assumptions about how that "everyone gambling against everyone else" would look like? I just don't see how my model could predict total utility being depleted very quickly while the model having good chance to stay close to equilibrium.

My model is very simple: apply utility function on wealth. When you model people flipping coins against each other you will see a lot of busted ones and a lot of rich ones pretty quickly and that will mean significant utility decrease.

Ok, take 100 people, with $100 each, and have one round of $1 coin flips between each 2. A significant number of bets overall, 4950. Each person has wagered 1% of their net worth 99 times, something that we all agree sounds quite scary. And yet there will be no busted people, most will likely be between $80 and $120. Repeat this 10 times, a ridiculous amount of gambling - still most likely no bankruptcies, and the total utility, if we assume log, has barely dropped by 1%.

I simply do not believe that we are making such a subtle societal optimization by frowning upon gambling while encouraging all kinds of other risk taking, like investments and properties.

And the other scenario where insurance just acts as a drain on the overall system seems to indicate that it is not inherently positive for utility either

It's unlikely anyone's busted but utility is unquestionably lowered. A negative for society. Insurance increases equality, gambling lowers it.

This is a bit of a stretch from what I said - 1% drop after the entire population has gambled through 10x their net worth is not meaningful. I also pointed out other speculative activities which we encourage, presumably because they compensate by growing the economy. Insurance might preserve or increase equality, but it also might extract so much rent that the overall utility is lower. There is simply no cut and dry explanation - for some parameter choices things work the way you say, and for some they don't

I think you are simply wrong about your assumptions. If the system is semi-stable the total utility won't decrease that much. If it's not stable it will. I am not sure exactly what you are missing there but maybe that it's expected utility going down, not utility going down with every outcome. For example if people with 80 and 120 net worth flip a coin for 20 it might be go up or it might go down but u(60) + u(140) < 2x u(100). Maybe that's why you utility model predicts the total utility collapsing quickly while in fact it predicts slow utility decrease (if the whole setup is close to being stable).

My model was not to demonstrate that utility doesn't go down ever, it was to show that it can do that extremely slowly, which makes the utility argument about why we discourage it societally a bit weak - we're clearly not very good at discouraging any other behaviors resulting in long-term bad outcomes (for society or the planet), and we reward all sorts of risk-taking.

I think the simpler explanation is that gambling is seen as addictive and destructive on an individual level, and there is no need for total utility to explain why that's undesirable

well you can hedge your bets, a form of insurance. people do this with stock too.

Isn’t this typically explained via marginal utility, not just utility? You can’t really compare the utility of the same amount of money in the hands of different people, but for a single person each additional unit of money is worth less than the last along some non-linear curve. The $1k you spend on insurance is further along this curve than the first $1k of the insured loss (and the second, and the third, etc) and if you do the naive expected value calculation it ignores this curve.

That insurance companies are able to make a profit implies that in the aggregate, people lose money on it, just as with gambling.

Not losing money so much as making money for a service (insurance). Hopefully it’s reasonable one and not exorbitant for the customer if there’s enough competition in the insurance market

"Food companies are able to make profit implies that in the aggregate, people lose money on it, just as with gambling".

The argument is simply incorrect. Insurance companies provide a service, not +EV (money wise) investment. Same as any other service companies - they make profit, the customers benefit.

This is the reason I always play the lottery. I won't miss $2 a week or whatever, but I will notice if I win an 8+ figure payout.

Are your odds better than waiting payout/$2 * days buying lotto tickets?

2$ per week for a few years is a day off work or a few stake dinners. You could definitely notice it if you wanted.

Gambling can be a completely rational thing to do. If you are old, poor and tired, your odds to become a millionaire from work are exactly zero. But if you buy a lottery ticket, you buy yourself a week of hope, adrenaline, and a non-zero chance for a life of your dreams.

https://www.foxbusiness.com/money/fred-smith-fedex-blackjack...

> With this in mind insurance is a service worth paying for as long as the fee is lower than utility you gain from it.

Insurance is invariably a "for profit" enterprise so the utility or return across all participants has to be lower than the value invested/paid. Clearly you are protecting an unlikely situation so the utility value of peace of mind would need to be quantified.

Gambling has utility too...entertainment. How someone measures that is up to them I guess. Excessive gambling, just like excessive insurance, is wasteful as well.

IMHO, I don't think your argument stacks up.

>>Insurance is invariably a "for profit" enterprise so the utility or return across all participants has to be lower than the value invested/paid.

This is wrong and the reason you are confused about the argument. If insurance is priced fairly all parties benefit utility wise. It's true that the buyer has negative expected value money wise and the seller positive one but as the utility function is concave both parties benefit. The important thing is to be able to see value in insurance. Once you are able to see it you will understand why it's worth a premium.

One natural question is why the insurer can afford to sell the insurance and not lose expected utility. The answer is that the insurer has a bigger bankroll and the utility curve is flatter for them than it is for the buyer. That's why they can offer a lower premium than an individual in similar position to the buyer would be.

Insurance is not always a for profit enterprise. There are very many “mutuals” who are literally owned by their policy holders.

There is still some cost to the policy holders, though: they still need to pay for the overhead of managing the policies (generally realized via paying the salaries of some employees).

Yes people can come together at their home and gamble as well

It is just the same can’t find any logical argument that makes it different in any post. Feels like everyone is trying to justify it

> It's true that the buyer has negative expected value money wise and the seller positive one...

This is obviously the insurer's goal, but in practice competition and relaxing underwriting standards to win business means that many insurance companies do not turn an underwriting profit (the buyer winds up with a positive expected value). But premiums are paid up front and payouts to policy holders do not occur until later, and the insurer can invest the "float" in the meantime, so they still make money.

Obviously the customer could have taken the premiums and invested them themselves, but that also takes time and effort, and may come with risk itself. It is not obvious that insurance is a bad deal even ignoring arguments about the concave nature of the utility of money.

Hm I don't follow. Could you please define "expected value in money terms" vs "expected value in utility of money terms"

It's a convoluted way of saying "use value" vs. "exchange value".

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.

It doesn't really matter much if you have a million dollars or a million dollar house (+/- liquidity of assets but this is not really important for the discussion).

>>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.

Utility is quite a complex and badly defined concept - its also central to economics. The idea is that the value to you of an extra amount of money goes down as you have more. i.e. getting £10k could be life changing for a poor person, unnoticeable to a rich one.

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.

Ive never seen a definition of utility which wasn't self referencing.

It's a highly unscientific concept.

Utility of money is just how much value one (an individual or entity) can derive from having x amount of money. Utility and value might be defined by self referencing each other but that's true for many other concepts or words in a language for that matter. It doesn't make it problematic or unscientific.

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)

>Utility and value might be defined by self referencing each other but that's true for many other concepts or words in a language for that matter

Precisely. Like when a priest says that "love" is "god" and "god" is "love".

Plenty of our language is deeply unscientific.

It's not like that at all. If you want to argue that one can't define value then I am out. If you admit "value" has well understood meaning then utility function of wealth is just how much value one can derive from it. We usually measure wealth in money for convenience. I really don't know why you are so against it. There might be a lot of nonsense associate with it but the concept itself is pretty simple and useful.

> never seen a definition of utility which wasn't self referencing

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...

[2] https://en.m.wikipedia.org/wiki/Revealed_preference

"Utility" isnt axiomatic or analogous to holes. It's "vibes" dressed up in sciency sounding language.

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

"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.

What’s your opinion of game theory?

> 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.

Except that having multiple valid definitions of something that is foundational to a discipline is a bit unsettling.

> having multiple valid definitions of something that is foundational to a discipline

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.

> Almost all of finance, for instance, doesn’t bother with utility functions.

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.

Number of dopamine molecules secreted by a person during his lifetime?

>>Hm I don't follow. Could you please define "expected value in money terms" vs "expected value in utility of money terms"

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.

If you have 10% chance to lose -$91 and 90% chance to get +$10, the expected value in money is -$0.1. It sounds bad.

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.

In the real world it always goes the other way--the next dollar is never worth as much as the previous dollar, thus any fair bet costs more (the previous dollar) than it gains (the next dollar.)

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).

This has really made insurance click for me because while I understand it intuitively, I wanted a more scientific foundation to understand its value.

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.

I don't know why you said "the other way", cause this is the exact thing I decribed in my previous comment.

A simpler way of explaining it is that both activities have a negative expected value but insurance usually reduces variance while gambling increases it.

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.

But why is reducing variance desirable? It's exactly because there is utility of money function which is concave. Variance being undesirable comes from the shape of utility of money function.

And at some point that function bends hard once you hit bankruptcy, for instance many places in US you go to jail if you run out of money, especially if you have children with someone to whom you're not currently married.

Yes that’s one factor. But there’s also a “going bust” factor which is kind of a fundamental dynamic as well.

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.

Variance can be good though. Imagine you want some expensive service like a waterline for your house that's difficult to steal but you live under rules of gangsters or oppressive government so holding anything more than a little money at a time is risky.

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.

That's a very contrived scenario and your hypothetical response is very unrealistic. For one thing, the gangsters either wait outside the gambling joint or simply take it outright and farm the rake. For another, real communities with such dynamics don't accumulate cash, they might accumulate tangible goods or a little infrastructure but they are not going to have large sums of cash-equivalents lying around. For all kinds of reasons you need either a high-trust society or an army to accumulate liquid wealth.

Informal gambling between low tier non gangster class people outside a joint is common amongst the lower class most everywhere and the whole scenario was about minimizing liquid wealth and dealing with cash intensive problems in places where cash is risky.

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.

Thanks for the example.

Maybe but when you see seemingly irrational behavior by "the underclass" it's always worth spending a little more time trying to understand what kinds of issues they may be facing that you're not intuitively aware of.

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.

Another example could be needing money for life saving expensive treatment for either yourself or a loved one.

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.