Judgment in Seattle: A Theorem Goes on Trial

April 16, 2000


Demonstrators in Seattle protested hardships attributed to core World Trade Organization Policy---which, according to the author, has origins in a theorem of convex analysis.

James Case

It is rare indeed that a mathematical theorem becomes a political hot potato. Yet that is exactly what happened in Seattle, during the first week of December 1999. By disrupting an important meeting of the World Trade Organization, an unlikely assortment of demonstrators delayed the next round of international trade liberalization talks, probably by several years. They also forced reluctant news media to publicize a litany of ills attributed by the demonstrators to core WTO policy---key elements of which are predicated on a theorem of convex analysis.

The crowds in Seattle were asking their leaders---more or less as Tevye the milkman (and father figure in Fiddler on the Roof) once asked God---if it "would spoil some vast eternal plan" to grant a few modest wishes. Tevye dreamed of becoming a wealthy man. The protestors were seeking relief from increasingly onerous burdens: cheap foreign imports for apple growers; "dumping" by foreign producers for the steel industry; deforestation and pollution in the third world for environmentalists; the proliferation of slums, sweat shops, and child labor for human rights activists; job loss to countries in which worker exploitation is deemed a legitimate source of "competitiveness" for organized labor. Although the demonstrators clearly won the Battle of Seattle, they remain underdogs in the holy war of which it is part.

The crowds got two different answers to their question. From elected leaders came word that, although violence can never be condoned, the points made (and the harm sustained) by responsible protestors deserve every consideration. That left it to the news media to point out that the requested relief would amount to economic protection, and would spoil the very vastest and most eternal plan the world has ever known!

The media were referring, of course, to Adam Smith's plan for generating "that opulence which extends itself to the very lowest ranks of the people." Crusaders for open markets and (global) free trade honestly believe themselves to be making important strides toward that holiest of grails. They insist---despite considerable evidence to the contrary---that global free enterprise is in the process of ending the abject poverty that still grips a significant portion of the world's burgeoning population. Moreover, trade liberalization, trade expansion, and globalization are largely responsible for America's recent prosperity, including the 30 million new jobs created during the last ten years. Would the protestors care to stop all that?

The demonstrators, who might once have expected sympathetic press coverage, got little of it in 1999. Commentators accused them of sloth, greed, and---above all---ignorance. Even liberal reporters now seem to know, with Nobel laureate Milton Friedman [4], that "international free trade is in the best interest of the trading countries and the world." Almost every U.S. newspaper is steadfastly pro-NAFTA, pro-GATT, and pro-WTO. While The Wall Street Journal and The New York Times were accusing protestors of everything short of child abuse, The Economist ran a cover story on "the real losers from Seattle . . . the world's poor." Readers were urged to pity third-world residents denied a sweat shop to toil in and a slum to trudge home to late at night!

Understanding the Simple Logic of Free Trade
The World Trade Organization was formed in 1995, pursuant to agreements reached in Uruguay, during the final round of negotiations under the General Agreement on Tariffs and Trade (GATT). A cursory examination of the WTO Web site reveals that the organization has its headquarters in Geneva, and that no other international agency currently oversees the rules of international trade. Closer inspection reveals that the organization is unalterably opposed to all forms of "protectionism." Its reasons are explained in a brief titled "The Case for Open Markets," which, after a few inconclusive remarks linking expanded international trade with accelerated economic growth, introduces the relevant principle of economic theory---transformed by modern scholarship into a theorem of convex analysis---by means of the following anecdote:

Nobel laureate Paul Samuelson was once challenged by the mathematician Stanislaw Ulam to "name one proposition in all of the social sciences which is both true and non-trivial."

It took Samuelson several years to find the answer---comparative advantage.

"That it is logically true need not be argued before a mathematician; that it is not trivial is attested to by the thousands of important and intelligent men who have never been able to grasp the doctrine for themselves, or to believe it after it was explained to them."

Other accounts of the famous exchange tend to omit mention of the years that elapsed between challenge and response. Former Harvard economist Todd G. Buchholz [2] retells the story, describing the response as "immediate," Ulam as "an insolent natural scientist," and the principle of comparative advantage as "perhaps the most complex and counterintuitive principle [in the whole] of economics." He then proclaims it "the key to modern economic understanding," and ruefully concludes that because "few politicians . . . can follow the analysis . . . quotas, tariffs, and trade wars mar the world's economic history."

Buchholz's enthusiasm for a priori logic is nothing new in economics. The author of an article on free trade in the 1928 edition of the Encyclopaedia Britannica deplored the then recent "revival of protection that makes it impossible to secure a hearing for the coldly rational arguments for international free trade." More recently, 1986 Nobel laureate James Buchanan [1] found it "discouraging" that we "who do understand the simple logic of free trade have not been at all successful in disseminating our message." Initiates seem convinced that anyone who finds the "logic of free trade" unpersuasive has simply failed to understand it. If that obliges them to conclude that the crowds in Seattle were composed exclusively of village idiots, and that every protectionist is a dullard unable to "hack it" in the "new economy," then so be it.

Expert testimony concerning free trade typically ignores an important distinction. Theorems concerning circles, triangles, and other subsets of the Euclidean plane are indeed irrefutable. But theorems asserting that bumblebees can't fly, or that thrown baseballs can't curve in flight, are not. They may be true as they apply to particular models of a baseball or a bumblebee in flight, yet false as they apply to actual baseballs and actual bumblebees. Likewise, a theorem may be true as it applies to the "neoclassical model" of commercial interaction, yet false as it applies to actual commerce.

Ludwig von Mises, a co-founder (along with F. von Hayek) of the famous "neo-Austrian" school of economic thought, expressly denied the foregoing possibility. In a book published in 1949, he stated that "the ultimate yardstick of an economic theorem's correctness or incorrectness is solely reason unaided by experience" [3]. The "particular theorems" of his chosen discipline "are not open to any verification or falsification on the ground of experience." In other words, economic principles are theorems, and theorems are irrefutable. A child can complete the syllogism. His thesis is familiar to most trained economists and is taken seriously by surprisingly many. Samuelson [5] speaks not of irrefutable theorems, but of "eternal verities," although the effect before a Senate subcommittee or a gathering of reporters would be much the same.

The Principle of Comparative Advantage
What is this principle of comparative advantage? Is it really a theorem? If so, how plausible are the axioms from which it is deduced? Can a single theorem actually justify the policies---indeed the existence---of an organization like the WTO? Are the claims made for open markets and free trade to be taken seriously? Or does the doctrine of free trade survive on its propaganda value alone? It alone seems to justify the ongoing process of globalization, which one third-world delegate to the Seattle meeting characterized as "a game about corporate profits," in which "the world's wealthiest countries are setting about a process designed to enrich themselves" at the expense of increasingly resentful trading partners. How resplendent are the clothes worn by the Emperor Free Trade?

Apart from a few posters bearing slogans like "fair trade, not free trade," the crowds in Seattle seemed to bear the Emperor no ill will. While some observed that he wore no shirt or coat, and others that he lacked pants and shoes, there was an absence of small voices suggesting that in fact he had no clothes. It was not the common goals of U.S. and WTO policy---chiefly open markets and global free trade---that the crowds seemed to oppose. It was the means by which they are (allegedly) being realized. The demonstrators, many of whom were having trouble making mortgage payments and keeping families together, seemed to think that the desired ends would be better achieved more gradually and less disruptively.

To their credit, no branch of the open markets lobby made any effort to deny that the transition from an old to a new economy can be brutal. They merely wondered whether postponing the inevitable might not increase rather than decrease the pain and suffering for which the protestors blamed the WTO and---by implication---its core commitments to open markets, free trade, and the principle of comparative advantage.

The principle in question was first enunciated in 1817 by a former banker and member of parliament named David Ricardo (1772-1823). Born to a Jewish family active in the emerging European money markets, Ricardo abandoned formal education at the age of 14 to enter the family business. There he prospered, acquiring sufficient wealth to retire at the age of 42 to the life of a country squire. Though little known to the modern public, he is second to none in his reputation among economists.

The content of Ricardo's theorem can be expressed in terms of gross domestic product (GDP). It asserts, in its simplest form, that if two or more countries have already expanded their respective GDPs as far as possible under a given set of restraints on international trade, they can expand them still further by relaxing those restraints. Modern proofs draw on convex analysis and generalize, to a situation involving competition, the obvious fact that the maximum value of a function f(x) over a feasible set X can only increase as X expands. Ricardo's own (remarkably brief) explanation of the matter focused on the conditions that distinguish the ordinary case---in which the maximum value of f actually does increase as X expands---from the exceptional one, in which the maximum remains unchanged.

Perhaps the most remarkable (a.k.a. complex and counterintuitive) feature of Ricardo's principle is that it applies to any group of potential trading partners. It thus allays the not unnatural suspicion that wealthy, productive nations have little or nothing to gain from trade with poor ones.

David Ricardo, the first to advance (in 1817) the principle of comparative advantage.

Ricardo's original example involved the trade between England and Portugal in wine and wool. Because both goods could at the time be produced more cheaply (in fewer man hours) in Portugal than in England, the curious wondered what Portugal stood to gain from the trade. Ricardo's answer was that, where-as Portugal's advantage in wool production was slight, its advantage in wine was enormous. Hence, England could make it worth Portugal's while to produce more wine and less wool than Portuguese consumers really wanted; the desired balance would be restored through trade with England. Specialization and trade made it possible for each country to consume more of both goods.

Even though Portugal enjoyed an "absolute advantage" in the production of both wine and wool, England possessed an exploitable comparative advantage in wool. It can be shown that, with probability one, every nation possesses some such advantage. There can be too little trade, but never too much. That is what Buchholz---and no few others---call "the key to modern economic understanding"!

The Efficiency Principle
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Ricardo's theorem comes in strong and weak forms. The weaker ones, which apply only to productive potential, assert that almost any group of nations can increase the size of their individual economic pies by lowering barriers to trade between them. The stronger forms assert that they not only can but will. Passage from the weak to the strong form requires an extra hypothesis---that mankind's commercial nature abhors unrealized productive potential. Only the strong form strengthens the case for open markets and global free trade. Not surprisingly, the neoclassical model of commercial interaction includes an assertion of exactly the required sort. One leading text [6] describes it as follows:

Adam Smith discovered a remarkable property of a competitive market economy. Under perfect competition and with no market failures, markets will squeeze as many useful goods and services out of the available resources as possible. Smith's so-called "discovery" has come to be known as the "efficiency principle." Exceptions, though numerous, are seldom acknowledged in the rhetoric of open markets and free trade. There, any hint of competition is considered to be "perfect competition," and market failures---save perhaps those involving Microsoft---are dismissed as artifacts of a bygone era. Such rhetoric is seldom challenged in the media, which, as mentioned earlier, are increasingly controlled by proponents of open markets and (global) free trade.

Space limitations prohibit an in-depth review of the evidence for and against the efficiency principle. Yet its history is easily summarized. During the "classical" period, which ended sometime after 1850, it was deemed a self-evident truth. Later, during the "neoclassical" period, the appearance of Das Kapital caused even professional economists to temper their faith in competitive markets. Yet it was not until about 1930 that both the possibility and the desirability of supporting evidence were widely perceived. As a result, the efficiency principle remained---until after World War II---a completely unverified article of faith! Even now, evidentiary support is less than conclusive. Like evidence of the existence of God, it seems to persuade only those who never doubted the conclusion in the first place.

Seattle settled nothing! The proponents of open markets and global free trade will redouble their efforts to bring about future rounds of trade liberalization talks, although the next one probably can't begin for two or even three years. Opponents of further trade liberalization will again be portrayed as village idiots, unable to "follow the analysis."

Members of the mathematical community---acting alone or in concert---could render a useful service by reviewing the evidence (beginning with that concerning the critical efficiency principle) for and against open markets and global free trade. Their endorsement of the case in favor, should it be forthcoming, will add newsworthy gravitas to the establishment position. Or, should even a few mathematicians prove unable to "follow the analysis," the crowds in Seattle will have found a much needed ally.

References
[1] James Buchanan, Essays on the Political Economy, University of Hawaii Press, Honolulu, 1989, 52.
[2] Todd G. Buchholz, New Ideas From Dead Economists, Penguin Putnam, New York, 1999, 71.
[3] As quoted by J. Eatwell, M. Milgate, and P. Newman, eds., The Invisible Hand, W.W. Norton, New York, 1989, 102.
[4] Milton and Rose Friedman, Free to Choose, Harcourt Brace & Co., New York, 1980, 39.
[5] Paul A. Samuelson, Economics, Fourth Ed., McGraw-Hill, New York, 1958, 672.
[6] Paul A. Samuelson and W. Nordhaus, Economics, Sixteenth Ed., Irwin McGraw-Hill, New York, 1998, 29.

James Case is an independent consultant who lives in Baltimore, Maryland.


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