Leo's Legacy

Mechanism Design
Decades ago, the late U of M economist Leo Hurwicz developed an abstract theory called "mechanism design." Just months before his death in June, he was honored with a Nobel Prize for the theory, which now shapes solutions to some of the world's most mind-boggling problems. But what on earth is it?
By Douglas Clement

leo.jpgOn December 10, 2007, the Nobel Prize committee assembled in Stockholm to present the 2007 award for economics to three American scholars. Two of them took the stage to accept their gold medallions. The third, University of Minnesota professor emeritus Leo Hurwicz, remained in Minneapolis.

It wasn't a protest, by any means, simply a recognition that international travel, especially for a worldly 90-year-old, is sometimes more burden than adventure. (And really - Sweden in December?) Staying home was also symbolic of the work for which Hurwicz was being recognized: Rules aren't immutable; changing them can result in better outcomes. The trick, mastered by Hurwicz, is in knowing how to change them.

So, also on December 10, Jonas Hafstrom, the Swedish ambassador to the United States, arrived at the Ted Mann Concert Hall at the University of Minnesota and presented the Nobel Prize in Economic Sciences to Leonid Hurwicz—who was surrounded by more friends and family than could ever have flown to Sweden.

A better outcome, by design.

Abstract but Applied

"Mechanism design" is the formal name of Hurwicz's theory. It is a field he invented a half-century ago and developed over subsequent decades. Today, mechanism design is as fundamental to modern economic thought as quantum theory is to physics, and in its mathematical density perhaps as difficult to understand.

But while the theory is complex and abstract, it is also intensely pragmatic, and finds light now in a wide range of applications—from the creation of better voting procedures, to improved provision of credit to farmers in Thailand, to carbon emissions markets that may help curb global warming. Thanks to mechanism design, medical schools design procedures to find residency matches, donated kidneys find their way to the best recipients, and electricity producers better supply their markets.

It's all due to theorems devised years ago in a small office in Heller Hall on the University's West Bank solely because Leo Hurwicz asked the question: "Why should we take existing institutions for granted?"

"The success of emissions trading is further proof that the private sector brings forth enormous creativity in solving social problems if we introduce a profit motive and a price signal." —Richard Sandor, U of M alumnus, founder of Chicago Climate Exchange

Easy as pie

"Mechanism design" is the idea that social, political and economic institutions (mechanisms) can be shaped (designed) to yield superior results.

"Whether one considers auctions, elections or the taxes we pay, our lives are governed by mechanisms which make collective decisions while attempting to take account of individual preferences,"wrote the Nobel Prize committee in explaining the economics behind the award. "Mechanism design can be described as the art of producing institutions that align individual incentives with overall social goals."

Consider this familiar example: Two people agree they want to divide a pie equitably. How can they achieve that "social" goal? By the rules of the optimal mechanism, known to us all since childhood:

  • One person divides the pie into two slices.
  • The other chooses the first slice.

Because the second person, out of self-interest, will likely choose the larger of the two slices, the first person has an incentive to cut the pie perfectly in half. The rules don't rely on either person being honest or altruistic. Rather, they harness the self-interest of each individual in such a way that the best possible outcome is achieved.

Rules for dividing a pie might seem child's play, but changing the variables quickly increases complexity. Increase the number of people or pies, make one person the pie's owner, introduce money or differing preferences or types of pie, and the rules—and the math—become much more difficult.

But what about the "invisible hand," Adam Smith's famous metaphor? A student of introductory economics learns that perfectly competitive markets harness the self-interest of individuals to achieve the best possible allocation of scarce resources. Doesn't that cut through the confusion?

Not quite, the Nobel committee observed. Although these ideal competitive markets do a remarkable job of satisfying people's preferences with maximum efficiency, "in practice," the committee said, "conditions are usually not ideal. Competition is not completely free, consumers are not perfectly informed ... [and people] may use their private information to further their own interests."

This is where Hurwicz offered Smith a helping hand, designing mechanisms for situations that are less than ideal.

"People are not angels"

When Hurwicz began research on mechanism design, he ignored the issue of whether people would obediently follow the rules he designed. "Whenever I was asked to present some of my work," he told an interviewer, "I would start by saying 'Of course, the incentive problem is very important, but I will assume that people are angels ....' At some point I decided that since I know people are not angels, perhaps I should not completely ignore the incentive aspect." And that, really, was his breakthrough. Rather than rely on co­ercion or unrealistic assumptions about human behavior, he would insist that mechanisms be "incentive-compatible," he said, "a system of rules designed in such a way that people would have an incentive to obey these rules."

"What Leo brought to the table was the insistence that any mechanism must be incentive-compatible," says V.V. Chari, professor of economics at the U of M. "That is, we cannot rely on individuals to act in some social interest. Instead we must expect them to act in their private interests. And given that, any mechanism must provide people with the incentives to take the right action at the right time. Leo developed that language and brought it to the forefront of economics."

Global warming

Perhaps the most global of all applications of Hurwicz's theory is climate change, the object of a mechanism designed by University economics alumnus Richard Sandor (Ph.D., 1967).

In a 1995 alumni profile, Sandor highlighted courses with Leo Hurwicz as among the most valuable he took as he worked toward his doctorate in economics, saying they provided "a rock-solid foundation" for his future work. That future included a professorship at University of California, Berkeley, and years as chief economist at the Chicago Board of Trade.

But today, Sandor is best known for creating markets for trading carbon emissions credits, a direct application of mechanism design. The social goal: Curb global warming by limiting the quantity of carbon released to the atmosphere. The mechanism: the Chicago Climate Exchange (CCX), a privately run exchange founded by Sandor in 2003.

CCX is like a Craigslist for carbon dioxide. Its paying members—corporations and government bodies—commit to voluntary emissions targets, and if they manage to beat their target—producing cars or cement or electricity without emitting as much carbon as expected—they can sell those carbon credits to members that have exceeded their target.

The United States has yet to enact mandatory carbon caps, but European governments have already done so, and firms like Ford Motor Co. have joined CCX because they see it as in their self-interest to anticipate federal or state carbon regulations. As Sandor testified to the U.S. Senate several years ago, "The success of emissions trading is further proof that the private sector brings forth enormous creativity in solving social problems if we introduce a profit motive and a price signal."

Private information

The Hurwicz theory also finds clear application in the government auctions that have flourished in recent years to sell public resources as tangible as timber and amorphous as radio frequencies.

When Hurwicz decided to deal with the fact that people aren't angels, he meant, in part, that we don't always speak the truth: We might not work as hard as we tell our bosses we will, we might tell a used car dealer that we can't spend more than $5,000 when our actual budget is twice that. This "private information"problem has been especially problematic when governments sell public resources because private buyers may understate the value they place on timber, for example, to get it at a bargain price.

Mechanism design theory has allowed economists to design better systems for selling public resources through auctions. "In the last 12 years or so, there has been a big push to move beyond theoretical mechanism design and bring it to bear in real markets," notes Peter Cramton, an economist at the University of Maryland. "The shift is to what I would term 'market design,' where economists play a big role in the design of actual market mechanisms. Applications include timber auctions, spectrum auctions. The electricity market is another big area."

"An auction is a particular mechanism and mechanism design has us thinking about what the incentives are for participation and bidding strategy and so on," Cramton says. "A big aspect of it is addressing the informational issues and trying to establish rules so there is better information conveyed in the bidders' bids."

Voting mechanisms

It might be crass to suggest that elections are the ultimate government auction, but mechanism design is also finding direct application in improving voting procedures.

"Often we have problems like finding a voting system that will have certain properties, and the techniques we use to figure out the answer to those problems are mechanism design," observes David Epstein, professor of political science at Columbia University. "The same theory used in economics to figure out a good auction mechanism is used in politics because voting is a type of mechanism. As we say, it's a way of allocating or producing results and you get different results depending on how people value the object in question. Here it's an election, not a spectrum to be auctioned off, but the idea is the same."

Epstein has studied how legislatures and courts can design political maps so that voters can achieve specified goals. "Do you want a political map to promote 'substantive representation' or 'descriptive representation'? That is, do you want to focus on the type of people that get elected or the type of outcomes that a legislature produces?"

Political scientists like Epstein help policymakers figure out what kinds of redistricting will further legislative goals. "In fact, the Supreme Court has a lot to do with that in the voting rights area," he notes. "They're going to lay down basic principles of redistricting and given those principles, the different states will implement them."

Of course, mechanism design isn't confined to U.S. voting systems. Roger Myerson, one of Hurwicz's Nobel co-recipients, has done recent work on how to structure voting that will promote democracy in Iraq. "Democracy doesn't come by edict," he told The New York Times last year, "but by institutions and mechanisms that ensure politicians must compete for the trust of the voters."

Epstein himself has applied mechanism design in international contexts, consulting with the World Bank. "These projects are on democratization and corruption, one of the oldest mechanism-design problems there is," he observes. "How do you design a government that is strong enough to make laws and enforce them, yet isn't so strong that it overruns individual freedom? You see applications of mechanism design all over in political economy."

From kidneys to credit

Indeed, once you start looking, mechanism design seems ubiquitous. The process of matching medical school students to hospital residencies used to be one of ultimate pressure and potential disasters. It's still stressful, but techniques derived from mechanism-design theory have rationalized the process considerably, achieving optimal matches between new doctors and the hospitals that need them. The same is true for kidney donations, where finding the right recipients for a particular organ donation has long been open to delay and mismatch. Here, too, mechanism design has smoothed the process by establishing rules of the game that are incentive-compatible and oriented toward optimal solutions.

The arcane formulas and abstract theory that constitute mechanism design even find relevance in the daily life of farmers in rural India and Thailand, where University of Chicago economist Robert Townsend conducts his research. For nearly two decades, Townsend (U of M Ph.D. 1975), has studied the work patterns, production methods and credit markets of Indian and Thai farmers and found that mechanism design theory is an incredibly fruitful way of understanding those economies.

In the Indian villages that Townsend studied, for example, small groups of farmers would cooperatively rent farm acreage from a landowner. Through careful data gathering and analysis, Townsend better understood how these farming arrangements actually worked. Would some farmers work less than others, pretending to be sick? If so, how would other farmers share the harvest? How was weather- risk shared between farmers and the landowner?

"We wanted to know if they shared risk within the village reasonably well or if dealing with incentives caused them to deviate from an optimal allocation," says Townsend.

He's studied similar situations in Thailand, as part of a 10-year research project to understand how microcredit—small loans given to farmers with varying arrangements for repayment—can be better structured.

"By writing down these explicit models in the tradition of mechanism design," notes Townsend, "you can back out implications for observables." That is, you can see how incentives and rules of the game resulted in observed outcomes. Then you can grasp what­ever problems are amenable to solution. "If it's an information problem, then potentially the [lender] might want to do a bit more monitoring to get more information about the borrower's actions. Or if it's a commitment problem [where borrowers don't repay loans], then the [lender] ought to think about more stringent penalties imposed on borrowers."

In both India and Thailand, Townsend's exhaustive research has applied the theory of mechanism design at the most basic level. "We've been gathering an enormous amount of data and found that these principles apply throughout," he says. "It's all been geared toward first, understanding how things actually work, and second, thinking about possible remedies."

Catching up

Had the contributions of Leo Hurwicz been recognized earlier, before he turned 90, he might have traveled to Stockholm for the award ceremony. But no one would suggest that the Minneapolis celebration was a lesser affair. By staying at home, he shared his honor with the people who surrounded him during the years spent creating and refining this seminal theory.

One of them, his son Maxim, shared these words at the gathering: "When Leo first started talking about mechanism design ... there was no immediate, concrete application for his theories. But these days we don't have to look far to see what Leo was imagining and trying to explain a half century ago ...."

It has just taken a few decades for the world to catch up.

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This page contains a single entry by CLA Reach Magazine published on February 13, 2009 10:04 AM.

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