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Kenneth Arrow, a founding father of modern economic theory, passed away this week. For ten years Ken and I co-directed the Jerusalem Ph.D. summer school in economics. The very many conversations we have had on economics, society and life have made me a different person.
Arrow’s most prominent contribution is known as the “Impossibility Theorem”, a contribution recognized as path-breaking in multiple disciplines. Advanced students in economics, political science, philosophy and computer science all get to study this theorem. It asserts that no voting procedure can be satisfactory, and that election outcomes can be irrational even when all voters are rational.
Arrow sets forth three desirable properties for voting procedures: 1) efficiency; 2) consistency; and 3) no-dictatorship. He then proves that no voting procedure will allow all three to coexist. If you maintain two of them, you will have to give up the third one. This brilliant but very frustrating result initiated a new research field in economics called “Social Choice”, aimed at discovering flaws in various voting procedures and proposing remedies. The “runoff” procedure that will be used in a few days in France to elect the president is susceptible to such a flaw: if one candidate becomes highly unpopular (as was indeed the case with Francois Fillon), the social ranking of all other candidates can be completely reversed. Yet the most important implication of the theorem is in explaining the difference between individuals and societies/nations. Individuals and nations are two very similar kinds of entities. Individuals have emotions and so do nations; they can both be compassionate or aggressive, prosperous or impoverished. Individuals make friends and enemies, and so do nations. Most importantly, both kinds of entities invoke reasoning to make decisions. Quite surprisingly, and in spite of the prominence that crowd wisdom has been receiving in recent years, when it gets to collective decisions - such as in politics—individuals are often wiser than the crowd. The electoral success of populism, from Brexit to Trump, is to a certain extent a manifestation of Ken’s Impossibility Theorem.
Ken Arrow used mathematical models to express ideas in almost every field of economics, but he was always explicit about the limitation of these models. Real life, he knew, is too complex for any of these to fully capture. To demonstrate the discrepancy between theory and practice, I recall Ken relating a story he was exposed to in his capacity as a mathematician working for the US air force during WWII.
In 1944, the military attached great importance to conquering the Pacific island of Saipan, about 2,000 miles from Tokyo. The direct conquest of the island was to be accomplished by landing Marine invasion forces, after a massive aerial bombardment by an elite Air Force unit. Dropping the necessary quantity of explosives would require, in turn, that every pilot in the unit conduct several bombing sorties. Each such sortie exposed the pilots to significant risks from antiaircraft gunners. Clearly, the more bombs loaded onto a plane, the more effective each sortie would be. Yet adding bombs also increased the risks to the pilots, as it limited the plane’s maneuverability in the face of enemy fire.
Army Air Force mathematicians were charged with the task of calculating the optimal way of getting the requested amount of ordnance dropped while minimizing the expected number of pilot fatalities. The dilemma was whether to conduct many low-risk sorties or a small number of high-risk ones. A bit of brainstorming led to a consensus: the optimal plan would be to conduct a lottery among the pilots, selecting a quarter of them. Each of those selected would then set out on one, and only one, sortie, with his plane loaded as heavily as possible with bombs. The remaining three-fourths of the pilots wouldn’t be needed, and would be relieved of duty. However, to enable the planes to get off the ground with that many bombs on board, the amount of fuel carried by each plane would only suffice for a one-way flight to the bombing target. This plan, which sent some pilots to their certain death, provided a survival rate of three quarters. Any other plan, so proved the mathematicians, would have a significantly lower survival rate.
Ken used this amazing story to argue that while traditional rationality analysis is important, it cannot stand by itself. Compassion and intellectual honesty led him to view this recommendation as wrong. Indeed, it has never been implemented.
Ken’s ingenuity amazed everyone who knew him. Even after he passed 90, his sharpness was phenomenal. In Ken's later years, he was often caught napping at seminars, but on waking up he would pose questions to the speaker which made it clear that he understood the lecture better than anyone else in the audience.
His death is a great loss for me. It is a great loss for us economists, and for humankind in general.
This piece by Eyal Winter appeared in Forbes on Feb 24, 2017
