How can mathematics help create a better world?

They say a truly talented individual is gifted in more ways than one. And, when you’re listening to the gentle sound of the clarinet, played by Eric Maskin, Professor of Economics at Harvard, it’s not hard to believe that statement. Born into a musical family, Maskin played music from a young age, but it’s not his musical talent that he’s famed for. In his twenties, Maskin wrote an article that formalized the field of mechanism design in economics. This article, recognized by the Nobel Committee in 2007, was inspired by the work of Maskin’s friend and co-laureate Leo Hurwicz, and it set up conditions under which mechanism design theory can be used to achieve social goals.

Eric S. Maskin

Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel, 2007

At a glance

Born: 1950, New York City, New York, USA

Field: Microeconomics

Prize-winning work: The foundations of mechanism design theory

Peculiar dwelling: Maskin lived in the Princeton home of Albert Einstein (his childhood hero) for 12 years

What he sees himself as: A composer in mathematics

Rules of research: Only dealing with interesting questions, working on several projects at once, collaboration

Improving the world with mechanism design

Mathematics and social awareness, classical music and jazz piano: these are just some of the passions that define who Maskin is and what he does.

"For me, harmony is taking different parts, different lines of music, of economics, of anything, and putting them together in such a way that makes them seem like they belong together. Harmonizing is making many parts into a unified whole."

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Maskin uses a similar approach to his research on mechanism design. He takes different interests and mixes them together to create valuable ideas that enrich our world.

Mechanism design, it seemed to me, could help improve the world and affect many people’s lives," he notes, thoughtfully. "So I thought that was a great combination, the best of two worlds: the mathematical world and the social world.

The problem with relative-majority elections

For Maskin, the world has been in need of a helping hand for quite some time. Economics could, for example, emphasize how our electoral systems might not really be democratic. He cites the 2003 US presidential election, the outcome of which was determined by the state of Florida. There were three names on the ballot: George W. Bush, Al Gore and Ralph Nader. Of the three candidates Bush won the most votes, but evidence suggests that had Nader’s name not been on the ballot, there would have been a different outcome. “If it had been a head to head contest, Gore would have won quite easily", Maskin asserts. "What you should do is to allow voters to rank candidates, as this would be more likely to lead to a 'true majority winner'."

"As I went to college in the late 60s and early 70s, it was a time of considerable political and social unrest. I think it was pressed on us all that we had an obligation to think not only about our careers but also about important issues facing the world. I realized that economics was one way of doing that.

Getting the outcomes you want

When he was majoring in mathematics at Harvard, Maskin happened to take his first undergraduate class in economics, where he studied under Nobel laureate Kenneth Arrow. It was in there that Maskin learned about mechanism design, the engineering aspect of economics: there’s a goal you’d like to reach and a mechanism in place to help you reach it. "It’s actually reversed engineering," Maskin explains, hardly hiding his excitement in illuminating the theory to a new audience. "We start with outcomes, we say these are the outcomes we would like to have, and then we work backwards, to figure out a mechanism or an institution, which will generate those outcomes."

Watching Maskin cook together with his wife brings this theory to life: he thinks of a goal he wants to accomplish and blends the ingredients together to achieve the result. Similar to recipes, the economist explains:

Mechanisms are the set of rules that participants might follow in order to determine an outcome. Each participant in the mechanism will, of course, be following their own rules and trying to achieve their own goals - which aren’t necessarily the same as the goals of the mechanism designer.

One of the biggest challenges in mechanism design is that the goal of the designer doesn’t always match the goals of the participants. For instance, while a government’s goal could be to reduce CO2 emissions, an electricity company’s goal might be profit maximization. To see whether it’s possible to achieve the designer’s goals through a mechanism, Maskin came up with a condition to test: monotonicity, often referred to as the Maskin Monotonicity. This is "a property of the mechanism designer’s goals and the connection of those goals to individual goals, which, if satisfied, means that you can find a mechanism. In fact," he suggests, "you could actually follow an algorithm, which would lead you to such a mechanism."

Which real world problems can be solved?

There are many situations where mechanism design can be applied to achieve a socially desirable outcome and solve pressing real-world problems. Maskin’s theory has relevance in everything from environmental policy, electoral systems and financial markets, and many more besides. On top of these theoretical potentials, Maskin has actually had the opportunity to implement his work, and three concrete examples outline the far-reaching implications of his ideas. Mechanical design was central in the design of decentralization and privatization mechanisms in Poland in the 90s; it allowed the Bank of Italy to reform the system of selling treasury bonds; and it helped the British government to develop restrictions on CO2 emissions for electricity-generating companies after it signed the Kyoto protocol.

"Mechanism design can be used whenever markets alone are not going to solve all your problems. Whenever markets need a push or a modification or a tweak, mechanism design is there to tell you what modifications to the pure market system might help," explains the economist.

Think of the problem of getting clean air. We can’t expect purely private markets to give us clean air. There is no place where we can go to buy clean air. Instead, you need the government to step in and limit the amount of pollution that electricity companies, people driving their cars, and all of the various polluters put into the atmosphere.

It’s the mechanism designer’s job to find the mechanisms, and the rules, that could be directed at the sources where reductions in pollution would be the cheapest and easiest to make. In other words, "You want to direct your pollution reduction to the polluters who are most-able to make those reductions," Maskin concludes. This means that a designer needs a mechanism that can distinguish multiple players in a system, low-level polluters from high-level polluters for example, and identify where changes and regulations can be most effective in their overall implementation.

What music and math have in common

Mathematical modeling is at the core of Maskin’s work. According to the laureate’s former student, Michael Kremer, Maskin’s work has an elegance to it. He makes different pieces "fit together in a coherent story or model, trying to achieve results that are as general as possible." And Maskin achieves this in an almost-artistic way by connecting the abstraction and beauty of math with concrete problems at hand.

The beauty Maskin sees and shows in math is also there in his music. "Both activities, music and math, are driven by aesthetic demands. Musicians are looking for the most beautiful succession of notes, and mathematicians are looking for the most beautiful formula. They are both quite abstract activities. Music, unlike visual art, has no direct connection with the physical world, it lives in its own world. And the same thing is true of mathematics. If there is life on other planets, you can bet that they probably have the same mathematics that we have. It’s not dependent on particular physical space." Maskin’s gentle face softens in expression more than usual, as he reflects on his two passions.

The simpler the model, the more beautiful it is.

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What does Maskin’s work mean for us?

"With the innovation and changes of the modern economy, mechanism design could become increasingly important for investors."

Paul Donovan 
Global Chief Economist
UBS Wealth Management

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