Octobre 23, 2012

The charm of ideology lies in its power to intoxicate the adoring crowds and free its priestly class to peacefully profit from their lies. No matter how much George Orwell exaggerated his celebrated caricature, sudden glimpses of reality occasionally reveal the verisimilitude of Newspeak.

When respected citizens with public office potential conflate liberty with licence and libertinism, they dragged down the republic below the decadent level of the monarchy it swept away. Has not Montesquieu assigned virtue to be the principle of democracy (1)? When capitalists confuse capitalism with a mania for monopoly, they tie the hidden hand which feeds our economy. Is not fair competition a condition of true capitalism?

Perhaps my indignation is naive. Cynics have long suspected fairness and virtue have been priced out of the market, so universal the demand, so meager the offer. Yet who would have thought central planning is on the ascendency in America? Who would have guessed such a publicly discredited practice would be privately honored among the cognoscenti with the newly announced Nobel Prize in economics?

Do not dismiss the winners as hopelessly irrelevant academics. "The practical application of Mr Roth's ideas has never been in doubt", a Financial Times editorial accurately reports (*). Do not imagine I am singling out an obscure feature of their works. The same editorial correctly summarizes the work of Mr Shapley, who, together with the late David Gale, showed "how to design a centralised system for allocating husbands and wives".

Do not pounce on the "whimsical" nature of the application which illustrates the Gale-Shapley algorithm (2). The tools pioneered by Llyod Shapley and Alvin Roth power real matching markets ranging from residency programs to paired kidney donations in the United States to job allocation in France and Turkey (3)(4). And please do not look down on matching markets as undeserving of the holy name of market. As instances of what I call value markets, they represent the future, despite the present dominance of price markets, where price subsumes all other characteristics.

On price markets no participant can complain as the right price maximizes the number of transactions. Sellers who asked for too high a price and buyers who offered too low a price are the only ones unfulfilled and they know why. No such luck on value markets, where participants express personal preferences based upon multiple attributes, including price or not as the case may be. As every potential transaction becomes a unique match, a serious issue arises as the market loses liquidity. On a marriage market, it can quickly lead to tragedy in the manner of Andromaque (5).

It is this issue that Shapley and Roth tackled successfully. They showed how, on a value market, the right process can also maximize the number of transactions in such a way that no participant can complain. Sure Orestes prefers Hermione who prefers Pyrrhus who prefers Andromache who prefers Hector who happens to be dead. But assume women get to pick first, Pyrrhus renounces violence and Orestes is Andromache's second choice and vice versa. With Shapley and Roth's blessing, Orestes weds Andromache and Pyrrhus Hermione and no living soul remains single.

Surely such a solution is far from perfect. Hermione aside, nobody got first choice. Yet nobody will break one's vows, as no other partner can be found to be both better and eager. In the winners' jargon explained by Chris Giles, this elusive and desirable quality is "a stable outcome [...], one in which [...] parties perceive no benefit from seeking a different match" (**). With no hope for a better lot, can anyone complain?

The case of Andromaque is the one which is academic. As soon as the number of market participants starts to rise and the selection criteria become more involved, the design of an algorithm to drive the process and the mathematical proof it is the right one become worth a Nobel prize.

Yet the price to pay to operate a value market in the way paved by the winners is rather high. In the best Stalinist tradition, all participants must declare their personal preferences to a central authority and await its benevolent and irrevocable decision. If I cast my comments in these words, it is to elicit in my readers what should be a most crucial concern. Is the decision truly benevolent, or is Newspeak involved?

It will surprise no one if I balked at the idea that privacy is sacrificed without due process. I do not doubt the market operators will explain they cannot do without our data and make the most extravagant promises to preserve it. But would not it be better if they did not need to promise anything at all, having been denied access to personal data in the first place? If markets are good, market organizers are no saints.

Still confidentiality is not an absolute good. If the result is worth it, who will complain? And precisely doesn't the process deliver an optimal set of stable matches? Moved by envy, as my proposal for decentralized paired-kidney donations has failed so far to win approval (6), am I implying the optimality guaranteed by the winners is tainted by some mathematical error? Not in the least and the science behind it can be verified by all (7).

Nevertheless and however strong and elegant the demonstration, its conclusions are no more valid in the real world than its hypotheses. Whenever those who spin ideology hides debatable premises behind the unassailability of the proof to set policy, they risk subjecting science and complicit scientists to the authority of a new religion. Should we so readily accept decisions derived from centralized planning run by an interested party?

Ask for one whether the stable solution thus set forth is unique. When it is not the case, Michel Balinski offers proof positive that some "optimal" results can be more "optimal" than others (4). Expect the authority managing the process to bias the latter to pick the "optimal" outcome it favors.

Ask also how stable is the input. The vagaries of the human heart is why the Financial Times called "whimsical" any attempt to manage a global marriage market via central planning. Input variability is in part responsible for the relative stagnation of communist economies. If paired-kidney donations attracted the thousands of participants it should serve nationwide in the US, would no unknown donor incompatibility, no new patient, no patient death occur before the "optimal" solution selected before hand had been fully carried out? If input is not frozen, output stability is a myth.

Now that they have been consecrated with a Nobel prize, much more thought must be given to value markets. Take the way participants declare personal preferences. Strict ranking of the opposite parties does not often reflect reality as most people work with acceptance thresholds. But why arbitrarily deny further selectivity to participants who found their threshold was too low? No value market can work without central rules but enforcing central rules is not the same as imposing central decisions under cover of mathematical "optimality".

We should not rush to dismantle existing implementations and demonize central planning on principle. But blame me if I prefer Abraham to Stalin.

Philippe Coueignoux

• (*) ... Practical approach secures Nobel Prize, by editorial (Financial Times) - October 16, 2012
• (**) . Economics prize goes to matching academics, by Chris Giles (Financial Times) - October 16, 2012
• (1) see The Spirit of the Laws on wikipedia
• (2) College Admissions and the Stability of Marriage, D. Gale and L.S. Shapley (The American Mathematical Monthly, Vol. 69, No. 1) - January 1962 pp. 9-15
• (3) Unless I am mistaken, Ecole Polytechnique used such a tool to allocate the jobs offered by the French government to the class which graduated in 1970
• (4) Les enjeux du recrutement, Michel Balinski (Pour La Science, No 288) - October 2001 pp. 64-70, listed in (7).
• (5) See Andromaque on wikipedia
• (6) to request more information about NOAM (Network for Organ Automated Matching), please send an email to the author
• (7) for a starter, I recommend this bibliography, if Harvard University maintains access to Alvin Roth's personal page now that he has moved to Stanford