Micromort
en.wikipedia.org
en.wikipedia.org
Blastland was one of the creators of the excellent 'More or Less' on the BBC that looks at how numbers are used and mostly abused by the media, politicians and everyone else.
Spiegelhalter is a prof of stats.
The book addresses a number of the criticisms that have been leveled at the concept in comments here. They also talk about the 'microlife' which is what you get by exercising or whatever. They also acknowledge the problems with these ideas as well.
While on the subject, "More or Less" is quite a good program, and fun to participate in.
Say hello to David/Michael, he does a great job!
Second-hand smoke does have some health consequences -- for instance poor air quality is strongly linked to childhood asthma. It's also certainly considered a nuisance by most people.
Anyway, I'm not surprised at all that living in a polluted city would expose you to far more danger than a smoker at home. 30x sounds fairly reasonable.
All the lottery and insurance business is just a scam against us taking advantage of this miss computation of micro risks.
Some extra money when you are in trouble is worth more than the money itself, it is also worth the trouble it gets you out of.
Your expected utility is not your expected dollars. The average person will pay more into insurance than they get out of it. However it's worth it for the small chance that disaster could strike and you could lose everything. Better to sacrifice a small amount of utility to prevent losing a large amount from becoming homeless.
My point is that the current insurance system and price is a scam, because it is much too expensive and covers to many silly cases. That's because it is very hard for human beings to evaluate the risk of something rare and its price. While this evaluation is exactly the job of insurance companies. It is the classic situation for a scam: the buyer can't know the real price. And we also have the symptoms: way too much money is spent on luxury in this industry, they have the most expensive tv ads, etc.
I am a credentialed actuary responsible for the pricing of insurance risk. It is absolutely true that the consumer cannot price his or her own insurance policy (and I can). However, the end result of this is not some nefarious scenario where insurance companies are charging consumers ten times the fair price to insure their car or home. There is a functioning market for insurance, and consumers are going to tend to select the lowest-price option from amongst their choices in that market. This means that if you overcharge your customers, you will lose them to a competitor. Systematic mispricing of policies relative to the competition will lead to adverse selection, which is even worse - the insureds that you were making money on leave, and the insureds that you were losing money on stay.
Because of these factors, the insurer's goal is to price your policy as accurately as possible. Profit margins in the personal lines are so thin that many insurers engage in what's called cash-flow underwriting. The only money they make on the policy is the investment income they earn on your prepaid premium.
On top of all this, insurance (especially insurance marketed to consumers) is heavily regulated. Rate changes and new rating plans are scrutinized by each state's department of insurance. These regulators function like you wish the banking regulators did. They have enormous authority and their relationship with insurers is adversarial.
I could go on at some length but I will cut it off here. Suffice it to say that insurance, particularly property/casualty insurance in the United States, is about as far from a scam as you can get.
Your strongest point is competition, but competition only works fully for economically rational agents, which we are not.
Regulations are making my point stronger: they exist because without them the clients would be defenseless.
Sorry to be short, I'm on a phone.
Unlike any other product you buy, the price of insurance may not be excessive, inadequate, or unfairly discriminatory. This is the law. Unlike any other product you buy, personal insurance prices must be filed with regulators who have the power to block the sale of any insurance product that does harm to the public. Unlike any other product you buy, an entire profession is devoted to the pricing of insurance. You cannot even propose to sell an insurance policy if your pricing scheme has not been signed off on by a credentialed actuary. Those credentials are not easy to come by, and actuaries are bound by standards of practice that preclude us from doing anything unethical.
If my employer asked me to violate an actuarial standard of practice, I would quit on the spot, and I don't know any other actuary who wouldn't do the same. And finding an actuary willing to throw away their livelihood would only be the first step in the process of attempting to charge a consumer an excessive rate. There are so many safeguards in place that bypassing them all doesn't seem like it would even be possible, and even if it were, the insurer would not reap any rewards due to the force of adverse selection.
I don't often post on HN, and I know that the actuarial profession is not very well known, but arguing with an actuary about the pricing of insurance is like arguing with a heart surgeon about where the aorta is. I can tell you with the authority of an expert that you are mistaken.
I have friends in the insurance business and I think it is a very honorable profession in most of the cases but you can't wipe out 1) the door to door insurance salesman scamming fragile old people, 2) the possibility that, much like finance, the whole insurance profession is based on wrong equations that makes it apparently robust but inherently fragile (in the sense of Nassim Taleb).
It is true, though, that many people fall into the trap of over-insuring. For example, people who could easily afford to replace their car yet pay for comprehensive insurance.
For risks you can self-insure against, you should do so. Otherwise you're just gambling against actuaries, and they're better at the game than you.
For catastrophic events, insurance is a completely sensible bargain for both parties.
Financial insurance also build a corset to let the card castel grow higher, until it falls apart on the floor. Idea taken from Antifragile.
Then how much would you bet on the hope that insurance companies are not taking advantage of this psychological weakness for their benefit?
From there, it's up to you to determine whether it's worth it. I personally don't have health insurance (though I live in a country with universal healthcare), but I have 3rd-party car insurance in case I accidentally drive into someone's Lamborghini, and it was fortunate that my girlfriend's dad had life insurance so that her mum had some money after he passed away prematurely last year. Just because money is being made doesn't mean it's a scam.
This to me is where our perceived realities differ with real life.
Spending the money on defensive driving and/or car safety makes much more sense, but we can only see the future where the accident happens (And we survive) not all the accidents we can stop.
I have no idea about your girlfriends father and what happened but I'd prefer to spent money on not dieing than paying for what happens if I do.
If you don't see the value of insurance, then don't buy it unless the law requires. And if you don't like the law, then do something about it.
But if you're family has money, or if you do, it would be smart to put a few bucks into your insurance policy and relax knowing that your capital is not at risk. And if you don't have a lot of money, its nice to know that there's cash available for you when something bad happens.
The whole reason insurance exists is because of differences in risk tolerance. What is a huge risk for me, such as a fire destroying my house, is a relatively small risk for an insurance company that is insuring against fires across the entire state. What I pay the insurance company for is to assume part of that risk.
Consider homeowners insurance, and more specifically fire insurance, in this admittedly contrived example. Suppose that in the next year there's a 1/1000 chance of a fire that will cause damage that will cost $100k to repair. That has an expected value of $100. Well, since $100k is a lot of money to me, I'd rather pay someone $200 than take a bet with an expected cost of $100, even though paying $200 has a negative expected value. That means I am risk averse for potential gains and losses on the order of $100k, and would rather take the more certain side of a bet, even if it means it has a lower expected value.
Take another example. Suppose I'm worried about losing or breaking my cell phone over the next year, and it would cost $500 to replace. AT&T charges $6.99/month for insurance on the phone. Over the course of a year that's about $84. And furthermore suppose there's a 1/20 chance that I'll lose/break/etc my phone during that year. Without insurance, the expected value of the loss is $25. Unlike the $100k example, $500 isn't that big a deal to me, so the insurance is a horrible deal for me, because I'm risk neutral for a $500 loss.
Of course, real life is more complicated. Homeowner's insurance protects against risks other than fire. Risks to the insurance company can be correlated - something on the order of the 1906 SF fire is a large risk, even to an insurance company, which is why there is reinsurance. There are deductibles that change the pricing. But still, as a simple example, that's how insurance works.
A rational agent would pay 100$ plus the processing fee for the home insurance. It would not pay for "piece of mind", just as it would not pay for the "excitement" of a lottery ticket.
We are not rational agent, but my point is that those who are closer to rational choice based on statistical truth are the one who win the game (in average).
Besides, it's all about risk preference. As long as my preferences are consistent and transitive, I think it's safe to say they are rational. Take the fire insurance example. Suppose I have a job that pays $10k/year. I would gladly pay $200/year to avoid the possibility of a $100k loss. Those are my preferences, and as long as you can't a non-transitive loop, it's perfectly rational of me to have those preferences. In this case, I'd value the guaranteed loss of $100 to be a much better outcome than the risk of loss of $100k.
In short, rational != risk neutral.
Proof is easy: I give you the choice to play on the flip of a coin, one side you win $1200 other side you loose $1000. You'll likely refuse because of fear of loss. Then consider I propose the bet 1000 times in a year, under different disguise so you don't recognize it. You lost 200 000!
It is not rational to refuse a net positive bet it of irrational fear of loss. It is even more obvious for the lottery, because we would all agree that paying lottery ticket is irrational, right?
Lottery isn't really a scam either if you derive pleasure simply from playing the game.
Lottery pleasure is empty. Play poker with friends, you may loose money but at least you get friends.
The problem pointed in Kahneman book is that we are irrational, and (AND) it's usually the less irrational among us who win.
Okay, but small is relative.
For example, an insurance company has to pay for investigators, the number of which would likely scale linearly with customers.
Nice offices and an advertising presence are also likely necessary to entice and maintain customers, probably more-so an an industry like insurance in which there aren't many tangible differentiators between competitors (see Coke vs Pepsi).
I don't see why insurance should be any different than any other industry regarding these issues and also the existence and legitimacy of profits (assuming they weren't derived from fraud).
Moreover the fact that insurance are highly regulated just makes my point. We are defenseless and the law puts some limits because a scam is too easy to build.
And I don't say you shouldn't pay for your own protection, I say you can't evaluate the risk correctly and are very likely to be ready to pay too much. Which is how insurance make money.
If you house burns down, sure that's reasonably catastrophically bad, But if you house burns down, there's a fair chance it'll happen at night, and there's is a fair chance you'll die.
Don't spend money on insurance, spend it on stopping your house burning down.
If there's a risk of it happening then the money should be spent on reducing that risk, not wasting it on, if I survive at least I won't be poor.
And if you tell your insurance about your extra measures for fire safety, they likely lower your rates. They might even consult you about which fire safety measures are actually useful (and they have the data: data driven fire safety, how does that sound?).
Since fire insurance tends to pay for damage repair when things didn't burn to the ground, they're also useful in situations that are not as life threatening as your example. We had a warehouse burn down in town, and the neighboring house was affected in that the windows on two sides of the house melted enough to be useless. The cost of replacing all those windows can easily exceed an individual's short-term liquidity (a single event might even exceed the rates paid for the insurance over its life-time) - for the insurance that was pocket change.
1. Securing the house from fire costs $5,000/year to reduce the probability of the house catching fire (it's still possible that it catches fire).
2. Buying an insurance which costs $500/year and will replace your home in the event that it catches fire.
2 is cheaper, and a better deal if your house catches fire. With 2 you are even more secure.
I mean really, 1 hour in a coal mine and you get black lung? Absurd. Would 1 minute in a coal mine be 1/60th of a micromort? Would 1 second in a coal mine be 1/3600th of a micromort? Of course not, and of course not. Black Lung is caused by long term exposure.
You are not rolling a million-sided die every hour you are in a coal mine.
By staying in a coal mine for 1 hour you increase the chance of death by 1 micromort, that by definition means if you did that for about a million times you would very probably die. If the average life expectancy is about 613000 hours, and if you spend every living hour in a coal mine you would still live every other lifespan.
There's also contexts missing from many of the other statistics: where you drive and the kind of car affects the mortality rate of driving, for instance.
The micromort is still a useful concept in specific controlled conditions (radiation exposure), or as a first approximation of quantifying risk, but the general statistics should definitely be taken with many grains of salt.
If you had two identical groups of a million people each and one group received 0.5 liters of wine per person, would you really be shocked that the group that got the wine had a single extra death?
[1] I would be shocked if, give two groups of a million, both groups had the exact same number of deaths in a predetermined time period. 1 death difference between two groups that large is pure background noise.
How about this way: you agree that if you drink enough alcohol it will kill you, right? So you could surely find someone who almost drank themselves to death. Perhaps they got liver disease and came very very close to dying, but survived. So there must be a line somewhere. Given a huge enough pool of people, it should be possible to find someone who came so close to death that a single extra drink could have killed them.
([1] It's a thought experiment. The two groups lead otherwise identical lives besides the additional alcohol.)
If the relationship were linear, then you could spread that 500 milliliters out over 100 days and see the same effect, which is plainly ludicrous. The rate of alcohol consumption plays a large role, a single binge can kill you, slow and steady drinking can plausibly extend your life. A single extra drink is also going to do way more harm to a long-term alcoholic than it will to a young healthy Mormon; that Mormon is at absolutely no chance at getting cirrhosis, the risk to the alcoholic is non-zero.
The relationship between alcohol and mortality is something that you could probably fill damn near half a medical library with. "half a liter is a micro-mortality" is silly oversimplified nonsense. It might work for radiation exposure (http://en.wikipedia.org/wiki/Linear_no-threshold_model) but it is nonsense for alcohol.
So long as the line is going up and to the right, it's specific shape only matters if you want to debate the micromort value, not whether the concept exists.
Some of these things plausibly can be modeled as LNT. Radiation possibly can, perhaps airplane rides too. Some of them cannot be, like alcohol consumption.
Its obvious that consumption is positively correlated to certain fatal conditions, but its not at all obvious that the risk is in proportion to (i.e., linearly correlated with) total lifetime consumption.
That's simply not the way things work.
If we had 10e20 people in each group and gave an extra 0.5 liters of alcohol to each one, would you be shocked that a millionth of them died?
Do you really think that a Mormon drinking 3 glasses of wine in his life has a one in a million chance of losing his liver?
If a million people each smoke two cigarettes in their lifetimes, it's not impossible that one of them might suffer a cigarette-related health detriment.
In low quantities of a toxin, up-regulation of repair mechanisms can sometimes improve outcomes (i.e. hormesis), but the risk of damage to critical genes still exists.
If you smoke 2 cigarettes on one day, chances are that you are actually a smoker and therefore you fall in the category of people that are more likely to die from cancer.
The actual impact of the cigarettes you have smoked isn't really taken into account here, it is the fact that you are likely be a smoker that increases the number of microdeath.
http://en.wikipedia.org/wiki/Talk:Micromort
for the article kindly submitted here suggests that the article still needs A LOT of work (as most Wikipedia articles doe) and that some of the statements now in the article may be flat wrong, misrepresenting the micromort concept as it was pioneered by Ronald A. Howard. See his presentation on microrisk analysis
http://ise.tamu.edu/isen627/Slides/25%20Life%20and%20Death.p...
for a possibly more sophisticated, exact, and accurate view of the issue.
The online mathematics lesson "Understanding uncertainty: Small but lethal"
http://plus.maths.org/content/os/issue55/features/risk/index
is also good for practicing understanding of micromorts.
Looking at the source, he seems to be lumping shorter plane rides in with the long-distance (safer) ones. The danger is largely in takeoff and landing, as far as I understand. I also can't tell if the source takes into account private jets, which are less regulated and likely more risky than passenger jets. I'd also imagine the statistic varies a lot of you limit yourself to flights involving the US and our colonies[1].
Or the source could just be wrong - he could have mistakenly used the chance of being involved in a crash, rather than the chance of dying. That would put it in the right order or magnitude, I think.
[1] With all the "evil empire" rhetoric flying around lately...
It's not for lack of trying. It's simply that commercial air travel in the US is so safe that there isn't enough data to compile anything like a reasonable risk figure. Prior to the Asiana crash, the last fatal airliner crash in the US was in 2009, and there were no fatalities in 2008 or 2007.
So, yes, they're much safer than that number would imply, but it's hard to say exactly how much.
They only assume the accidental nature of riding a bike and ignore the health benefits. A good article highlighting this http://www.mrmoneymustache.com/2013/06/13/bicycling-the-safe...
For example suppose I take a plane, then ride a bike to go hiking for a week with friends. Maybe this trip will save me many micromort from health and mental perspectives. Having a deeper friendship is certainly also a net positive.
http://www.youtube.com/watch?v=a1PtQ67urG4
The professor's conclusion is that one of the biggest risks is being too cautious.
> mathematically 1/e would only be an approximation anyway
If we're going with the definition that treats micromorts as independent, then it would make sense to define a mort as exactly a 1 - 1/e chance of death, and a micromort as a 1 - e^(-10^(-6)) chance of death, rather than a 10^-6 chance of death, but the difference is smaller than the degree of risk that we can measure or care about, so the difference is inconsequential, and it would still make sense to describe a micromort as a 10^-6 chance of death.
EDIT: I wonder how much the micromort exchange rate is with "The Death of Rats?"
We're done here.