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Kenneth Arrow, Rest in Peace

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The Nobel Prize winning economist Kenneth Arrow died recently (February 21). Let us give his work some thought on his way out of this world.

Arrow was best known for the "Arrow Impossibility Theorem," a powerful and very influential argument that given certain assumptions and five (quite reasonable sounding) goals, there is no actual or possible system of voting that will work every time -- that will avoid violating one or more of those goals -- because the conditions themselves are incompatible.

Arrow accomplished this result, one regarded every since as foundational to social choice theory and welfare economics, in his Ph.D dissertation in 1950, when he was 31.

It might have been tempting to spend the rest of his scholarly career defending and expanding on the terrain of that theorem. But he left that work for others, and many others have stepped in, including Amartya Sen. Arrow moved on, and among much else helped Gerard Debreu develop a rigorous proof of the existence of a "general equilibrium," a key and much sought-after pillar of microeconomics. A general equilibrium is a model that involves a finite number of distinct but interrelated markets, in which each separate market can achieve its own particular equilibrium: its own market clearing price.

So long as there was no proof of the mathematical existence of a general equilibrium, there was the possibility that a market economic system was a perpetual motion machine, in which equilibrium in some respects can be achieved only at the expense of disequilibrium somewhere else. The Arrow-Debreu effect sets that spectre to rest.

Tim Harford, in The Undercover Economist, a wonderful survey of contemporary economics and its discontents, gave Arrow pride of place, as a man who scrambled the older thinking of fairness-versus-efficiency, which had seemingly reached a dead end.

I wonder, these days, what first comes to a philosopher's mind when someone doing a word association game says the word "arrow"? Is it Zeno? or Kenneth?

 


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