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Just replying to point out this is an insightful take, thanks for making it.
Thanks, it’s an under-appreciated state of affairs I like to harp on. We may be the descendents of winter people who always had to anxiously stack their grain, but we now live in a land where no one even remembers what true hunger feels like. Most financially literate people understand that it is irrational to insure your TV or phone against breakage, yet claim it is reasonable to insure anything bigger. Even your house burning down does not threaten your existence in any way, there is no need to preemptively hyperventilate by giving some slimy salesman thousands of dollars per year.
By the time you get up to the scale of home insurance, they're correct. That's how diminishing utility of money works. You have a risk r of losing v value from your total wealth of w, and your utility is generally an affine transform of log(w). r·log(w-v)+(1-r)·log(w) < log(w-r·v) for 0<r<1, so if somehow you could find someone who would insure you with no transaction costs or expected profit then you'd want to take it every time. Transaction costs c are roughly constant and expected profit P scales like p·v, though, so now your right hand side is log(w-c-(r+p)·v) and (for p>0 and c>0) you only get the same inequality for large enough v.
Gambling that you won't lose a few days' pay is a better bet than gambling that you won't lose (for the median homeowner considering home insurance) the majority of your net worth, even if the odds and the profit margins you're paying for are the same in each case, because bigger gambles are worse. This is the same reason why it's a good idea to invest most of your money in a stock market index, a worse idea to invest the same money in an average stock, and a crazy idea to invest most of your money in stocks at 4x leverage. It's one way to derive the Kelly criterion. For the same expected returns, less volatility is better, and since it's not infinitesimally better, it's still better even if it comes with slightly reduced expected returns. Your house burning down doesn't have to threaten your existence to be worth insuring against, it just has to be worse in expected utility than paying an insurer. You don't even have to pay a slimy one.
That is the high brow justification for it, but I disagree with how they model people’s utility functions, and besides, people’s utility functions are neither set in stone nor economically justified.
People would be far better off with a flatter, less utility-diminishing curve, given that they spend near half their income to slightly reduce lifetime income volatility, and if the last century is any guide, they want to spend even more, no future loss is too small to be tolerated, should it cost half of gdp.
There’s no real difference between the TV insurance and home insurance, it all depends on the assumed steepness of the diminishing utility curve.
People’s utility gets modeled as a steadily diminishing curve. In reality there should be one huge drop in utility when you go from from starving to non-starving income, and then very very flat. Because the only way to lose all future utility, to get wiped out in the kelly sense, is to die irl.
And on that subject, people also gamble. A lottery is very similar to insurance. You pay a small sum, and after a random event you sometimes get paid a multiple. It’s a negative EV transaction because the losses in the pipes are large. Any rational man with a sufficiently flat utility curve would reject them.
But one of the two is supposedly justified while the other breaks their model and makes no sense whatsoever. Gambling people are spending good, high utility money, then losing some in the pipes, and for what? To get low utility money.
Insurance
n. An ingenious modern game of chance in which the player is permitted to enjoy the comfortable conviction that he is beating the man who keeps the table.
INSURANCE AGENT: My dear sir, that is a fine house — pray let me insure it.
HOUSE OWNER: With pleasure. Please make the annual premium so low that by the time when, according to the tables of your actuary, it will probably be destroyed by fire I will have paid you considerably less than the face of the policy.
INSURANCE AGENT: O dear, no — we could not afford to do that. We must fix the premium so that you will have paid more.
HOUSE OWNER: How, then, can I afford that?
INSURANCE AGENT: Why, your house may burn down at any time. There was Smith’s house, for example, which —
HOUSE OWNER: Spare me — there were Brown’s house, on the contrary, and Jones’s house, and Robinson’s house, which —
INSURANCE AGENT: Spare me!
HOUSE OWNER: Let us understand each other. You want me to pay you money on the supposition that something will occur previously to the time set by yourself for its occurrence. In other words, you expect me to bet that my house will not last so long as you say that it will probably last.
INSURANCE AGENT: But if your house burns without insurance it will be a total loss.
HOUSE OWNER: Beg your pardon — by your own actuary’s tables I shall probably have saved, when it burns, all the premiums I would otherwise have paid to you — amounting to more than the face of the policy they would have bought. But suppose it to burn, uninsured, before the time upon which your figures are based. If I could not afford that, how could you if it were insured?
INSURANCE AGENT: O, we should make ourselves whole from our luckier ventures with other clients. Virtually, they pay your loss.
HOUSE OWNER: And virtually, then, don’t I help to pay their losses? Are not their houses as likely as mine to burn before they have paid you as much as you must pay them? The case stands this way: you expect to take more money from your clients than you pay to them, do you not?
INSURANCE AGENT: Certainly; if we did not —
HOUSE OWNER: I would not trust you with my money. Very well then. If it is certain, with reference to the whole body of your clients, that they lose money on you it is probable, with reference to any one of them, that he will. It is these individual probabilities that make the aggregate certainty.
INSURANCE AGENT: I will not deny it — but look at the figures in this pamph —
HOUSE OWNER: Heaven forbid!
INSURANCE AGENT: You spoke of saving the premiums which you would otherwise pay to me. Will you not be more likely to squander them? We offer you an incentive to thrift.
HOUSE OWNER: The willingness of A to take care of B’s money is not peculiar to insurance, but as a charitable institution you command esteem. Deign to accept its expression from a Deserving Object.
-Ambrose Bierce, The Devil's Dictionary
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This is true only in the same sense that negative ten is similar to ten. They're both numbers, right? But they're opposite numbers. Likewise, here one gamble increases volatility (because the payoff is the only random event), and the other reduces it (because the payoff happens only when it cancels out a random expense; the net change from the random outcome is reduced).
It makes sense, for the reasons above. Does it make sense to you too, now? If not, I'm afraid that's probably the best I can do. I've taught grad school math classes, which says good things about my math ability but bad things about my teaching ability...
I understand this is what is taught, I was taught it in uni. Nevertheless, I disagree.
This model of a man they have conjured to justify insurance, is neither a homo rationalis economicus (for whom it would be far too inefficient), nor your neighbour (who enjoys gambling).
There is no good reason to privilege the 'original state', your living standard now. Yes one (insurance) maintains it and the other (lottery) changes it, but why does that matter?
Some people live in a house, but they prefer some randomness in their life, so they take a 50/50 chance of living either in a mansion or a condo. It's fine. I mean I think it's a cool way to live, but it's an aesthetic preference, I would never advise people to essentially burn money to get that volatility (like economics profs are advising people to burn money to get rid of it).
You could say the neighbour is just gambling when he purchases insurance, it's just that he uses the high from winning to compensate for the psychic pain of the loss of his house.
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