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…