Class - Applied Statistics

# Taleb’s Curious Views On Probability — Part I: Probability Does Not Exist

Ye Olde Statistician points us to an essay (a book chapter?) by our old pal Nassim Nicholas Taleb called “The Logic of Risk Taking“. Let’s examine it.

You, dear reader, do not have a probability of being flattened while crossing the street. Nobody does. Nobody has any probability of anything. Nothing has a probability of anything.

The reason is this (quoting de Finetti in word and typeface): PROBABILITY DOES NOT EXIST.

You cannot have in abundance or in fraction that which does not exist. Yet Taleb says, “the risk of being killed as a pedestrian is one per 47,000 years.” Ignoring the number, but the proposition itself will not sound wrong to most. It is wrong. Since probability does not exist, there is no blanket risk of you being killed as a pedestrian.

Probability, absolutely all of it all of the time, is conditional. You walk to a corner and desire to cross. At this point you must form premises on which to act. You might say, “I might get hit”, which adds nothing to your ability to form a probability of “I will get hit”. (This, and everything else, is proved in Uncertainty.)

You might instead think, “There are no cars coming anywhere”, and form a very low probability of “I will get hit”. Or you might say, “If I hurry, I can make it.” A higher probability.

Now suppose you are an actuarial (a statistician with less personality, as the joke goes) and want to guess how many pedestrians will go to their reward next year for having the audacity to cross the street. No easy job, that. Are you limiting this to the once United States? Everywhere? You still need premises to form probabilities of propositions like “There will be X killed”. Which premises?

Well, you might take the number flattened last year and use that as a base for some ad hoc model, which may or may not be useful in making predictions. You could form premises state-by-state, and then feed these into an ad hoc model. Or county-by-county. Or city-by-city. Or individual-by-individual.

Have the idea?

Change the premises, i.e. assumptions data and the like, and you change the probability. I don’t know what premises Taleb used to arrive at “one per 47,000 years”, but they must exist somewhere, at least in his imagination.

That probability depends on assumptions is the very point made in the last two articles discussing Taleb and the precautionary principle (here and here). Other words for assumptions and premises are model and theory.

Now suppose you meet the actuarial on his lunch hour and he tells you of his recent calculation, a model with various assumptions that led him to state “You’ll be dead street meat at the rate of one per 47,000 years”. This might form your new premise, from which you deduce (circularly) you have that chance of being killed.

When you get to the intersection, and you insist on using the actuarial’s number (he being an expert), it means ignoring all that is before you except that it is an intersection which you will cross. So if you live on a New York City avenue, it means ignoring that Access-a-Ride bus rocketing your direction towards the red light at which, by law, the texting wild-eyed driver must stop.

If you believe probability exists, and you believe an expert has discovered the probability for your particular situation, and Taleb is an expert, then ignoring circumstance is the rational thing to do; it is the only thing to do and stay consist with your belief probability exists.

Or you could chuck the idea that probability exists into the trash heap and hope the Access-a-Ride bus meets that perpendicular oncoming City bus and duels it out with him.

We need this demonstration probability does not exist as a baseline to discuss the remainder of Taleb’s article. The 47,000-year figure, for instance, comes from this:

About every time I discuss the precautionary principle, some overeducated pundit suggests that “we cross the street by taking risks”, so why worry so much about the system? This sophistry usually causes a bit of anger on my part. Aside from the fact that the risk of being killed as a pedestrian is one per 47,000 years, the point is that my death is never the worst case scenario unless it correlates to that of others.

I gather his over-educated pundit meant “We take risks by crossing the street”, which is true—but only on the premise that all actions possess a risk, that all risk is contingent.

I do not know if Taleb believes probability exists; he at times appears to imply it, at other times perhaps not. I’m not familiar enough with his writings to know if he has made a direct statement on the matter. So that if you love Taleb, there’s no reason to become upset with me.

More to come…

### 9 replies »

1. Michael Dowd says:

For those pedestrians who wish to be killed by a passing car the “probability” is nearly 100% that this will happen. This would be part of Taleb’s 47,000. My point is that many accident cases have nothing to do with probability. They were intentional and intentions can change dramatically perhaps causing Black Swan events. Maybe my comment is just adding to the confusion or misunderstanding.

2. I like Taleb, but we’ve already got an example of inordinate concern over carbon dioxide- European air quality is actually poorer than America’s because they prioritized lower carbon fuel over and above lower sulfur fuel. So they went down the diesel route, while America didn’t.

Taleb may be on firmer ground when he suggests caution with GMOs. They aren’t really modifying them for our health- they are modifying them so that they can withstand more of Monsanto’s products. So we are ending up with more of their products in our food supply. But there’s also some small chance of some sort of ecological disaster. It seems much more preferable to find a plant (or animal) that fits the ecology.

But you ought to read his books.

3. JohnK says:

OK. I’ve just done the work and spent at least 15 minutes looking up what Dr. Taleb says about probability. (I didn’t time myself, but I know it was at least 15 minutes that I’ll never get back).

One thing that leaps out in almost every page is the Taleb Dictum, which (implicitly and explicitly) appears repeatedly: if you lack “erudition,” you’ll never understand.

I lack erudition.

Part I of The Black Swan is apparently: “Figuring out Probability and What It Means.” But then I thought I read Dr. Taleb writing in Part I, in effect, that “statistics” is something that academic statisticians do, and (because they lack erudition) “statistics” has nothing to with risk assessment and management, which has to do with events that occur beyond the 99% confidence intervals, events which erudition-free people of all types ignore.

The good Doctor (or rather, PhD) says that this section of the book “…provides a rigorous definition of probability as used in real-world decisions, mapping distinct classes of payoffs and their sensitivity to model or representation error.” So he is defining “probability” as used in “real-world decisions”, not probability on the hoof.

So I couldn’t figure out what he meant by “probability” from that.

Then I found a talk by the eminent scholar in which he says, “the lower the probability, the more theory you need to be able to compute it.”

So I (lacking erudition) think to myself, “That’s kinda-sorta like probability is deduced or computed from a model.”

But then, a mere two paragraphs later, he says, “The smaller the probability, the less you observe it in a sample, therefore your error rate in computing it is going to be very high. Actually, your relative error rate can be infinite, because you’re computing a very, very small probability, so your error rate is monstrous and probably very, very small. The problem we have now is that we don’t care about probabilities. Probabilities are something you do in the classroom. What you care about is what you are going to use the probability for, what I have here called lambda of the impact of the event, the effect of the event, the consequence of the event.”

And that kinda sorta sounds like “probability” is an actual thing, and it’s real. It kinda sorta sounds like a “probability” is a property of things, and that if we wait a REALLY long time, the low probability event, always hiding in there, will show itself. Nonetheless, those who aim to possess erudition rapidly get beyond mere probability.

My conclusion: because I lack erudition, I can’t quite understand whether Dr. Taleb ever uses the word “probability” in an unambiguous and rigorous way.

4. Bill R says:

It is almost as if probability is a property of a reference set (either enumerated, deduced, or theorized)! Change the reference set and the probabilities change. Gadzooks! Holy Kolomogorov! WWLD: What would Laplace do…

He is fascinated by ergodicity, though. Comes from playing with infinities, I think.

5. Joy says:

Reading Jonk’s remark about ‘erudition’ and the linked post below where I’m given the side swipe by JH, wow!

That aside, I do recall being conned into thinking or should I say trusting that lack of technical understanding in the field, I can not possibly hold and certainly not express an opinion in the subject of

‘Quantifying Uncertainty’…

Anybody thoughtful can see that this is not possible!
Hence I assume this is because I am mistaken of the quality and beauty of the thing; there must be something I’m missing, these people can’t be carrying on like this.

You don’t need an actuary to tell you,
“nothing to see here, move along…”

Ahem, Well excuse me, but there is such a thing as using money from the public purse, complicit or not, governments, customers, businesses and individuals in many fields who are relying on and trusting nonsense spoken by unworthy individuals.

It IS what it looks like,
A pure maths professor said,
“All applied maths is rubbish’! And would not be dissuaded. It’s not the pie charts and the graphs that are wrong it’s the Opel using them, drawing them and looking at them.
I’m sure he’s right.

Probability, is likelihood masquerading as something superior.
Which statisticians are very good at.

Since the future is unknowable all prediction is only ever a case of using information which has only some small amount to do with and does not necessarily have to involve numbers at all.

Since anyone sensible knows the future isn’t reliably predictable or is unknowable to start with, ?
The concept of using thinking that uses prediction in any form to show some cause is just preposterous.

…and for the trolley problem which is a common thing in San Fransisco,

Love Robbie Williams.
A Wiser man than Taleb, and the rest.

6. Oldavid says:

Obviously, the best no risk plan to crossing a street is to wait until the most recent 47000th pedestrian has been killed and then cross with absolute impunity.

Statistics! the sure way to omniscience!

7. M E Emberson says:

Completely lost as usual. Probably I don’t understand the word ‘Probability’.

I never understand Dawkins after all . How can he prove anything does Not Exist, let alone God.?
I’m reminded of a slogan on the back of a bus, ‘God probably doesn’t exist, so enjoy yourself.’ Which means He might exist . But what His existence has to do with non enjoyment is not clear.
So therefore, I claim that many Atheists are just agnostic, and that means they just don’t know . Why can’t they say so and stop writing books on the subject?
Think of all the trees sacrificed to make the paper !