Logic, Rationality and Common Sense (2)

Posted on June 10, 2017


What is rational behaviour? The mathematician Leonard Jimmy Savage tried to answer this question in his book on the Foundations of Statistics, first published in 1954.

Imagine a choice of possible lines of action in a situation that involves uncertainty. We do not know what the world is like. Depending on how the world will turn out to be, the various lines of action that we can take can meet with success or failure. Savage gives the example of a situation where we want to make an omelet. We have five eggs broken already in a big bowl. Question: “What to do with the sixth egg?” The table gives an overview of the various possibilities, of what we could do, and of what the effects could be.

act state
good rotten
break into bowl six-egg omelet no omelet
five good eggs destroyed
break into saucer six-egg omelet five-egg omelet
saucer to wash saucer to wash
throw away five-egg omelet five-egg omelet
one good egg destroyed

So given this, what should we do? According to Savage, this depends on how likely we think a given state of the situation is. If we are almost sure that the eggs we have bought are fresh, we can afford to make a six egg omelet by breaking all eggs directly in a big bowl. But if we suspect that an egg is bad, we better break it in a saucer to check. Disadvantage: saucer to wash. Advantage: risk of destroying five good eggs avoided. It was my own experience that the eggs I buy at Albert Heijn are always good. Some years ago, when I had to prepare mash for forty pancakes that I had to agreed to bake for the yearly Fancy Fair of my daughters’ primary school, I broke all my eggs in a big bowl. My last egg that day - or so I thought - was the thirtieth egg. It was rotten. The only rotten egg I ever bought at Albert Heijn. Also the most expensive egg I ever bought at Albert Heijn.

This way of looking at action under uncertainty can be used to understand grim situations in real life. Take the MH17 example, a war situation in the Donbass. You are the commander of a surface-to-air missile unit and you get the information that an aircraft is approaching, and is now within range of your battery. The question: “Shoot it down or not?”

action state
enemy military plane civilian airliner
shoot down enemy plane destroyed innocents get killed
major international incident
hold fire enemy plane escapes nothing happens

This analysis makes clear that the commander of the battery must have been out of touch with reality at the moment that he decided to fire his Buk missile. For had he considered that there was a real possibility that his rocket would hit a civilian airliner, then he would certainly have known that the outcome would be very bad, and he would have held his fire. The MH17 disaster was caused by a tragic mistake, we can be sure of that.

Actions can be seen as moves in a game that is played under uncertainty. If we know what is good for us and we know enough about our situation, then we know what is rational for us to do.

Rational decision making in a situation where we are aware of the various possible outcomes of our action and have a clear picture of the desirability of these outcomes, is a matter of deciding what risks of a possible bad outcome we are willing to take while aiming for a good outcome.

However, in real life the situation is often not so clear cut. There is a nice joke about a professor in decision theory who had written various books on the subject. Because he had made a name in the field, he received a tempting job offer from another university. What should he do? When he consulted a friend, she offered an obvious suggestion: “Why don’t you apply the theory of your own book?” His reply: “You do not understand. This is for real.”

This is funny, but the professor has a point. We often do not know what we desire, what is good or bad for us. A further illustration of this is a question I had planned to ask at the PhD thesis defense ceremony for Paolo Galeazzi, last January. Paolo had written an excellent thesis on evolutionary game theory, and I was a member of his thesis committee. The thesis tries to explain how rational action emerges when we see the decision making process as an evolutionary game, where rational players learn from the outcomes of each decision, and gradually learn how to play without regretting their moves afterward. Paolo assumes that these games are played with only partial knowledge of the situation we are in, but with full knowledge of our utilities. Utility is the game theorist’s way of encoding the desirability for each player of each outcome in the game.

Unfortunately, I wasted my questioning time at the defense on preliminary moves, so I wrote to Paolo afterwards to pose my real question. This has to to with something that happened to me just before I came to Amsterdam to take up the job at CWI I have held for the last 27 years, so it is about a situation of 27 years ago. At that time, I was in the process of selling my house in Cambridge. It was a house that I loved, with bay windows, lots of Victorian details, functioning fireplaces in all the rooms, and very conveniently situated in Emery Street, off Mill Road. 33 Emery Street, if you want to go and have a look.

One of viewers interested in the house was a particularly nice man. He told me that he loved the house, and that he was going to make me an offer. He just had to inquire with his bank what he could afford. Later the estate agent called me to say that the offer was made, 10 percent below the asking price. But the estate agent advised me to accept. I was quite pleased with the offer, and I liked the guy, so I told my estate agent that I accepted. The next day, my estate agent called me again. “Mister Van Eijck, I have good news for you. There is another ten thousand pounds for you to be made. I have a client here who is willing to pay the asking price.” “But I have given my word.” “Oh, that is not a real problem. There is nothing on paper yet, and according to British law nothing is binding until there is a written agreement.”

I wrote a blog post with the question I would have liked to ask Paolo: Can game theory give useful advice for my next move in this game? Here is Paolo’s reply, from an email he sent me:

About the house sale problem in Cambridge, game theory and decision theory would say to go for the higher offer I guess. Maybe more precisely, they would say that if you reject the new offer, it means that your word and promise has a weight in your utility function, and that it weights more than ten thousands pounds. I consider this a very good thing of course, because I like persons that I can trust, and I would have the same problem in that situation, but on the other hand it can be true that we might have evolved this high consideration for our words and promises in much smaller societies..

There is an obvious tension between the descriptive and the normative here. Does game and decision theory say how rational agents should behave, or does it describe how agents do in fact behave? Does game theory tell me I am stupid (irrational) if I do not go for the higher offer? Or does game theory construct my actual behaviour as rational in any case, by assuming that it reveals something about my utilities? The third person perspective on me, as someone who might have picked up strategies for behaviour that are disfunctional in a money-based globalized society, obviously jars with the views I hold about myself. The outside view that defines me as someone who has a consideration for words and promises that is more suitable for smaller societies restricts me. We are fortunate if we can transcend such limited beliefs about how we have evolved, how we have come to be by our history. Self-reflection gives us the power to jump out of any game that defines us. And that is wonderful.

Our actions in the world get their meaning from inside. My acting in the world reveals what my values are. Whether I value ten thousand pounds more than my given world or not says something about the person I aspire to be. Discovering and defining oneself through action is an often painful process, for it is our human fate that we have to act under partial ignorance. We do not know for sure how our acts will turn out. We can only learn to listen to an inner voice that guides us in such moments, if we are lucky. “To thine own self be true, and it will follow, as the night the day, thou canst not then be false to any man”, to quote Polonius’ advice in Shakespeare’s Hamlet.

Our acting in the world is a balancing act. We should try to follow Shakespeare’s advice, but we should also strive to stay attuned to reality.

This is difficult, for the truths that reality has in store for us may be hard to swallow. One extreme way to avoid any confrontation with reality is to deny that it exists, that is to say, to assert that reality is a social construct. To counter that, the following definition of reality is useful:

Reality is that which, when you stop believing in it, doesn’t go away. (Philip K. Dick)

Often it is more comfortable to close our eyes than to look reality in the face. But who has ever told us that the life well lived is a life of comfort?

Scientists have a special obligation here. As scientists we have been trained to distinguish false from true in areas where non-scientists have more trouble to see clearly. Areas that are crucial to all of us. Scientists understand - or should understand - the problems caused by exponential growth of our consumption of non-renewable resources better than non-scientists. This understanding creates an obligation. The obligation is to explain the implications of the following picture again and again. And to challenge, again and again, those that do not wish to see that exponential growth in a finite world is impossible.

Scientists are not used to speaking up, especially if they mainly live in their heads, or are obsessed with certainty. Also, the voice of science is often cynically perceived as a voice of self interest. The professors are marching for science because they are afraid to lose their very pleasant jobs. They want more money for science because they want to strengthen their already very comfortable positions in society. Obviously, the only way to combat this is by making it clear in our behaviour that there is much more at stake than our jobs. So there are things to be learned here. What we should learn is to re-establish the connection with non-scientists, with anyone who is willing to listen to us, really. We should also enter into a conversation with economists who write as if they believe in the possibility of exponential growth, although, deep down, they must know that what they write is nonsense. In computer science, if the execution time of your algorithm grows exponentially with the size of your input, that is bad news, and you had better design a better algorithm. Should be the same in economics, really.

Let me mention a few scientists that I admire for speaking up, for demonstrating to us what it means to be alive as a scientist and as a human being. David MacKay was a physicist, mathematician and engineer who was born in 1967. He died very young, in April 2016. He was professor of physics in Cambridge, but he decided to devote two years of his life to write a book for the non-specialist on the possibilities of and limitations to scaling up our use of renewable energy resources.

In the picture (taken from this Youtube video) you see him speak about the insane amounts of energy people in the West consume. David MacKay is holding a 40 watts lightbulb. In the UK (and also in the Netherlands, I presume) each of us keeps burning one hundred and twenty five of those all the time: that is how much energy each of us consumes, on average. In the US it is much more.

If you really want to get informed about what our options and difficulties are with the transition to renewable energy resources, you should read his book, freely available on internet:

Without Hot Air

This book, of which I have bought and given away many copies, is a true delight to read. I also think of it as a must read. MacKay starts by narrating what happened at the beginning of the industrial revolution, explains in detail at what rate the use of fossile energy has multiplied since then, gives an overview of the known reserves of fossile energy sources (handicapped by the fact that data about this are state secret in some of the oil and gas producing countries). The book discusses our options for saving energy, and gives an overview of various possible strategies for sustainable energy production. Everything very well informed, well argued, well documented and well illustrated, and written in an erudite, humourous, entertaining style. Only thing is, the conclusions of the book are not reassuring.

If reading the book is too much hard work for you, then maybe the above Youtube video or this Ted talk is an alternative. Here, MacKay explains in brief what our options are, and what are the difficulties with each of these options. Each of these options suffers from - to use MacKay’s words - a popularity problem. But the fact that all options have unattractive aspects does not mean that we are allowed to close our eyes for the facts. MacKay’s book, and his public lectures that you easily find on Youtube, are an appeal to us to face some inconvenient truths about our society’s dependence on abundant cheap energy. Here are some quotes to give you the flavour:

That is exactly right. Unfortunately, professor David MacKay died in April last year from cancer. This brilliant, gentle, witty, adorable man who was willing to put his scientific career on hold because he wanted to do something that he considered more important, unfortunately had to leave us before he was fifty years old. But he spent two of those years to figure out precisely what our energy situation is, because he was irritated by the uninformed claptrap (his words) he heard every day about sustainable energy. Let’s be thankful for the treasure trove of crucial information that MacKay left us, make good use of it, and try to keep it up-to-date. As far as I am concerned, his book should be required reading at all secondary schools. MacKay explains everything, including the how and why of the use of logarithmic scales in the many graphs of exponentially growing functions that illustrate the text.

There is a lot of nonsense being told about sustainable infinite growth. And uninformed people love to listen to it, because they want very much to believe in it. Energy has been dead cheap for about three hundred years, because we could extract it with relative ease from mother Earth in well-nigh unlimited amounts. We are now at the end of that period. For us three hundred years may seem a long time, but compared to ten thousand years of human civilisation and several hundred thousand years of presence of homo sapiens sapiens on the planet it is just the blink of an eye.

We are in a time of transition, and I admire scientists who go out of their way to make us aware of that fact. Scientists such as Marten Scheffer, who wrote a beautiful book about Critical Transitions in Nature and Society.

This book starts with examples of transitions in biology, lakes that suddenly turn from chrystal clear to limpid. Or systems that become unstable, and then start to oscillate between two states. Next, this is applied to transitions in society. It is clear that the author believes that our society is at a point of critical transition.

I share this belief with Marten Scheffer. Here is some literature from my student days that is still relevant today. A book that I love very much is Small is Beautiful, a rethinking of the foundations of economics, by E.F. Schumacher.

This book was first published in 1973, but it has lost none of its bite. It is a critique of mainstream economics that is even more relevant today than it was in the Nineteen Seventies. Schumacher insists that economics should make, but by and large neglects to make, a crucial distinction: that between renewable and non-renewable resources. Natural resources such as fossil fuels are not renewable, and at some point they will be depleted, but mainstream economics finds it convenient to ignore this absolutely crucial fact.

Here is another book from my student days, The Limits to Growth, the report of the Club of Rome, published in 1972, that was pioneering the use of computer simulation to get a clear picture of the consequences of exponential economic and demographic growth.

The theme of the book is an exploration of how exponential growth interacts with finite resources, that is to say, how exponential growth inevitably has to come to an end in a finite world.

You would expect scientists to amplify these voices of reason, by echoing every time they are in the limelight the ceterum censeo of Cato the Elder: “Furthermore, we remind you of the undeniable fact that exponential growth of economic activity is impossible in a finite world.” Alas, the public reaction of scientists to the huge many-sided crisis that human civilisation is facing now has by-and-large been the same as that of laymen: a lame mixture of ironic distance, denial, and resignation.

To create new science, head is crucial. But to speak up about stuff that we can see, stuff that really matters, head is not enough. We also need an open heart to be able to connect and communicate, and balls (for men) or clit (for women) to have the nerve to speak up in situations where the truth we have to speak is inconvenient. Or to express this in a more gender neutral way: what we need is head, heart and guts, all connected. Speaking up when it is inconvenient requires new skills. It requires no less than that we transform into complete, balanced, aware, courageous human beings.

(to be continued)