Systems and badminton at the Olympics

Systems don’t have to be very complex to demonstrate unusual behaviours. The badminton tournament at the Olympic Games has thrown up an interesting example.

Eight players (from China, Indonesia and South Korea) in the women’s doubles tournament have been disqualified for “not using one’s best efforts to win”. Most of the sporting and press comment of this issue has focused on the behaviour of the players. For example, the Chinese Olympic Committee said that it opposed behaviour which violated “sporting spirit and morality”. It’s difficult to disagree with such sentiments. However, the design of the tournament is equally at fault.

The badminton tournament has been designed as a round-robin/league stage followed by a knock-out stage. Two teams from each league qualify for the knock-out stage, and the draw for the knock-out stage is predetermined based on performance in the league stage. This arrangement means that there are very predictable situations where, towards the end of the league stage, it can be in the interest of one or more teams to lose a match in order avoid a particular team in the knock-out stage. The design of the tournament provides a perverse incentive. The best way to do well in the tournament is to lose a particular match.

There are at least four ways by which the administrators who designed the tournament could have avoided, or at least minimised, these perverse incentives:

• A purely knock-out tournament
• A league stage from which only the winner of each league qualifies for the knock-out stage
• A league stage from which two teams from each league qualify for the knock-out stage, but where the draw for the knock-out stage does not take place until after the end of the league stage
• A league stage from which two teams from each league qualify for the knock-out stage, but where related matches in each league are played at the same time.

In placing all of the blame on the players, the administrators are ignoring their own tournament design. The administrators set the rules but do not appear to have thought about their implications. It is not as if problems with this type of tournament design are unknown. Similar situations have arisen in international football tournaments, while, in tennis, the ATP experimented with round-robin tournament designs before abandoning them (and here) except in the season-end championships.

One of the hard and fast principles of human systems is that smart people will always seek to exploit the rules of any system. As a result, the designers of any human system should try to anticipate likely scenarios and build in rules to avoid “unfair” exploitation. When administrators point to violations of “sporting spirit and morality”, they are avoiding taking any responsibility for their own tournament design.

Of course, sporting administrators are not the only people who fail to take responsibility for their designs. When politicians design taxation and benefit systems which create multiple loopholes and perverse incentives, they also fail to take responsibility for their designs when people exploit the loopholes and follow the perverse incentives. As with the sporting administrators, they blame the morals of those who bend the rules rather than their own failure to anticipate such behaviour in their system designs. At best, all of these people are naive system designers.

Is the solar system stable?

In an introductory post, I wrote about Henri Poincaré’s attempts to model the behaviour of three bodies orbiting each other. He found that the mathematics of this problem showed that the behaviour of such a system was complex and could become unstable.

As the solar system is made up of a lot more than three bodies (one sun, eight planets, several moons, and many smaller bodies), the obvious question arising from Poincaré’s work is to ask whether the solar system is stable. Indeed, this question seems to have been one of the drivers of Poincaré’s work.

Ian Stewart has written a fascinating article which attempts to answer this question. The short answer is ‘probably not’. Luckily, the timescales involved are unlikely to worry us.

The article doesn’t require any prior knowledge of astronomy but it does use a few specialist terms such as Hohmann transfer orbits, Trojan points and Lagrange points.

Metronomes, people and starlings

The essence of a complex system is the interaction between its component parts. The fascination of a complex system is that apparently simple interactions can produce unexpected behaviours. Here are three examples featuring, in turn, metronomes, people and starlings.

When several metronomes are set up on a single moveable surface, such as a board on two rollers, and when they are set in out-of-phase motion, they will gradually synchronise with each other. This process is called entrainment. The scientific explanation is that the metronomes interact with each other through small vibrations in the moveable surface.

The Nobel prize-winning economist Thomas Schelling asked himself why racial segregation occurs in human populations. He could equally have asked about segregation based on nationality, caste, religion, ideology or any of the many other ways in which people identify themselves. He carried out an experiment using counters on a chess board and saw that, even with a very mild preference for the colour of a neighbouring counter, the ‘society’ of counters segregated fully into black and white. Even though individuals are rational and fairly tolerant, the societies we produce together may be neither rational nor tolerant.

Flocks of birds and shoals of fish often move in unison to create complex and beautiful patterns without any leadership and without any obvious rationale. For example, scientists have studied the behaviour of murmurations of starlings. Explanations (pdf) (and here) of their collective behaviour suggest that it may help protect the birds from predators.

Watch demonstrations of each of these three phenomena after the jump.

Franklin’s Gambit and political decision making

John Kay has written an excellent article on decision making in business and politics. His main point, which he refers to as Franklin’s Gambit, is that, even when we appear to follow a rational process for making a decision, we are often looking merely to justify a decision we have made already.

A typical rational decision-making process would be:

1. Scope problem
2. Decide options for solving problem
3. Decide evaluation criteria and relative weightings of these criteria
4. Establish facts
5. Evaluate options based on facts, criteria and weightings
6. Make decision.

In fact, what can often happen is:

1. Scope problem
2. Make decision
3. Decide options for solving problem
4. Establish facts
5. Decide evaluation criteria and weightings which support decision made in step 2
6. Evaluate options based on facts, criteria and weightings
7. Confirm decision made in step 2.

In particular, the weightings of evaluation criteria are always subjective, so they can be chosen, or adjusted after the fact, to produce any desired outcome.

The Civil Service prides itself in its neutrality, and I have worked with many Civil Servants with impeccable ethics. They produce rational reports to support government decisions. Nevertheless, the conclusions of these reports almost invariably support the ideology of the government of the day, and, when the government changes, the conclusions change as well.

In business decision making, reports have an uncanny ability to reflect the views of the Chief Executive and other senior managers. On-message reports can result in promotion. Off-message reports can end careers.

In personal decision making, we often interpret new facts as confirmation of an existing bias. This extends from major decisions through to the trivial. For example,

• When we cast a vote in an important election, we may choose the candidate with the same background or ideology as ourselves irrespective of the merits of the debate during the election campaign. Alternatively, we persuade ourselves that the candidate who offers us the biggest cut in taxes, or increase in benefits, or the ability to buy our council house at a knock-down price, has the best policies for the broader community
• When a player from our favourite football team dives in the penalty area, we see an obvious penalty. However, when a player from an opposing team dives in the same situation, we see a cheat.

We exhibit this type of behaviour in making even routine decisions, so what happens when we have to make an important decision relating to a complex system which we don’t fully understand, such as the climate or the economy?

A 2011 report (pdf) shows that there is a strong correlation between views on climate change and political ideology. If significant future man-made climate change could be proven beyond doubt, we might require expensive new government interventions and many new regulations on private sector businesses. Of course, it is not possible to prove, beyond doubt, the extent to which the climate will change over the next 50 or 100 years. Neither is it possible to prove, beyond doubt, the impact of specific changes in human behaviour. As a result, people on the right of politics, who don’t like the political implications, are mostly sceptical of climate change, while people on the left, who are more comfortable with the implications, tend to be believers.

Correspondingly, in economics, politicians on the right have decided that the solution to the current economic crisis is for government to spend less, while politicians on the left have decided that the solution is for government to spend more. Despite the fact that economists provide conflicting advice on both the causes of, and solutions to, the crisis, the political left and right agree on two things:

• The correct policies are clear and beyond doubt
• The correct policies are the ones which are consistent with their existing ideological beliefs.

The most interesting aspect of this is that there are at least two conflicting aspects of any solution to the economic crisis: the need to create jobs and the need to reduce debt. Policies to create jobs include increasing government spending to provide a stimulus to the economy, and reducing taxes to encourage entrepreneurs and to stimulate demand. Policies to reduce debt include decreasing government spending and increasing taxes. The policies required to solve one of these problems are the opposite of those required to solve the other. Solving both problems at the same time is anything but clear and beyond doubt.

As a result, both left and right justify their policies mostly by pointing out the flaws in their opponents’ policies:

• The right says that the left prioritises jobs over debt. Increasing government spending in the hope of creating jobs will increase the debt further. This will lead to disaster. Look at Greece!
• The left says that the right prioritises debt over jobs. Reducing government spending in the hope of reducing the debt will increase unemployment further. This will increase the level of unemployment benefit payments, so might not even reduce the debt (or the annual deficit). Austerity leads to more austerity!

Both sides argue convincingly that their opponents’ policies won’t work, so their own policies are the best ones. This is false logic. It doesn’t occur to either ideological wing that they may both be correct in assessing that their opponents’ policies won’t work, and that we may be facing a Sophie’s Choice where there are no good outcomes.

Richard Feynman would point out that a search for the truth, in the face of complex systems which we don’t fully understand, should involve both humility and doubt. These qualities appear to be entirely absent in our politicians and their ideologies.

More on economics models

When you are trying to diagnose and cure a problem in a business or a government organisation, business models are extremely useful. There are all sorts of ways of modelling a business. However, they can be divided into two main classes: top-down models and bottom-up models. Top-down models aim to give a management perspective on a problem while bottom-up models give a shop-floor perspective.

Economists use a similar distinction between top-down macroeconomic models and bottom-up microeconomic models. A key issue in both business analysis and economics is the relationship between the top-down and bottom-up models, and the level of consistency between them. Business analysts have debated these issues for many years, so what does business analysis have to contribute to the current modelling debates in economics?

Most people have no interest in, or experience with, either business models or economic models, so I’m going to use a more familiar set of models to make some relevant points, although I learned these lessons through developing business models.

Let’s start with a top-down view of the geography of the earth. Here is a photograph taken from Apollo 17. It’s known as the Blue Marble.

The Blue Marble

At this scale and perspective, we can see that the earth is round, and we can identify feature such as continents, the sea, the snow-covered poles and large areas of cloud. A second model, at a similar scale, might help us understand that the earth orbits the sun with its polar axis at an angle of around 23 degrees. This model would allow us to explain the seasons of the year.

When we change scale to look at the earth in greater detail, we move to atlases and maps. As these models show a round object on a flat surface, we need to use projections such as Mercator, Gall-Peters and Mollweide to produce these models. Projections distort the relative size and position of different objects on the earth. Different projections distort the earth in different ways. At this scale, and subject to the rules of any specific projection, we can use these models to see the relative size and positions of countries, and large features such as mountain ranges, large lakes and the biggest rivers.

When we change scale again to look at an individual country, the distortions of different projections become less pronounced, particularly for small countries. At this scale, we can use different maps to see more detail. For example, we might see geographical and political boundaries, towns and cities, and major road and rail networks. Even if we are unfamiliar with a country, we can ask interesting questions which can help expand our knowledge: why are the states in the north-east of the USA often small while the states elsewhere are much larger; why do some states have regular boundaries while others have jagged boundaries? If we are not familiar with the distortions in the map, we may misunderstand the picture we are viewing: is Alaska really an island off the south-west coast of Texas; and what happened to Canada and Mexico?

Map of US States

Finally, when we change scale again, we can use street maps to navigate around a single town or city. We can also use highly stylised maps to navigate tube and subway networks. In these latter maps, we may even lose a sense of the physical distance between stations. However, these maps are still useful in helping us to select the correct train line and to understand when we need to change from one line to another.

What general rules can we take from these geographical models which could also be applied to business and economic models?

General Modelling Rules

Rule	Description
1	Models can be developed at different scales and with different perspectives
2	All models are simplifications of reality
3	Models should be judged as useful rather than correct. Models which distort reality can still be useful as long as the reader understands the distortion and its limitations
4	It is vital that any model helps you answer specific questions. It is often better to develop several simple models, with different perspectives, to answer different questions. A model which helps you understand the seasons of the year may not help you find your way round the London tube network, and vice versa
5	It is essential to develop models which provide insights for the layman into the complexities associated with the questions he is asking, and into the answers to these questions. This does not preclude the use of expert-only models but such models cannot, and should not, be used to communicate with non-experts
6	A model presented as a diagram is normally easier for a layman to understand than an equivalent verbal description
7	Different people may need and expect to see the same situation from different scales and perspectives, so multiple models may be needed to communicate with different audiences
8	It is not always possible to develop top-down models simply by combining bottom-up models. You cannot tell that the world is round from a city street map.

In general, business analysts have recognised these characteristics in their use of models. Perhaps that’s because their customers hold them to account in providing useful answers to specific questions, and because they insist on models that reflect the facts as they understand them. In contrast, the debates in economics seems to focus more on the correctness and consistency of economic models rather than their usefulness in solving problems or in explaining problems and solutions to non-experts.

Paul Krugman and economics models

During my quest to understand the mental models used by economists, I came across a fascinating 20 year-old article by Paul Krugman. The article’s title is ‘How I Work’ and it outlines Krugman’s basic rules for conducting interesting research. The reason the article is fascinating to me is that it provides a rare insight into how a leading economist thinks about economics rather than merely what he thinks.

The article includes a number of interesting insights into Krugman’s background. For example, he makes the following observation about what distinguishes the way he thinks, and his attitude to models, from most other economists.

Most young economists today enter the field from the technical end. Originally intending a career in hard science or engineering, they slip down the scale into the most rigorous of the social sciences. The advantages of entering economics from that direction are obvious: one arrives already well trained in mathematics, one finds the concept of formal modeling natural. It is not, however, where I come from. My first love was history; I studied little math, picking up what I needed as I went along.

Paul Krugman

Economics and models

The development of mental models is one of the most important ways through which we make sense of the world around us. That’s true of everything from the earth orbiting the sun to the internal workings of a jet engine, and from the maps that help us navigate to our political systems. When we have good models, we call them scientific and, when we don’t, we think in terms of belief and ideology. When we share a common model, it is easy to debate how to improve the model, and when we don’t we tend to struggle to make any advances.

The image of the world around us, which we carry in our head, is just a model. Nobody in his head imagines all the world, government or country. He has only selected concepts, and relationships between them, and uses those to represent the real system.
Jay Wright Forrester

In order to work out what is wrong with economics, and economists, I wanted to understand the mental models that economists use to drive their thinking. What does the economy look like? Who are the main participants e.g. banks, businesses, households? How do they interact with each other?

When I looked for this type of insight, one of the first surprises I found was that economists seem to make little use of diagrams. Although this might seem trivial, it means that it is very difficult for a layman to envisage how economists picture the economy, why they expect a particular policy change to improve the economy, or how the view of one economist differs from that of another.

A picture is worth a thousand words, except in economics.
Jamie

A verbal description is the next best option. The economics profession set up the Institute for New Economic Thinking (INET) to promote novel ideas following the advent of the current economic crisis. It held an inaugural conference, attended by many of the world’s leading economists, in April 2010. At this conference, Joseph Stiglitz gave an excellent presentation (including 23 slides with, of course, no diagrams) where he discussed many of the limitations of the models and methodologies used by mainstream economists prior to the crisis. He also proposed some areas for research to improve these models. Here are just a few key points.

Stiglitz began by discussing some of the mainstream economic beliefs which had turned out to be wrong. One of these was incredible.

There is no such thing as a bubble.
The mainstream economics profession

Now, bubbles have been known since Tulip Mania in the 1630s, and the Internet bubble burst only a few years before the current crisis. As a result, this statement, on its own, seems to be sufficient evidence to discredit the entire mainstream economics profession.

Stiglitz then discussed some of the assumptions that mainstream economists use in their models. These include an assumption that all people are identical and can be modelled as a single representative agent, and a further assumption of rational expectations which suggests that the representative agent always behaves rationally and with perfect information on the state of the economy. Again, these statements seem to discredit the entire profession. As Stiglitz indicated, if there is a single representative agent then how do financial markets work e.g. who sells to whom, who lends to whom, how can bankruptcies happen, who causes a run on the stock market? Most importantly, these assumptions preclude the current crisis.

One of Stiglitz’s main overall points was that there is no possibility of interactions between agents in these models. He concluded that one of the biggest modelling challenges for the profession is the inclusion of various types of interaction. These include regulation and control interactions as well as the transactional interactions which drive markets.

One of my initial observations on this blog concerned double pendulums. A single pendulum is the equivalent of the economic vision of a rational agent with very predictable behaviour. A single pendulum has perfect information on the influence of gravity on its behaviour. However, when two pendulums interact, the resultant system can produce unpredictable and unstable behaviour. It seems that the vast majority of the economics profession is oblivious to this type of behaviour.

Taking these points together, the pre-crisis economics profession resembles a religious cult more than a group of professional experts investigating the behaviour of a complex system. At the very least, they come across as a closed community with limited ability to draw analogies, and inspiration, from similar fields of study such as meteorology. As a pseudo-scientific endeavour, pre-crisis mainstream economics resembles a modern equivalent of alchemy.