Trading kidneys, repugnant markets and stable marriages win the Nobel Prize in Economics

Roth and Shapley charted a course for economists to go beyond simply arguing for markets in everything.

The 2012 Nobel Prize in Economics - technically the Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel, but nobody cares - has been awarded to two American Economists, Alvin Roth and Lloyd Shapley "for the theory of stable allocations and the practice of market design". The Nobel Committee explains what that means:

This year's Prize concerns a central economic problem: how to match different agents as well as possible. For example, students have to be matched with schools, and donors of human organs with patients in need of a transplant. How can such matching be accomplished as efficiently as possible? What methods are beneficial to what groups? The prize rewards two scholars who have answered these questions on a journey from abstract theory on stable allocations to practical design of market institutions.

Lloyd Shapley used so-called cooperative game theory to study and compare different matching methods. A key issue is to ensure that a matching is stable in the sense that two agents cannot be found who would prefer each other over their current counterparts. Shapley and his colleagues derived specific methods – in particular, the so-called Gale-Shapley algorithm – that always ensure a stable matching. These methods also limit agents' motives for manipulating the matching process. Shapley was able to show how the specific design of a method may systematically benefit one or the other side of the market.

Alvin Roth recognized that Shapley's theoretical results could clarify the functioning of important markets in practice. In a series of empirical studies, Roth and his colleagues demonstrated that stability is the key to understanding the success of particular market institutions. Roth was later able to substantiate this conclusion in systematic laboratory experiments. He also helped redesign existing institutions for matching new doctors with hospitals, students with schools, and organ donors with patients. These reforms are all based on the Gale-Shapley algorithm, along with modifications that take into account specific circumstances and ethical restrictions, such as the preclusion of side payments.

Even though these two researchers worked independently of one another, the combination of Shapley's basic theory and Roth's empirical investigations, experiments and practical design has generated a flourishing field of research and improved the performance of many markets. This year's prize is awarded for an outstanding example of economic engineering.

The committee have yet again reaffirmed the old adage that the most important thing to do when trying for a nobel prize is to live long enough that your achievements are recognised. The Gale-Shapley algorithm, for instance, was devised in 1962, when Lloyd Shapley was 34. It concerns a maths problem known as the stable marriage problem: if you have an even number of men and women, can you always come up with a set of marriages where there are no two people of opposite sex who would both rather have each other than their current partners? (1960s maths problems: usually heteronormative.) If you can, then the marriage is "stable".

The Gale-Shapley algorithm is a way of always ensuring stable matches; and much of Shapley's work covers the same areas, straddling the boundaries between economics, mathematics, and computer science.

Roth is the younger of the two winners, and works in a far more empirical sphere. As the committee points out, although the two men never actually collaberated, Roth took Shapley's theoretical work and applied it to actually existing markets. For instance, Roth used the Gale-Shapley agorithm to ease the kidney shortage in the US. David Wessel explains (£):

As of noon yesterday, 58,470 people in the U.S. were waiting for a kidney transplant. Most won't get one this year. There aren't enough donated kidneys to go around. Surgeons transplanted just 15,129 kidneys last year. Now a band of transplant surgeons and economists are trying to fix that by creating a moneyless market for exchanging kidneys. Most transplanted kidneys come from a person who has died, a supply that grows slowly because of ignorance about the need for donations or grieving relatives' reluctance. But a kidney taken from a live donor works better, and almost everyone has a spare. As techniques improve for removing healthy kidneys and for suppressing the body's tendency to reject a transplant, doctors increasingly turn to kidneys from living donors, usually relatives. Last year, 43% of kidneys transplanted in the U.S. came from living donors, up from 28% a decade ago. But a biological barrier often blocks a transplant from a relative. In about a third of all would-be pairs, blood types are incompatible. In others, the sick person has antibodies that can initiate a rejection of the donated organ. It's heartbreaking "to have the treasure of the live donor and then have that not go forward because of a biological obstacle," says Massachusetts General Hospital transplant surgeon Francis DelMonico.

Occasionally, transplant centers spot a way out: One New England father with blood type A couldn't donate a kidney to his daughter with blood type B. So he gave a kidney to a teenager with blood type A, and the teenager's sister gave a kidney for the man's daughter. New England's transplant centers have done six such exchanges. Baltimore's Johns Hopkins University has done seven.

The crucial thing about Roth's work, from an economic point of view, is that it involves finding stable allocations using market-like situations without involving money. The kidney swaps in the New England situation are market-like, trading kidneys for kidneys in a way that makes all parties better-off, but they don't actually require kidneys to be bought and sold.

We can see the importance of this by looking at another paper of Roth's, not cited by the committee, on repugnance in markets (pdf). Roth demonstrates that some markets are limited because the very existance of a market in some goods is considered repugnant. He argues, for instance, that the trade in horse meat being banned in California is not done through fears that eating horse meat is unsafe; nor is it done for animal welfare reasons, since it is still legal to farm and kill horses. But banned it is, and Roth argues that the natural response of economists to situations of this type - to argue for freer markets - is wrong, since it ignores the very strong feelings involved in the situation. Instead:

Being aware of the sources of repugnance can only help make such discussions more productive, not least because it can help separate the issues that are fundamentally empirical—like the degree of crowding out of altruistic donations that might result from different incentive schemes compared to how much new supply might be produced—from areas of disagreement that are not primarily empirical.

Hopefully his new Nobel Prize should give that argument greater weight in the years ahead.

A patient receives a kidney in Johns Hopkins university in Baltimore. Photograph: Getty Images

Alex Hern is a technology reporter for the Guardian. He was formerly staff writer at the New Statesman. You should follow Alex on Twitter.

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Inside Big Ben: why the world’s most famous clock will soon lose its bong

Every now and then, even the most famous of clocks need a bit of care.

London is soon going to lose one of its most familiar sounds when the world-famous Big Ben falls silent for repairs. The “bonging” chimes that have marked the passing of time for Londoners since 1859 will fall silent for months beginning in 2017 as part of a three-year £29m conservation project.

Of course, “Big Ben” is the nickname of the Great Bell and the bell itself is not in bad shape – even though it does have a huge crack in it.

The bell weighs nearly 14 tonnes and it cracked in 1859 when it was first bonged with a hammer that was way too heavy.

The crack was never repaired. Instead the bell was rotated one eighth of a turn and a lighter (200kg) hammer was installed. The cracked bell has a characteristic sound which we have all grown to love.

Big Ben strikes. UK Parliament.

Instead, it is the Elizabeth Tower (1859) and the clock mechanism (1854), designed by Denison and Airy, that need attention.

Any building or machine needs regular maintenance – we paint our doors and windows when they need it and we repair or replace our cars quite routinely. It is convenient to choose a day when we’re out of the house to paint the doors, or when we don’t need the car to repair the brakes. But a clock just doesn’t stop – especially not a clock as iconic as the Great Clock at the Palace of Westminster.

Repairs to the tower are long overdue. There is corrosion damage to the cast iron roof and to the belfry structure which keeps the bells in place. There is water damage to the masonry and condensation problems will be addressed, too. There are plumbing and electrical works to be done for a lift to be installed in one of the ventilation shafts, toilet facilities and the fitting of low-energy lighting.

Marvel of engineering

The clock mechanism itself is remarkable. In its 162-year history it has only had one major breakdown. In 1976 the speed regulator for the chimes broke and the mechanism sped up to destruction. The resulting damage took months to repair.

The weights that drive the clock are, like the bells and hammers, unimaginably huge. The “drive train” that keeps the pendulum swinging and that turns the hands is driven by a weight of about 100kg. Two other weights that ring the bells are each over a tonne. If any of these weights falls out of control (as in the 1976 incident), they could do a lot of damage.

The pendulum suspension spring is especially critical because it holds up the huge pendulum bob which weighs 321kg. The swinging pendulum releases the “escapement” every two seconds which then turns the hands on the clock’s four faces. If you look very closely, you will see that the minute hand doesn’t move smoothly but it sits still most of the time, only moving on each tick by 1.5cm.

The pendulum swings back and forth 21,600 times a day. That’s nearly 8m times a year, bending the pendulum spring. Like any metal, it has the potential to suffer from fatigue. The pendulum needs to be lifted out of the clock so that the spring can be closely inspected.

The clock derives its remarkable accuracy in part from the temperature compensation which is built into the construction of the pendulum. This was yet another of John Harrison’s genius ideas (you probably know him from longitude fame). He came up with the solution of using metals of differing temperature expansion coefficient so that the pendulum doesn’t change in length as the temperature changes with the seasons.

In the Westminster clock, the pendulum shaft is made of concentric tubes of steel and zinc. A similar construction is described for the clock in Trinity College Cambridge and near perfect temperature compensation can be achieved. But zinc is a ductile metal and the tube deforms with time under the heavy load of the 321kg pendulum bob. This “creeping” will cause the temperature compensation to jam up and become less effective.

So stopping the clock will also be a good opportunity to dismantle the pendulum completely and to check that the zinc tube is sliding freely. This in itself is a few days' work.

What makes it tick

But the truly clever bit of this clock is the escapement. All clocks have one - it’s what makes the clock tick, quite literally. Denison developed his new gravity escapement especially for the Westminster clock. It decouples the driving force of the falling weight from the periodic force that maintains the motion of the pendulum. To this day, the best tower clocks in England use the gravity escapement leading to remarkable accuracy – better even than that of your quartz crystal wrist watch.

In Denison’s gravity escapement, the “tick” is the impact of the “legs” of the escapement colliding with hardened steel seats. Each collision causes microscopic damage which, accumulated over millions of collisions per year, causes wear and tear affecting the accuracy of the clock. It is impossible to inspect the escapement without stopping the clock. Part of the maintenance proposed during this stoppage is a thorough overhaul of the escapement and the other workings of the clock.

The Westminster clock is a remarkable icon for London and for England. For more than 150 years it has reminded us of each hour, tirelessly. That’s what I love about clocks – they seem to carry on without a fuss. But every now and then even the most famous of clocks need a bit of care. After this period of pampering, “Big Ben” ought to be set for another 100 or so years of trouble-free running.

The Conversation

Hugh Hunt is a Reader in Engineering Dynamics and Vibration at the University of Cambridge.

This article was originally published on The Conversation. Read the original article.