Unrealistic Nobel economics
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Stable pairwise matching won Lloyd Shapley and Alvin Roth the Nobel prize for economics. It is an idea that is simple, slightly illuminating for economists, occasionally useful for everyone – and profoundly misleading.
The matches in question are between members of two groups, for example potential husbands and potential wives, or medical school graduates and hospitals that might employ them. The “stable” is defined narrowly: the pairing off is stable as long as no individual can find a way to improve his or her situation by trading partners. What counts as “improvement”? The game theory of Shapley and Roth does not really address that question.
The simple idea, demonstrated by Shapley a half century ago, is that under certain conditions a methodical process of elimination – many rounds of tentative pairings – leads to stability. Take a pool of equal numbers of would-be brides and grooms. The men keep on proposing to their favoured women. At first, only the irresistible men garner acceptances from the most appealing women. Gradually, though, each less attractive man will win the favour of some less attractive woman, who accepts the sad reality that she cannot do any better. At the end, while many people may wish they had a different spouse, no one will be able to arrange a trade. Any alternative pairing will be less desirable than the current one to one side or the other. That is exactly game theory stability.
The research is illuminating for economists because it teaches them that money is not needed to arrange an efficient allocation. Economists used to assume, and many still do, that cash markets are the best way to ensure that everyone is able to satisfy as many of his or her desires as possible. Shapley showed that in matching, under certain conditions and by some definitions, nothing more is needed than clear and consistent rankings of potential partners.
The illumination should be slight. Indeed, it probably takes a few years of economic training to be surprised that monetary values do not always lurk behind effective allocation decisions. After all, parents need neither game theory nor cash to divide a cake among the children. Money rarely plays a direct role in deciding who gets what in government programmes.
Roth showed that the Shapley technique is socially useful. He designed “clearinghouses” which have successfully matched doctors with hospitals, students with schools and kidney donors with recipients. The accomplishment is real, but limited. Roth’s clearinghouses require unusual conditions – not only consistent rankings of possible partners but also a single pairing decision, limited and basically equal information on both sides and the existence of alternatives which are fairly close substitutes.
Such clearinghouses are not suitable for most important allocation decisions. Marriages, for example, feature in Shapley’s original explanation of the technique, but few people would actually sign up for any sort of marriage clearinghouse. The choice of a life mate is too complicated to be trusted to an algorithm. In the West, the uncertainty of courtship is an integral part of the effort to create a bond that will be truly stable – able to last through thick and thin.
The unsuitability of a marriage clearinghouse hints at why the Nobel-winning idea is deeply misleading. It, like game theory as a whole, relies on four false assumptions about human nature.
First, satisfaction is defined in terms of preferences which may be arbitrary, unfair and temporary. That is dangerously simplistic. The hardest part of match-making is evaluating what the various candidates are really like and getting a good fit. Marriage match-makers, employment headhunters and university admissions officers earn their keep.
Second, game theory is individualistic, paying almost no attention to the social context of decisions. People, however, are profoundly social. Allocation shapes, and is shaped by, society. A serious study cannot simply ignore society’s needs and desires.
Third, the allocation games have no moral dimension. People are free to think about morality when they draw up their lists of favourites, but just as they are free to think about astrology. In reality, though, people should search for the truly good, and not merely for the pleasurable. In general, they do make an effort to be virtuous.
Finally, pairwise matching makes allocation into a non-monetary form of what economists call a market process: a collection of interactions between a large number of independent and fundamentally self-interested potential providers and users. In reality, such markets often make people uncomfortable. They prefer to decide on who gets what by co-operation, through committees or consensus, or by trusting some authority – whether a parent, a boss or a bureaucrat – to make just decisions.
There are times when it is helpful to treat life like a game. Shapley and Roth deserve thanks, and their prize, for showing how to design a good game. Life, however, should be taken more seriously.
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Perhaps we expect too much? “Stable pairwise matching” need not be the “be all, end all” to all questions in order to be worthy of a Nobel. The “journey of a thousand miles” still begins with a single step FORWARD. To such extent as “stable pairwise matching” brings about permanent decisions there is merit. Every “permanent decision” reduces the relative chaos of individual lives, and subsequent decisions become progressively easier. Each of us travel this path from puberty to old age, and the pace is not always smooth or easy.
While TEMPORARY satisfaction may seem simplistic, let’s look a bit harder at marriage. When marriage results in a lasting personal and mutual economic alliance of assets and purpose. Simply because in the United States more marriages end in divorce than a lifelong relationship, is that any reason to disregard the institution as a worthwhile goal for all to pursue as best possible. It’s successes infinitely strengthen our society, entirely independent from it’s failures.
“Human nature” is something twelve people will define twelve different ways. Each of us has a different “life experience” and “role models”. Our very perspective is unique due to differences in intelligence, education, experience, all of which form our individual expectations. It is NOT at all a “one size fits all” concept, but one that varies very much with time and circumstance. To presume otherwise is to be silly or disingenuious.
Society’s “needs and desires” change almost daily because our existence has largely met all legitimate needs and our desires are without limit or definition and frequently self-contradictory or unrealistic. The “moral dimension” is less and less determinative in today’s “life choices”. The “most serious” can be distracted by lint in their navel.
Life is a game all must play. Those who “win” are, more likely than not, those who invest the time and effort to fully understand the rules and employ such advantage so as to ultimately prevail. That’s a lot easier to describe than it is to accomplish.
I generally don’t like game theorists, because they have a philosophical view on life that I find scary.
In sum, they believe that the universe is finite, and thus the implicit idea of any gain is predicated on some loss somewhere else. Most generally don’t recognize nor believe that things can come from zero, void, emptiness and thin air.
Many game theorist followers thus believe that “Life is truly a finite game” to the point that they have no intention of trying to create things from zero. To some of them, in life you have to lie, cheat, scam, steal from others. That’s what life is. The problem is how to do it without getting caught.
The immoral ones put effort into learning the rules and find the flaws (because nothing is perfect) in order to “game the system”, “milk the system”. The ones with good guidance of morality on the other hand learn to avoid and try not to lose what they already have, minimizing potential loss.
Some people take it further with their fear of “survival of the fittest”. I disagree with “Survival of the fittest” on two counts. The first is “survival” and the second is “fittest”.
I believe that if everyone, every group, every country works together then EVERYONE can survive with some acceptable living standard. We don’t have to live in constant fear. We will work out technological and scientific methods to achieve that.
So “survival” should be “expansion” “growth”, and “fittest” be “productive”. Everyone will survive, but only the most productive INDIVIDUALS, the ones who can contribute the most, the “richest”, the ones with the most to offer, the ones who offer the most to OTHERS (whether it is strength, beauty, intelligence, etc..) should grow and expand.
“Growth of the most productive” is a much more humane, civilized yet logical idea.
Some people will scream and curse but the reality is that there is unlikely any system which can withstand “growth of the takers”
I personally believe that we should learn the “system” and how the world operates in order to fix, remove or at least limit the flaws in the system instead. We still have to try to get “better” knowing that we cannot get “perfect”, we have to improve the system.
Perhaps a good way to live is to constantly be on the look out for new things to come out from zero, for new ideas to come to our mind, new things so we can enrich and add into what we have hopefully without incurring a loss on others.
Signed
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- A game theory hater
Oops, the above comment was not meant to bash the Nobel winners this year. It is meant to criticize people who see “game” as unavoidable part, the truth of life.