Former UNESCO Professor of Maths and Economics at Columbia University selects five intriguing books on catastophic risks, making statistical decisions and reasoned gambling

Essays in the Theory of Risk-Bearing
by Kenneth J Arrow

5

Inequalities for Stochastic Processes
by Lester E Dubins and Leonard J Savage

Former UNESCO Professor of Maths and Economics at Columbia University selects five intriguing books on catastophic risks, making statistical decisions and reasoned gambling

Graciela Chichilnisky

Graciela Chichilnisky is the author of the carbon market of the Kyoto Protocol and of a new framework for evaluating catastrophic risks. She is a professor and director of Columbia Consortium for Risk Management at Columbia University, New York and a Managing Director of Global Thermostat Inc.

Your first book is Catastrophe: Risk and Response by Richard Posner.

This is a book by a Chicago judge where he tries to explain what catastrophes are, why they are important to us and what are the outstanding issues that we need to resolve about them. It is about tsunamis and super-volcanoes, major tornadoes and floods – rare events that have momentous consequences. It is pretty accessible, not really technical but analytical. What interests me about the book is that it prompted me to develop a whole new way of looking at catastrophic risks.
The book shows that in many ways we respond to catastrophic risks in what the author believes to be an irrational way. He is saying that for some reason we behave irrationally and we dismiss catastrophic risks because they are infrequent. But he doesn’t say why this is happening or what to do about it. This prompted me to explain why we dismiss them; why traditional ways of looking at risks do not work for catastrophic risks, and what to do about it.

And so how did you revise your ideas after reading this book?

Having read it I developed a special way of explaining my new framework for understanding catastrophic risks and managing them – which I had developed mathematically before. And I focused on this question of irrationality. Essentially I showed that Richard Posner calls humans irrational because our decisions don’t tally with the received wisdom. Traditionally we use expected losses as a way to measure and track risks; we essentially ‘weigh’ a risk by the probability of its occurrence.
For example, a ten per cent chance of your house burning is worth half as much as a risk involving a 20 per cent chance. We look at the probabilities and we say, ‘Aha, one is twice as likely as the other.’ We weigh losses by the probability of occurrence. Of course what happens with this approach is that when the event is very infrequent, and it happens once every 100 years, we dismiss it. He thinks that this is irrational. I believe that the old theory does not fit and that we need a new approach.

Y

our second book is linked to Posner’s: it is Optimal Statistical Decisions by DeGroot.

Yes, that book is essentially the mathematical foundation on which Posner’s book is based on. If you read this excellent book you can see why is it that we dismiss catastrophic risks, as Posner finds. DeGroot’s book lays out the whole mathematical foundations of Posner’s theory. And for me this was very interesting because I was able to trace directly the roots, the source of the problem. Why do we dismiss catastrophic risks in the conventional statistical analysis that is widely used today, even in US Congress? I was able to trace it to one axiom which comes out of DeGroot which has no real reason for its existence but we accept it because it makes mathematics simpler. Lo and behold, this axiom is the cause of our dismissal of catastrophic risks and the enormous losses that we could have avoided and we didn’t rely on it. It is called SP4.
For example, if we had not used DeGroot’s approach prior to the financial crisis, if instead of weighing down the results of the crisis and dividing by a hundred…things could have been better. We could have taken action. Reading these books together I started to realise why this is not the right approach. These two books fit together and they helped me pinpoint where the traditional theory went wrong and what had to be changed.

What about The Foundations of Statistics, by Leonard Savage?

This book is by a famous statistician who is now dead. Savage didn’t fall into the trap of DeGroot, who dismissed catastrophic risks. Instead he went to the other extreme. Savage’s approach can focus solely on rare events. So DeGroot underestimates rare events and Savage’s approach (which was very controversial at the time) can underestimate frequent events. That is no good either.

So why do you think he did that?

I don’t think he understood that there was anything else. I think that the classical theories were all like DeGroot’s. Savage saw their limitations and went the other way. But he didn’t understand that you can take both frequent and rare events seriously simultaneously. This is what my work does.

Considering that you are critical of his work, how has he helped you?

Savage has been very valuable in showing the importance of rare events because they are the moment of change when something totally unexpected happens. That is what you call change and what he was focused on. And that is what a catastrophe is – a rare event that has monumental consequences. So, based on these very important works, my work doesn’t fall into one or the other extremes. I don’t focus on frequent or on rare events. I integrate both.

The authors that you have mentioned are the pieces in the puzzle that fit together to form your new theory which you believe works?

That is right. It does work mathematically. It is unexpected that it should work, and I can understand why people shied away earlier from doing the statistics of change because you get treated like you are a sorcerer or a witch. I often joke that if I had lived 200 years ago I would have been tried as a witch and burned at the stake.
I started with something that wasn’t necessarily logical and did it in a free way without thinking about what my colleagues thought, which is a huge risk to take in academia. Freethinking is considered dangerous. What happened to Savage was really savage. He suffered a great deal of criticism.
As for me I have had some positive responses but don’t be fooled. I get very positive responses because people right now are starting to understand we had better open our eyes and do something differently since what we are doing isn’t working. We have run into New Orleans without preparation when we knew this could happen. We have run into a global financial crisis when we saw it coming. The only place that has recently got it right is the way that Chile prepared for 8.8 earthquakes, which, even though they don’t happen that often, are still a good thing to prepare for. As a result Chile sustained fewer losses than Haiti, who had a much smaller earthquake.
In general, as Posner says, we seem to be paralysed or deliberately ignore catastrophic risks.
The theory I developed is the idea that, even though DeGroot’s and Savage’s theories seem to be radically opposed, it is possible to put the two extremes together. I show they are part of the same universe and they can co-exist. Sometimes you are in one position and sometimes you are in the other. Our current experimental work in France and with the US Air Force shows that when you make a transition from a sequence of normal events to one that is catastrophic, people start oscillating widely with their decisions. It is almost like they become unpredictable. But they don’t, that is a normal reaction – it is rational and my work shows that. And this is not purely theoretical it is also experimentally tried. Experiments can’t prove a theory, they can only be consistent with a theory, or can disprove it. Our experiments sustain my theory.

Your next book is Essays in the Theory of Risk-Bearing by Kenneth Arrow.

This is a classic book. In both cases DeGroot and Arrow are rooted in the classic foundational work of John von Neumann. He was the first one who thought about weighing risk by the chances of occurrence. So you weigh a risk to be less important if it is less frequent.
DeGroot is doing statistics. What Arrow is doing is a parallel theory. Arrow develops decisions theory in the sense of looking at how you react to uncertainty. The book is about economic decisions and it is really simple and very focused. In that book I found another aha!
I found the Pandora’s box which produces the same result as I found in DeGroot. His is called SP4 and with Arrow it is an axiom called Monotone Continuity. Although those two look very different I proved they are the same. And by focusing on those I was able to explain to people why we have to do things differently and how to do it. My recent article The Topology of Fear explains all this.

Your final book is another book by Leonard Savage and also Lester Dubins, How to Gamble if You Must.

Yes, it doesn’t fit the sequence like my last books do but it is very interesting. Perhaps it is not as well known as it should be. It does something really simple and yet incredibly complicated. The book develops Savage’s idea in the context of gambling and says suppose that you need a certain amount of money by a certain date and you go to a casino to gamble. How should you play?
Imagine yourself at a casino with $1,000. For some reason you desperately need $10,000 by morning; anything less is worth nothing for your purpose. What ought you to do? How should you play? The only thing possible is to gamble away your last cent if need be in an attempt to reach the target sum of $10,000. The question is how to play, not whether.
The answer provided in this book may be surprising to many. Under the circumstances, an optimal strategy for you is to play boldly: that is, always to stake on each bet all the money in your possession or just enough to arrive immediately at the target sum in case you win the bet. It is ill advised, at a roulette table, to bet on more than one number at the same time.
What he shows is the strategy you should follow to get as safely as possible to the level of money you need. It is a matter of survival, strategies for survival.
Lester Dubins was a professor at UC Berkley when I was a student and did my PhD in mathematics. And he is now not well which is very sad. I tried to go and talk to him about my latest work but because he is ill it is very difficult. It is a great shame because I know he would have loved to talk through all my latest theories.

Five Books aims to keep its book recommendations and interviews up to date. If you are the interviewee and would like to update your choice of books (or even just what you say about them) please email us at editor@fivebooks.com

Five Books interviews are expensive to produce. If you've enjoyed this interview, please support us by donating a small amount, or by buying some of our most recommended books from Amazon. Since we are enrolled in their affiliate program, we receive a small percentage of any product you buy, at no extra cost to you.

Graciela Chichilnisky

Graciela Chichilnisky is the author of the carbon market of the Kyoto Protocol and of a new framework for evaluating catastrophic risks. She is a professor and director of Columbia Consortium for Risk Management at Columbia University, New York and a Managing Director of Global Thermostat Inc.