Skip to main content

Kenneth Arrow, Rest in Peace

Image result for kenneth j arrow

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?

 


Comments

Popular posts from this blog

A Story About Coleridge

This is a quote from a memoir by Dorothy Wordsworth, reflecting on a trip she took with two famous poets, her brother, William Wordsworth, and their similarly gifted companion, Samuel Taylor Coleridge.



We sat upon a bench, placed for the sake of one of these views, whence we looked down upon the waterfall, and over the open country ... A lady and gentleman, more expeditious tourists than ourselves, came to the spot; they left us at the seat, and we found them again at another station above the Falls. Coleridge, who is always good-natured enough to enter into conversation with anybody whom he meets in his way, began to talk with the gentleman, who observed that it was a majestic waterfall. Coleridge was delighted with the accuracy of the epithet, particularly as he had been settling in his own mind the precise meaning of the words grand, majestic, sublime, etc., and had discussed the subject with William at some length the day before. “Yes, sir,” says Coleridge, “it is a majestic wate…

Great Chain of Being

One of the points that Lovejoy makes in the book of that title I mentioned last week is the importance, in the Neo-Platonist conceptions and in the later development of the "chain of being" metaphor, of what he calls the principle of plenitude. This is the underlying notion that everything that can exist must exist, that creation would not be possible at all were it to leave gaps.

The value of this idea for a certain type of theodicy is clear enough.

This caused theological difficulties when these ideas were absorbed into Christianity.  I'll quote a bit of what Lovejoy has to say about those difficulties:

"For that conception, when taken over into Christianity, had to be accommodated to very different principles, drawn from other sources, which forbade its literal interpretation; to carry it through to what seemed to be its necessary implications was to be sure of falling into one theological pitfall or another."

The big pitfalls were: determinism on the on…

Philippa Gregory

My recent reading includes large helpings of Philippa Gregory's latest, THREE SISTERS, THREE QUEENS (2016), another of her fictionalized takes on love and betrayal among the royals of Renaissance Europe.

In this book, the focus is on the early Tudor dynasty, and especially on Margaret Tudor, the eldest daughter of Henry VII, founder thereof, and the older sister of the future Henry VIII. Margaret became Queen of Scotland with an arranged marriage to James IV. She reigned and ruled under the title of Dowager Queen after James' death at the Battle of Flodden in 1513.

So who, you ask, were the other two sisters of the novel's title? One is Margaret's blood sister, Mary Tudor, who was known as one of the great beauties of the age. Mary was the inspiration for the name her brother Henry gave to his older daughter. More important for Gregory's story, she wed the King of France (Louis XII) in 1514, and Anne Boleyn served as her maid of honor at that ceremony.

The third &…