Hacker News Reader

> Some events are low probability but high cost.

Yes, and I sometimes think about the inverse - that people like to hate on lottery players (which I'm not) with a clever sounding argument like E[X] < 1, so don't play, you'll lose.

But this fails to acknowledge the harder to model 'but I can pay £1 to play, I won't miss it, who cares, it's insignificant, and on the tiny chance I win, the win is significant'. I.e. 'but Var[X] is massive'.

You're absolutely right, the thing to look at here is the St Petersburg problem.

You have a coin, and each time you don't get heads the payout doubles. Get heads and get the payout. What do you pay to play this?

It turns out that you can't work out an E[X] for this, as it's a series that doesn't converge. But also if you go around and ask people what they'd pay, surprisingly they don't say infinity. Expectation is thus not the last word in decision making.

Turns out utility is a thing that matters, and we can come up with some thoughts on it (von Neumann-Morgenstern etc).

re: surprisingly they don't say infinity

I'm not sure it's that surprising, the expectation is only infinity if you think the person making the payout has the capacity to pay an infinite amount. The second you think this amount is finite (which must always be the case in reality), then the expectation becomes finite and probably quite small.

I agree in the more general point, expectation is not always the best tool for extremely rare / extremely significant scenarios.

The parent is correct, and shouldn't be downvoted IMO. If you set the max payout to world gdp of ~$100 trillion, you get an expected value of ~$50 for the game. So people are actually calculating expected value correctly with their intuition. It's just that in their instinctive calculation they're also making better assumptions about reality than mathematicians do.

Indeed, it is one of the proposed solutions as listed in the corresponding wikipedia article on the St. Petersburg paradox. There is a table with quite low expected values, mapping the wealth of the bank to the expected value.

Utility function of big lottery win is way larger then of string insignificant looses. For most people.

https://en.m.wikipedia.org/wiki/Utility

Not a series of insignificant losses that, due to the low win-probability is such a long series, amounts to more money than the lottery win, and thereby cannot be called insignificant anymore, which is by definition how lotteries are set-up.

I think there's two factors. One is the nonlinear utility of money, and the other is the cost/value of losing/winning.

In general money has a diminishing utility, your first dollar is worth more to you than your millionth dollar. In order for it to be worth it to play a -EV lottery not only does you utility graph need to be nonlinear, it cannot decrease monotonically. At some point your nth dollar needs to be worth more (to you) than your first dollar. For example, you have one dollar and a life saving drug for your terminal disease costs 1 million dollars. You would see a sudden spike in utility at the 1 million dollar mark. It would be rational to play the lottery in this case.

Another possibility is that the event of winning money or even just the thought of possibly winning that money gives you more value than simply having the money alone, and this tips the scale. This would be like the opposite of insurance. For some people the experience of losing, or worrying about the possibility of losing money is so negative that it still makes it worth it to buy insurance.

Payouts are also non-linear though, with enormous discontinuities.

Your millionth dollar might have less marginal utility, but you were never going to win 10^6 -1 dollars anyway. So really to consider marginal utility you need 'margins' as wide as the payouts. (Really stretching/breaking the meaning of marginal, but hopefully you see what I mean.)

You frequently see this same pattern in games. A low cost gamble with a low chance of success, but a huge payout. Players seem to (often) view it as worthwhile, because if you do succeed then the payout changes the entire experience. Keeping the cost spent on the gamble, however, would make little difference.

> You're unlikely to crash your car, but if you do, it might cost you a heck of a lot to fix

There is also time. You may be able to afford the lawsuit that will come from the owner of the car you wrecked. But having your insurance company handle that, something they have developed expertise in, can be worth the cost.

insurances cost a lot of time too. I don't think you can really avoid that, we're in a society where everybody believe that other people's time and attention are disposable.

Not only time, also market knowledge in certain exceptional insurance fields: the insurance that takes care of flying you out when you end up in a hospital abroad likely knows a thing or two about procuring that service that you don't know.

> - You want people in the pool to be similar risks. If they aren't and they know they aren't the low risk people will decide they don't need to insure, leaving everyone else with a higher average cost. Also, the high risk people will see a good deal and join. Adverse selection.

I think that is not necessary, and is a choice we have to make for our society.

For example, for health, do we want "sicker" persons to pay more, leaving healthy people the choice to not pay ? Or should we make it mandatory for everyone to pay what they can afford, and insure everyone, even high risks people ?

For cars, it might be a little different, but I think I'd rather have a system where everyone pays the same, and insurance is mandatory (although it's not as critical as health care).

Yes but there's also a time factor: do you want young people to pay while healthy.

When you're young you want to think only abt yourself, when you're old you want younger people to think abt you so :D

Yeah, that's why I think everyone should pay, not based on their age, but on their ressources.

Do you think there should be differences based on lifestyle? For instance, should someone that works out everyday pay the same as someone who is 400 pounds?

I think they should both pay based on their income, not their lifestyle.

That seems really unfair to me. I would definitely be against that system. If someone chooses to smoke or heavily drink or eat too much it shouldn't be my responsibility to subsidize them.

Just to explore the idea further, are you also against care for people who get snake bites while hiking, have a beer once a week, or choose to live in an area with environmental toxins?

I mean, it's about the statistical consequences of your lifestyle. I would expect hiking overall to have a positive impact on your health and health expenses statistically even with the risk of a snakebite, and a beer a week to have no impact at all. I'm talking about the people who come home and drink whiskey every night. And I'm not against my insurance paying for peoples care, I'm against paying the same insurance rate as them. Health insurance should be higher if you live in a area with high environmental toxins, as well, sure. Should everyone in the country carry flood insurance so that people in flood planes can pay less?

It seems to me a lot of this is about responsibility to society, but that only goes one way. If it's my responsibility to pay into social Healthcare, why is it not their responsibility to not be a heavy smoker, or morbidly obese, or a heavy drinker? It seems to me that the moral tables are turned around in this argument, where I'm a bad person for not wanting to pay, but they arnt bad people for doing things that virtually garuntee they will need payouts.

I suspect the people who are "virtually guaranteed" to need payouts are a small population compared to the majority of people that live somewhere in the gray zone between the two extremes.

Then, to quantify the people in that gray zone, it becomes a question of which variables to we include? Sure, alcohol is bad, and junk food is bad. But what is junk food precisely? And if you run ultra-marathons, it surely doesn't matter as much. If you live in a city with higher pollution, if you drive a cheaper older car with a worse safety rating, if you work two jobs and thus have higher stress levels, on and on.

And if we're talking about social healthcare, do you really want a faceless bureaucracy to be tasked with calculating those risks and putting a price on all your life choices?

What if someone's work makes them subject to more diseases, like a factory worker ? Should they pay more ?

What about people that are not as well educated as you are, and thus don't know that too much sugar is bad for them ? Should they pay more ? What about overweight people that are from a genetic pool of people that are more subject to this issue ?

Sometimes it's hard to know if a disease comes from lifestyle or other factors.

Universal health care is basically a special case of “people in the pool having similar risk,” because the idea is to have only one pool with everyone in it. The “with everyone in it” part solves the adverse selection problem.

But health care is, or rather shouldn't be, an insurance. Otherwise the company would say:

"Sorry to hear you got cancer, here's your cheque. Please don't bother us anymore, as we terminate our contract. All the best."

Health care is more like a flatrate plan where some people receive much more intensive service.

Arguably a taxpayer funded service is still a form of insurance. In the UK we pay "national insurance" which is a form of income taxation (but gets accounted for separately), much if which gies towards paying for our health service.

A fixed rate plan for something with unknown and highly variable costs is just about the definition of insurance.

I don't think so. At least every insurance I ever bought had very precise definitions of the monetary obligations for each party. I think the highest would be my car's mandatory insurance (capped at, I think 20M€ per damaged person). My health "insurance" doesn't have such a cap. In fact, they are forced by law to pay for everything that I would ever need from a certain catalog of services. Also, the rates are not negotiable in my case but a fixed percentage of my income. It's similar for the pension "insurance" which is more like a perpetual pyramid scheme than an insurance.

You can put scare quotes around insurance, but they're really just counterexamples to your claim.

Many forms of insurance include a cap to reduce the insurer's risk, but that doesn't mean such a cap is necessary for it to be called insurance. The height of the premium can be defined by law, but it's still an insurance premium.

Pensions can be hard to understand because longevity risk is a bit counterintuitive, but depending on how they work in your country they can definitely be a form of insurance.

Your health insurance does have a catalog. It doesn't just pay for everything and anything.

Depending on your country this catalog is also shrinking and pushed into private insurance. Since there is such variability between countries and their systems these discussions become 'hard' to have because something that is normal for one guy works the opposite in the other guy's country.

In Germany I had dental covered by the state. Like you said, fixed percentage of my income covered all that (and all the other health insurance needs with a catalog of services). No need to think about it. Except someone actually decided on that catalog based on monetary concerns and calculations. Also while there is a fixed health insurance cost as a percentage of your salary, there are different actual insurance companies and they add a variable premium to this which they 'compete on' for clients. This is the public system which must cover you and you can go fully private (and never be admitted back into the public system if you do) which gives you "better service" (like private rooms being standard at the hospital and such).

Then they added private insurance on top for some stuff that wasn't covered by the public dental plan any longer. In Canada just a regular filling needs to be paid out of pocket and I really want private/employer extra insurance. Different for kids where I pay out of pocket for a white filling but Amalgam would be covered. I don't even know if this is the same in other provinces maybe.

Pension: Germany has a pyramid scheme and it collapsed a while back. Not enough payers any longer and suddenly they had to tax people's pensions. People who they told need not worry about their pension ever. Suddenly they were told they would need to pay tax on their pensions and oh btw. you should really have started paying into private pension like a decade or so ago. From after tax income. They do have various private insurance schemes that lower your taxable income but the fees are sky high and returns meager. It's a way to shuffle money into insurance companies. Thank's government! And other than that, you can get ~800 EUR of tax free interest/dividends per year. Everything else is taxed at 25%.

This is way different in Canada again where Old Age Security and your pension are not covering you and everyone knows. People either work longer because they can't afford extra insurance or have an RRSP (kinda like a 401k) they pay into. You know you will be taxed on this later but you aren't now. And all your money grows tax free in that account. Never pay a single dollar of taxes on those dividends over the years. And a non pension tax free savings account on top of that. Sure it's after tax income in there but you can take it out any time. No need for any insurance company fees either if you don't want to. Sure you can buy mutual funds and such but you arent forced to just to be tax exempt.

> Never pay a single dollar of taxes on those dividends over the years.

The complicating issue here being that you’ll eventually pay income tax rates on those dividends instead of (usually) lower dividend tax rates. If your income is high when you retire, you might pay more in taxes this way with the deferral. And it’s hard to know in your 20s and 30s what your income will be when you retire. But as a form of insurance, you should still build that nest egg.

You are correct in that, though dividend tax rules are complicated and differ all over the place too. In Germany you pay a flat 25% (which is already better than it used to be. You used to pay your regular tax rate, whatever that would've been. Probably higher than the 25%. But 0% sounds better to me.).

Now here in Canada you pay something like half of your tax rate and its different whether they're "eligible" or not and such things. But all that is only outside of tax sheltered accounts and at least on my end I don't make enough to worry about calculating that. Then again at least here in Canada you also need to be aware of the whole withholding tax thing on US stocks and the implications for your dividends coz the US recognizes RRSPs as tax sheltered but not TFSAs...

Of course I won't really know whether I maybe make more in retirement than I do now but I personally believe that I will definitely make less than I do now. And if I really do earn more in retirement than I do now then I am probably very well off an it will in part be because my RRSP and TFSA contributions were able to grow without loosing 25% of the dividends all the time. So if compounding then does its thing and make me rich (I doubt I'll actually be rich from that though) then I'm fine with being taxed on it then.

> I personally believe that I will definitely make less than I do now.

It's not so much about whether you'll make less or not, but if you'll make enough less to land in a lower tax bracket to take advantage of the deferral. And avoid dying and having to pay tax on it all at once (unless you can shift it to your spouse, but then they may have a high income problem too, negating the benefit of the deferral).

RSPs can be great, but I think they're oversold to the working class as a tax advantage.

If you don't mind my asking, what kind of income are you talking about if you are not gonna be in a lower tax bracket in retirement?

Different question since you seem not to like tax deferral. What makes you not like tax deferral and compounding on the extra ~25% of dividends you keep?

I can't do much about when I'll die. I do advocate for 'living now' btw. If you can do that 'trip around the world' now or put money into a pension fund, do it now. Don't wait, have kids and tell yourself you'll do it when you retire. That day may never come or you might not be up to it any longer for various reasons.

>The complicating issue here being that you’ll eventually pay income tax rates on those dividends instead of (usually) lower dividend tax rates.

This is the wrong analysis. While it's true that when you withdraw you pay taxes at the marginal rate, you also need to realize that your contributions are before tax. When you're withdrawing, you're not paying income tax rates on the gains/dividends, you're paying income tax that you previously deferred. The gains are still tax free.

> Suddenly they were told they would need to pay tax on their pensions and oh btw. you should really have started paying into private pension like a decade or so ago.

That's not true. The taxation of pensions in Germany is a gradual shift accompanied by a parallel shift to tax-free payments into the pension funds.

It is absolutely true and your extra information is also correct. It is gradual, you are correct but still people that didn't know they were gonna have to pay tax got hit with it. And when they were told you should've been privately saving already. I know because I have relatives there who have to pay tax (though like you said not at 100%) and it is not pretty.

Then your relatives did not tell you the whole story or should go to court over their taxation. German courts have made it pretty clear that pension income that was taxed when paying must not be taxed again. The decision is from May so you might want to talk to your relatives about that topic again ;).

> Pension: Germany has a pyramid scheme and it collapsed a while back.

Please stop that FUD.

> Pension: Germany has a pyramid scheme and it collapsed a while back.

The system did just fine, but was plundered by politics. During the German reunification, the people from the former Eastern Germany were added to the public pension fund without ever having anything payed in. This drastically increased the amount of recipients without bringing in additional money.

Politics decided that. They also decided to not put any tax money in the pension pool to re-balance it.

No matter how you design a pension fund: If you bring in an additional country as recipients without any additional capital, that pension fund won't survive.

[1]: https://www.bpb.de/politik/innenpolitik/rentenpolitik/290963...

Making everyone more healthy (resulting in everyone in the pool having the same baseline risk) is a net good for both society and the insurers.

Really the issue is people with incurable conditions. Universal health care is there for them. Private insurance fucks them over.

I don't think in a free market private insurance would necessarily fuck people over. For example the idea of creating a catastrophic insurance plan for healthy, fit young people would be wildly profitable and beneficial for those who would sign up for it, but the government wouldn't allow it to exist because it "discriminates" against those who are unhealthy or made different lifestyle choices.

>wildly profitable and beneficial

How could it be both?

And if it was beneficial, how could you describe the people to whom it was beneficial as "healthy and fit"? Aren't they really just people who the screening failed to identify as unhealthy?

It depends on your definition of "fuck people over". The insurance plan for healthy, fit, young people would likely be cheap. However, they were subsidizing older and/or less fit people. The rates for the "not young, fit and healthy" plan are going to go up. Drastically. I would also be unsurprised to see that the "healthy, fit, and young" group ends up becoming the "average" group, and that they use the other group to lump together people they don't want to insure, with rates so high people can't afford to pay them.

I.e. they keep you in the healthy, fit and young group until you get cancer, and then they move you over to the $7,000/month group.

The current system just averages that out. Your rates are higher than they have to be when you're young, but your rates are lower than they have to be when you're old. It negates the risk by lumping everyone together. Your form of insurance doesn't do much to reduce risk because you can always be moved to another category. The insurer really just becomes a middleman between you and your medical providers then, if the goal is to allow people to pay for what they use. It's basically an HSA.

An example to the last part in the real-world: Geico is widely known to be the cash float of Berkshire Hathaway, Buffett’s main investment vehicle. It’s basically a costless margin loan for Berkshire that it can freely use in investment. The main savings Geico passes onto you in part comes from the fact that they have a better use for capital (i.e. BH is wildly good at investing) than most other insurance companies.

I’ve always wondered about this logic: it makes sense for life insurance where the average person pays in for decades before withdrawing.

But for geico (primarily auto), where’s the float? I thought it was like a pyramid scheme: this years payments pay out this year’s claims. There would be minimal float for the future except to cover black swan events like a hurricane hitting a state every 10 years, and that might be what Reinsurance is for (something else BH does a lot of, and probably self-deals a lot). Float would be great for the insureco, but any insurer charging anything more annually than average annual claims will lose all their business.

> Float would be great for the insureco, but any insurer charging anything more annually than average annual claims will lose all their business.

What are you basing the assumption that insurance companies are working with low margins on? There are many competitors, sure, but what reason is there to believe that they must compete on price?

> You want people in the pool to be similar risks.

And yet my car insurance quotes only ask me my age, gender, and what car I drive. They presumably also use my history of car accidents, serious legal issues like DUIs, and car insurance claims (all nonexistent in my case) as input. This strikes me as a comically low amount of information to place me in a risk pool.

Also your address, which is surprisingly useful in predicting likely outcomes (even if the range of outcomes in a neighborhood are wide at the extremes).

It really is depressing just how much information, from life expectancy to health outcomes, can be gathered from a simple five digit zip code. Very accurate too.

Insurance companies apparently seem to think it’s useful, but I find it extremely hard to believe it would be more useful than, say, even the most basic information about one’s driving behavior, like whether one drives 1,000 miles a year or 50,000.

I don't think that'd be less useful, but they can't trust what you say: "sure, I only drive very little, very carefully, and very slowly" is not something they can check.

If they can, they'll use it: that is why black box car insurance exists.

If you’re just going by mileage count, you can look at the odometer.

They mostly deal with numbers on the macro scale. If 10,000 miles per year is a good representation of how much the general populous drives, it’s good enough for them. This is why we’re seeing more niche insurance companies pop up (MetroMile, et al) who can offer “smarter” rates based on a more granular assessment of risk.

All else equal a driver who does 5000 miles a year will have half the adverse events of Someone driving 10,000 miles/year. That’s a huge difference that makes no sense of lump together. And yet only a few (non-commercial) insurers, like metromile, account for it. It makes no sense.

I also think the simpler the algorithm, the harder it is to game.

“Oh wait, I almost never drive, but when I do, I’m either drunk or speeding. Well, I’ll sign up with this insurance company which offers me a discount because I drive so little!”

My car insurance definitely asks for that sort of information, so I’m not sure why yours doesn’t.

They do ask it, but it doesn’t affect the rates and they don’t have any way of verifying how much I actually drive.

They're not "supposed" to do that (at least in the US) because the practice of Redlining was made illegal by the Fair Housing Act of 1968.

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

https://web.archive.org/web/20170317143050/https://fairhousi...

Two things to this:

- That bit of info you give can be used to infer other info. Also it's possible those first three things explain most of the variation. We've all heard that young men in their 20s crash their cars a lot, I get the feeling it's true though I've never checked.

- You only need the risk groups to be granular enough that it isn't totally obvious that people are different risks (footballers and grannies).

They use a heck of a lot more than that. They use your name and DOB to run a backdoor credit pull and it turns out that is a pretty reliable indicator of what risk pool you belong in. There is also a "credit check" for insurance (You can get your report from LexisNexis) and they can see how many times you applied for other insurance products and how long you had them, which is another indicator.

To use more information, you make more granular risk pools. The pools need to ne large enough to actually pull risk.

If you try to ise 10 pieces of information with 10 possible values each, that could give you 10 billion risk pools, i.e. individual person. Alternatively 33 Yes/No questions alsp let you identify an insividual person on planet earth.

Having "individual" insurance has no real meaning, because at that point its not spreading risk.

Car insurance is almost entirely not about repairing the damage to your car.

> that's something actuaries have thought extensively about

But I don't think there is any solution. The further out on the "tail" you go, the more the total risk depends on the accuracy of information and assumptions you have. If there is an extremely large potential loss that is extremely unlikely, then the average becomes unknowable since the probability estimate in particular could be off by orders of magnitude. Nuclear power plants would be sort of the archetype of that, I think.

I mean, I reason like this to justify what I actually observe - that insurance companies don't want to insure things without strict limits. Despite reinsurance existing.

> they care about the extremes too of course, since they wouldn't want a bunch of payouts at the same time

Isn’t that pretty much handled by reinsurance?

Yep, there's a whole market in insurance risk where it can be sliced and diced and traded, much like most financial risks.

That's correct. As an insurance company you buy reinsurance to insure yourself from catastrophic outcomes (i.e too many claims for your reserves to handle).

> but of course there are laws about insurance

In the U.S. at least, you don't need to insure your own car. You just need liability insurance that will pay out to someone else if you're at fault in an accident.

It's usually possible "self-insure," too. Basically, you put up some amount of money (of order $30-50k) to the DMV as a surety bond. Then if you're held liable for an accident the state doesn't have to worry about you paying up because they already have the money.

$50k is comically insufficient to cover the damage you can do in a car in a single incident, though, and such a bond is a limp assurance at best.

I wonder if there should be a per-vehicle cap on damage where a vehicle is so expensive that the owner insures it for any damage over some amount, say $60,000, or the 95th percentile new car sale price.

Damage to vehicles isn’t the problem. The tail is hitting a car full of surgeons and ruining their careers so you are paying out gazillions in personal damage.

That’s the theory, I would be surprised if the reality wasn’t more messy with a lot of insuring money going into marketing, management, IT, with insurance price more based on what salespeople are able to decently add to a product, and company profitability discovered afterwards.

> That gives some room for investing the free float.

That's why Buffet bought National Indemnity, btw. He wanted the float which, for him, was a cheap way of financing investment.

Not a very folksy move, truth be told.

Fantastic summary. Thanks.