Excellent explanation. Is that Taleb discussion from a book, or an interview? I've read some of his books but not all.Paracelsus said:This right here is a perfect example of how statisticians conflate ensemble probability with time probability. Nassim Taleb sets out how computing your chances of survival on the basis that the chance of a helicopter crash is 1 in 300 years is horribly miscalculating your risks. Handsome Creepy Eel has it exactly right: it's the fact helicopter crashes are always catastrophic that makes the resort to "once in 300 years" statistic of use only as a mildly interesting math wank, on par with Sudoku. And quite the opposite to what he thinks, HCE is in fact thinking entirely rationally. It's the statisticians who are thinking thintelligently.Handsome Creepy Eel said:I might be thinking irrationally here, but my main beef with flying (or in this case helicopters) isn't how often accidents happen, but that when they happen they're invariably fatal. According to this stat, for 1 fatal helicopter accident, there are 7 where the helicopter somehow lands safely and I'm wondering "How? Helicopters can't glide or make an improvised landing..."911 said:That stat means that if you say, commuted on a helicopter 10 hours per week, every week of the year, the expected amount of time you would need to spend in order to be in a fatal crash is over 300 years... Probably safer than sailing, or on par with riding a motorcycle or a bicycle in traffic.Sooth said:RIP
It's a statistic. The more time you spend in a helicopter the more likely you'll get into strife.
"The U.S. helicopter accident rate in 2017 was 3.55 accidents per 100,000 flight hours, and the fatal accident rate was 0.59 per 100,000 flight hours, USHST said."
I don't know what the non-fatal accident to fatal accident ratio is for cars, but I seriously doubt that it's 3.55 to 0.59 - it's more likely 13.55 to 0.59.
The difference between 100 people going to a casino and one person going to a casino 100 times, i.e. between (path dependent) and conventionally understood probability. The mistake has persisted in economics and psychology since age immemorial.
Summarising for poor old Kobe Bryant: per 911's "expected result", as a group, commuter helicopters used 10 hours per week only crash once every 300 years. That's a probability of failure ascribed to a group. But Bryant, being a man who used helicopters a lot, had a 100% chance of eventually having something catastrophic happening to him. And that number played out. It was the exposure to the risk itself that killed him and his own daughter. Cost-benefit analysis is, simply put, not valid where the downside risk is outright catastrophe or death, any more than your "expected return" in a game of Russian Roulette is $833,333 assuming a 1 million dollar bet.Recall from the previous chapter that to do science (and other nice things) requires survival but not the other way around?
Consider the following thought experiment.
First case, one hundred persons go to a Casino, to gamble a certain set amount each and have complimentary gin and tonic –as shown in the cartoon in Figure x. Some may lose, some may win, and we can infer at the end of the day what the “edge” is, that is, calculate the returns simply by counting the money left with the people who return. We can thus figure out if the casino is properly pricing the odds. Now assume that gambler number 28 goes bust. Will gambler number 29 be affected? No.
You can safely calculate, from your sample, that about 1% of the gamblers will go bust. And if you keep playing and playing, you will be expected have about the same ratio, 1% of gamblers over that time window.
Now compare to the second case in the thought experiment. One person, your cousin Theodorus Ibn Warqa, goes to the Casino a hundred days in a row, starting with a set amount. On day 28 cousin Theodorus Ibn Warqa is bust. Will there be day 29? No. He has hit an uncle point; there is no game no more.
No matter how good he is or how alert your cousin Theodorus Ibn Warqa can be, you can safely calculate that he has a 100% probability of eventually going bust.
The probabilities of success from the collection of people does not apply to cousin Theodorus Ibn Warqa. Let us call the first set ensemble probability, and the second one time probability (since one is concerned with a collection of people and the other with a single person through time). Now, when you read material by finance professors, finance gurus or your local bank making investment recommendations based on the long term returns of the market, beware. Even if their forecast were true (it isn’t), no person can get the returns of the market unless he has infinite pockets and no uncle points. The are conflating ensemble probability and time probability. If the investor has to eventually reduce his exposure because of losses, or because of retirement, or because he remarried his neighbor’s wife, or because he changed his mind about life, his returns will be divorced from those of the market, period.
We saw with the earlier comment by Warren Buffet that, literally, anyone who survived in the risk taking business has a version of “in order to succeed, you must first survive.” My own version has been: “never cross a river if it is on average four feet deep.” I effectively organized all my life around the point that sequence matters and the presence of ruin does not allow cost-benefit analyses; but it never hit me that the flaw in decision theory was so deep. Until came out of nowhere a paper by the physicist Ole Peters, working with the great Murray Gell-Mann. They presented a version of the difference between the ensemble and the time probabilities with a similar thought experiment as mine above, and showed that about everything in social science about probability is flawed. Deeply flawed. Very deeply flawed. For, in the quarter millennia since the formulation by the mathematician Jacob Bernoulli, and one that became standard, almost all people involved in decision theory made a severe mistake. Everyone? Not quite: every economist, but not everyone: the applied mathematicians Claude Shannon, Ed Thorp, and the physicist J.-L. Kelly of the Kelly Criterion got it right. They also got it in a very simple way. The father of insurance mathematics, the Swedish applied mathematician Harald Cramér also got the point. And, more than two decades ago, practitioners such as Mark Spitznagel and myself build our entire business careers around it. (I personally get it right in words and when I trade and decisions, and detect when ergodicity is violated, but I never explicitly got the overall mathematical structure –ergodicity is actually discussed in Fooled by Randomness). Spitznagel and I even started an entire business to help investors eliminate uncle points so they can get the returns of the market. While I retired to do some flaneuring, Mark continued at his Universa relentlessly (and successfully, while all others have failed). Mark and I have been frustrated by economists who, not getting ergodicity, keep saying that worrying about the tails is “irrational”.
Now there is a skin in the game problem in the blindness to the point. The idea I just presented is very very simple. But how come nobody for 250 years got it? Skin in the game, skin in the game.
It looks like you need a lot of intelligence to figure probabilistic things out when you don’t have skin in the game. There are things one can only get if one has some risk on the line: what I said above is, in retrospect, obvious. But to figure it out for an overeducated nonpractitioner is hard. Unless one is a genius, that is have the clarity of mind to see through the mud, or have such a profound command of probability theory to see through the nonsense. Now, certifiably, Murray Gell-Mann is a genius (and, likely, Peters). Gell-Mann is a famed physicist, with Nobel, and discovered the subatomic particles he himself called quarks. Peters said that when he presented the idea to him, “he got it instantly”. Claude Shannon, Ed Thorp, Kelly and Cramér are, no doubt, geniuses –I can vouch for this unmistakable clarity of mind combined with depth of thinking that juts out when in conversation with Thorp. These people could get it without skin in the game. But economists, psychologists and decision-theorists have no genius (unless one counts the polymath Herb Simon who did some psychology on the side) and odds are will never have one. Adding people without fundamental insights does not sum up to insight; looking for clarity in these fields is like looking for aesthetic in the attic of a highly disorganized electrician.
To put the fallacy another way: nobody ever points out the total number of hours cigarettes are smoked across the planet without causing cancer or death as a demonstration of the safety of cigarettes. The point is that we cannot establish at what point a death-causing lung cancer first erupts into life, nor after what cigarette, so the rational person doesn't smoke.