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Lawrence H. Summers: Farewell to Kenneth Arrow, a Gentle Genius of Economics.

My mother’s brother, the Nobel economist Kenneth Arrow, died this week at the age of 95. He was a dear man and a hero to me and many others. No one else I have ever known so embodied the scholarly life well lived.

I remember like yesterday the moment when Kenneth won the Nobel Prize in 1972. Paul Samuelson—another Nobel economist and, as it happens, also my uncle—hosted a party in his honor, to which I, then a sophomore at MIT, was invited. It was a festive if slightly nerdy occasion.

As the night wore on, Paul and Kenneth were standing in a corner discussing various theorems in mathematical economics. People started leaving. Paul’s wife was looking impatient. Kenneth’s wife, my aunt Selma, put her coat on, buttoned it and started pacing at the door. Kenneth raised something known as the maximum principle and the writings of the Russian mathematician Pontryagin. Paul began a story about the great British mathematical economist and philosopher Frank Ramsey. My ride depended on this conversation ending, so I watched alertly without understanding a word.

But I did understand this: There were two people in the room who had won Nobel Prizes. They were the two people who, after everyone else was exhausted and heading home, talked on and on into the evening about the subject they loved. I learned that night about my uncles—about their passion for ideas and about the importance and excitement of what scholars do.

Kenneth’s writings resolved age-old questions and opened up vast new areas for others to explore. He likely was the most important economic theorist of the second half of the 20th century.

Is there a voting system that can be relied on to distill the will of a group of people? Many mathematicians have theorems named after them. Arrow’s impossibility theorem regarding voting and combining preferences is the only theorem I know of that is named for an economist.

Drawing upon mathematical logic, it shows that there is no possible voting scheme that can consistently and sensibly reflect the preferences of a set of individuals with diverse views. Any scheme that could ever be invented will be at risk of perverse outcomes, where, for example, the choice between options A and B is affected by the presence or absence of option C; or where a vote switch by one person toward option A makes it less likely to prevail. Mathematical and abstruse it was. But it also explained why committees have so much trouble coming to consistent conclusions and why, with an increasingly polarized electorate, democracy can become increasingly dysfunctional.

Economists have been drawn to Adam Smith’s idea of the “invisible hand” for hundreds of years. But until Kenneth drew on the techniques of topology (that is, the study of geometric properties and spatial relations), no one had ever been able to establish precise conditions under which there would be prices that would clear all markets, or under which one could assume that the market outcome was optimal. Writing in the early 1950s, he clarified the very specific conditions under which market outcomes were for the best and, of equal importance, the far more general conditions under which public interventions in markets had the potential to make things better.

For the rest of his life, Kenneth explored these conditions, writing articles on topics ranging from health insurance to public investment policy to economic growth to the limits of organizations. It is hard to imagine what economics would be like today without his contributions.

I saw him every Thanksgiving for the past 49 years with the extended family that he loved. In a family of professors, the conversation ranged widely. Save for the NFL, there was no topic—from politics to music, from classics to physics—on which Kenneth was not infinitely curious and apparently omniscient.

Kenneth knew more about everything than most know about anything, but he never flaunted his intelligence. It was another lesson for me when, many years ago, a paper was published correcting a famous analysis published by one of Kenneth’s teachers. At the time, it created a stir. I asked him what he thought. He said quietly that he had known of the error for decades, but such was his respect for his teacher that he did not publish his insight.


Rest in peace, gentle genius.

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