Broken Symmetry

Broken Symmetries and the Culture of the Ants

From Deborah M. Gordon:

Ants can show us how the rhythm of local interactions creates patterns in the behavior and development of large groups.

Via Teppo Felin at Orgtheory What Gordon suggests is that spatial and temporal periodicities could be used to coordinate (unconsciously) the behavior of groups of people. Isn't this what Thomas Schelling suggested decades ago? Why haven't economists (in particular) made more progress on these fronts? Here are my guesses:

1. The rational expectations model of group behavior is operationalized through revealed preferences, and tests of the model have been possible only through aggregate statistics like the CPI. (Maybe Google will have a hand in more fine-grained tests.)
2. Most economists never ask the why or how questions when it comes to preference formation. Take the Becker and Stigler classic as evidence.
3. (Most importantly) The data didn't exist at least until Csikszentmihalyi started handing out pagers for the ESM project in the 1980s.

One and two haven't changed.

Conor Clarke Interviews Thomas Schelling

At his Atlantic Correspondents blog:

I think rational expectations can lead to several alternative equilibrium situations, depending on what people choose to expect. If people expect the price of coffee to go up, they will make it go up. And if people expect the price of coffee to go down, it will go down. And the rational expectations model doesn't necessarily tell you what external ingredient beings to sway opinion in one direction or another.

Last year I wrote up a discussion of Schelling's classic explanation of how rationality is only a special case of symmetries in expectations here: Bounded Rationality or Broken Symmetry?

Creating My Own Create Your Own Economy

On Saturday, I received my hard copy of Tyler Cowen's latest work of popular economics, Create Your Own Economy: The Path To Prosperity in a Disordered World. Although a work of popular nonfiction, which read easily over the course of a few hours this weekend, this book is chock full of creative insights into what might be called an alternative economic vision of social life. I say "alternative" because until recently most academic economists had confined their interests to finance rather than culture, although Cowen is careful to trace the threads of Adam Smith, F.A. Hayek, and Thomas Schelling (among others) from which his unique vision is woven together. In the sense of developing this alternative vision, this book is actually the continuation of his last, Discover Your Inner Economist: Use Incentives to Fall in Love, Survive Your Next Meeting, and Motivate Your Dentist. In both books, Cowen assumes the point of view of individual consumers; his data is drawn from individual stories and experiences; his understanding of group behavior and consumption are correspondingly richer with local and temporary detail than most economic analyses of culture. Read in conjunction with Schelling's Micromotives and Macrobehavior and Robert H. Frank's The Economic Naturalist, one can see how the methodologies of Thomas Schelling are facilitating a gradual evolution in economic thought among his students and (thanks to their attention to the needs of non-economists), the public at large. All are recommended reading.

A central premise in Create Your Own Economy is that technology is fostering a more "autistic" lifestyle. Cowen envisions "autism" as a superior ability to filter out particular bits of information from the barrage of stimuli we experience in everyday life, to absorb those filtered bits, and to imbue those disparate bits with meaning by ordering and re-ordering them into a collage of our own creation. John Milton would be proud. It is part of Cowen's project in this book to encourage a more positive definition of autism, a definition that focuses on the cognitive strengths of people who might otherwise be called autistic only because of their inferior ability to communicate in traditional social settings. We might even call this "positive abnormal psychology." Although this aspect of the book is interesting, and is sure to get attention from both the autistic community and the community of psychologists and clinicians who specialize in working with people diagnosed with autism, my focus as reviewer will be on how this vision of culture could be seen through the lens of science. More specifically, I'm going to explain how Cowen's vision of a more creative economy fits with the systems theory that has been the theme of Broken Symmetry. I think it would give Prof. Cowen pleasure to see somebody using his own work as a source of information to be re-ordered within the particular mental framework I bring to bear on understanding economics and culture -- i.e., to see me creating my own Create Your Own Economy. So here's how this book fits within my interior world.

I see Cowen's book as premised on a particular epistemology of culture. Although that epistemology is not quite laid out systematically, what is clear from his unique vision of autism, Hayek's Sensory Order, and his pyramid diagram is that culture is embedded in the neural networks of individuals. For Cowen, economics and culture emerge organically from a process of filtering, absorbing, and reordering information. This is an appealing vision because it promises the possibility that someday economic theories might be understood in terms of biology. And Cowen mentions neuroeconomics in passing, but again Cowen's focus is on culture.

What is interesting is what Cowen does not say about these neural networks and their process of development. Cowen's emphasis is on the largely individualistic process of ordering information that flows into our neural networks. What he does not emphasize is the activity -- especially the social activity -- required to obtain desired bits of information and (perhaps more importantly) to decide what bits should be given privilege in our internal ordering.

For example, in his Chapter on the contrast between autism and Buddhism, Cowen's vision seems heavily weighted in favor of the autistic approach to interior life. On Cowen's view, educational institutions are mostly about using social influence to encourage non-austistic young people to develop more autistic habits. The trouble with this view is that it does not seem to leave enough room for the possibility that some learning and information processing may occur at the social level -- i.e., that some ordering of information cannot be done autistically.

In that vein, I find another theory of learning interesting. According to psychologist Mihalyi Csikszentmihalyi, learning is an individual process, but one that alternates between modes of openness and closedness to external feedback. There is potentially a deep scientific basis for Csikszentmihalyi's theory, which is drawn from the science of networks and self-organized criticality. Given the right balance of external stimuli and internal constraints, networks can self-organize into structures that optimize the flow of information. Optimal flow through networks was studied by Mandelbrot in connection with Zipf's Law. But today it is known that the same self-organized critical structure can be found in an incredibly diverse array of networks in nature, including neural networks and even our economy. In each case, the network structure emerges from an evolutionary process whereby particular network structures persist over time only so long as they can accommodate the stable or unstable variations in flow through the network.

This theory of flow is complementary with Cowen's vision of autistic culture. In particular, the closed mode of operating corresponds directly with Cowen's vision of autism. What seems to be missing from Cowen's vision is the other phase, the phase of extreme openness to feedback and diverse stimulus. (Is this what zen meditation is designed to facilitate?) Within the theory of autism presented by Cowen, it would seem that such openness would be difficult for autistics. Yet it would seem equally important to the creativity and learning characterized by Csikszentmihalyi as "flow."

But why is it so important to maintain balance between openness and closedness? By the end, what becomes clear is that Cowen envisions a radically different structure for society in which individuals cluster into small units -- perhaps even as small as one. And perhaps Cowen is right that this is where current technology is leading us. But can that kind of culture survive?

Robert H. Frank, also a student of Schelling, provides an answer in a recent NYT editorial titled, "The Invisible Hand, Trumped by Darwin?":

By calling our attention to the conflict between individual and group interest, Darwin has identified the rationale for much of the regulation we observe in modern societies... Ideas have consequences. The uncritical celebration of the invisible hand by Smith’s disciples has undermined regulatory efforts to reconcile conflicts between individual and collective interests in recent decades, causing considerable harm to us all. If, as Darwin suggested, many important aspects of life are graded on the curve, his insights may help us avoid stumbling down that grim path once again... The competitive forces that mold business behavior are like the forces of natural selection that molded elk. In each case, we see instances of socially benign conduct. But in neither can we safely presume that individual and social interests coincide.

Technology has enabled us to take finer and finer control over the flow of information and goods that we access as individuals. But over very long times, the benefits of finer control over flow have tended to accrue to the most well-organized groups rather than the most well-ordered individual minds. So perhaps the most dramatic impact of technology will be in how it enables us to be more social, even as autistics.

Letter Comment to the FTC on the Evolving IP Marketplace

Here are a few excerpts:

According to systems theory, innovation emerges from iterated cycles in which data, theory, and the people who collect data and form theory constitute feedback loops, which evolve over time. Each cycle manifests as the gathering and exchange of information among a network of experts who act as gatekeepers to a set of symbolic rules and procedures. Following the terminology of Mihaly Csikszentmihalyi, I call the network of experts a “field,” and the set of symbolic rules and procedures a “domain.” To give examples, topology, physical chemistry, and constitutional law are domains. Each of these domains is associated, respectively, with the fields of mathematicians who specialize in topology; academic and practicing physical chemists; and academics, practicing lawyers, and judges who work on constitutional law.

From the point of view of an economist, the most important difference between systems theory and neoclassical theory may be that systems theory permits for economic actors (the field) to have preference functions (the domain) that evolve over time. As a result, although neoclassical theory is still a useful model of economic activity when changes in preferences are small within the window of time in which economic activity is observed, more generally no stable equilibrium may be reached because preferences may change during the period of observation. In addition, because systems theory need not assume that economic actors know how their preferences have or will change over time, an assumption that actors will try to match their allocation of resources to their preferences can be called “rational” only in a weak sense. Under systems theory, whether an economic actor will engage in an activity of consumption, production, or exchange is a function of: (1) their history of preferences; (2) their history of consumption, production, and exchanges with others; and (3) the frequency of their exchanges with others. Whereas within neoclassical theory institutions are designed to promote allocative efficiency, within systems theory institutions are designed to promote the discovery of information about preferences, and thereby the synchronization and frequency-matching of consumption and production activities through exchange and cooperation.

For example, the systems theory makes explicit the spatial and temporal dynamics underlying the knowledge problem described by F.A. Hayek in “The Use of Knowledge in Society.” With the systems theory in mind, we can identify the function of markets with their facilitation of the exchange of information and coordination of economic activity independent of central planning. This is in stark contrast with neoclassical theory, which often identifies the function of markets with the maximization of aggregate utility based on an assumption of stable preferences — a function that cannot be carried out by a central planner beyond a small scale. The systems theory therefore identifies markets as a mechanism for rewarding information exchange and cooperation, thereby facilitating economic growth.

Download Letter Comment to FTC on the Evolving IP Marketplace (Final)

Nonpersonal Focal Points Promote Peace

From Giuliano Amato, professor of constitutional law at the University of Rome:

I believe that Carl Schmitt was right in saying that in politics there has to be an enemy. But does this enemy necessarily have to be the ‘other’, hence a political opponent or someone who is diverse? Could the enemy instead be hatred, intolerance and such issues, so that with such matters at stake the message sent through the media would be very different? One could say that this does not attract attention. This is not true. Political leaders have an undisputed advantage compared to anyone else. If they have something significant to say they obtain attention and visibility. Ordinary people can preach wonderful things without anyone paying any attention, while statements by national, regional and local political leaders become news, and not necessarily bad news.

Creative capitalism accounts for both money and time

What Adam Smith taught us is that cooperation is the source of endogenous growth within an economy.  Voluntary exchanges and divisions of labor literally create wealth within society.  When it's money rather than goods or services that are exchanged, residual income (i.e., profit) is an excellent proxy for cooperation and endogenous growth.  In fact, it's the best the world has ever known.

But several decades ago economist Thomas Schelling pointed out that rational self-interest alone would not determine when people cooperate.  Schelling sent game theorists (and economists, political scientists, sociologists -- okay, really all of us) out into the world to watch how people interact with each other, and develop new hypotheses about how and when people cooperate.

Schelling's exhortation has had profound consequences for us.  In effect, his theory of focal points has helped avoid many costly conflicts that would otherwise have resulted from plain-old, everyday misunderstandings and miscommunications.

It is puzzling therefore, that game theorists and economists have failed to move beyond where they were decades ago when Schelling gave them their task of identifying focal points.  But Schelling could have guessed that this would happen.  He knew that the reason that game theorists and economists had confused rational self-interest with symmetry was because symmetric problems were easier to solve.  Game theory and general equilibrium theory both assume time symmetry, an assumption that often fails, and always fails in describing growth.  It's not that game theorists and economists want their theory to be irrelevant to everyday experience.  It's that modeling human interactions is hard.

But some have pushed forward despite the difficulties.  Amartya Sen has been pushing a capabilities approach to economics, an approach intended to add dimensionality to the uni-dimensional measure of cooperation provided by profit.  The problem with this approach is that it is the uni-dimensionality of profit that has constituted cooperation.  By deconstructing profit, you may gain some understanding of the mechanism underlying any voluntary exchange; but without more it won't help you to increase cooperation.

If we stop what we're doing, go out into the world and watch how people are cooperating with each other, I believe another broad hypothesis about cooperation can be identified.  Specifically, it is beyond argument that the goal of profit must always be achieved through the means of a cycle of human activity.  Thus, both profit and time should be considered as independent variables in a measure of freedom or happiness.

Creative capitalism can stand for the idea of a capitalism that respects and promotes profit that is sustainable in view of the rhythms of life.  Both profit and time can be measured quantitatively.  By building institutions that measure and are accountable for how they handle both, we can build better institutions.

Bounded Rationality or Broken Symmetry? Revisiting Schelling.

Symmetries as Schelling Points

Game theorists know that games with symmetry in payoffs are easier to solve.  Appendix B of The Strategy of Conflict by Thomas Schelling is titled "For the Abandonment of Symmetry in Game Theory."  In this appendix, Schelling argues that

though symmetry is consistent with the rationality of the players, it cannot be demonstrated that asymmetry is inconsistent with their rationality (page 278)

In other words, symmetry is not a necessary condition to rationality.  But as Schelling documents in Appendix B, this truth was not clear to all game theorists.  In particular, Harsanyi referred to the symmetry axiom as the "fundamental postulate," and said that "the assumption underlying the axiom is that a rational bargainer will not expect a rational opponent to grant him larger concessions than he would make himself under similar conditions."

Schelling goes on to ask whether the symmetry postulate can be derived from rationality.  He concludes that it cannot.  Thus, he observes that

we must be careful not to make symmetry part of the definition of rationality; to do so would destroy the empirical relevance of the theory and simply make symmetry an independent axiom.

In other words, although we might want more than the assumption of rationality to predict the outcome of any game, we cannot rely on the symmetry postulate, which is violated by many empirical observations.  But then what, aside from the assumption of rationality, could be as fundamental?  Schelling does not give a direct answer.  Rather, he observes that

a theory of strategy ... is inherently empirical; it depends on how people coordinate their expectations.

From here he goes on to make his famous hypothesis that rational people will coordinate their behavior through focal points -- i.e., the most obvious answer known by prior experience to both people.  The theory of focal points resolves the paradox of symmetry and rationality by assuming that the Nash equilibrium will be the focal point for rational actors.  In other words, where obvious symmetries exist in payoffs, rational actors will tend to focus on those symmetries.

How Schelling Points Led to an Attack on the Rational Hypothesis

The explanatory value of focal points in understanding conflict and cooperation has led to advances in many fields of economics and politics.  Schelling later won a Nobel. 

Inevitably, the theory of focal points has pushed many economists and political scientists to undertake a more serious study of psychology.  If theories of strategy are inherently empirical afterall, then cognitive and behavioral limits must be important in determining focal points.

But somewhere along the way, some of the academics studying behavior forgot that the end goal was to observe and hypothesize focal points.  Their focus instead fell upon the hypothesis of rationality.  This isn't surprising given that the observed behavior of individual humans often seems to contradict the hypothesis of rationality.  The hypothesis of rationality is not a psychology; rather, it is a prediction about how, on average, large groups of people will behave over long periods of time.  It is thus an empirical hypothesis, not about individuals, but about groups -- very large groups, in fact.

Yet the attack on the hypothesis of rationality has been distracting for two reasons.  First, and less importantly, in many cases the attack on the rational hypothesis has led to a misunderstanding about what, exactly, the hypothesis of rationality hypothesizes.  I do not mean to impugn all research on the subject.  Much of it is quite interesting and useful.  But it has been misleading to non-specialists.

Second, and more importantly, the attack has distracted theorists and experimentalists from the task that Schelling gave them of identifying empirically useful focal points.  In fact, theorists of econometrics have gotten so distracted that some have given up entirely on identifying focal points that could be used to model collective behavior as complicated as market prices.  Their approach instead has been to substitute ad hoc models of psychology to limit the hypothesis of rationality.  This, in turn, has led to intractable mathematics and insoluble debates over what approximations are reasonable as limits to rationality.

Broken Symmetries as Schelling Points

Theories of economics and political science are starved for a new focal point theory that is useful and general as an empirical observation and consistent with the hypothesis of rationality.  There is such a focal point.  And what should not be surprising is that it was overlooked for the same reason that Schelling points were overlooked by other academics before The Strategy of Conflict.  Specifically, academics had reached a tacit agreement that symmetry would be the basis for theories of rationality.  Schelling's ability to see that symmetry was only one focal point among many that could have been chosen is the reason why he is justly lauded for his deep insights into human social behavior.

And since Schelling understood how Schelling points could lead to tacit agreement, naturally he was able to identify symmetry as a Schelling point for academic economists, and ask, in effect, "Why symmetry?"  The answer he suggests is that symmetric problems are easier to solve mathematically.

This is certainly true.  To wit, to be soluble, mathematical models for market equilibrium (and hence price) provided by economists must assume that wealth is conserved (i.e., is not created or destroyed).  Equilibrium cannot be defined when total wealth is unstable.  What only few economists may realize, however, is that (under Emmy Noether's Theorem) conservation laws are mathematically equivalent to symmetry invariance.  In this case, wealth conservation implies time invariance.

Given the empirical fact that symmetries are often broken, it is natural to ask, then, what hypothesis about the social behavior of large groups over long periods could be nearly as fundamental as the hypothesis of rationality -- remembering, of course, that the rules of the game are to find a hypothesis that is also consistent with the hypothesis of rationality.

My humble suggestion is the following:

The activities of people change in time according to rhythms that, averaged over a population within a period of time, have a characteristic distribution in frequency.

I call this the fundamental hypothesis of periodicity.  The hypothesis can be demonstrated to be consistent with the fundamental hypothesis of rationality by observing how supply and demand curves can be integrated up from underlying frequency distributions.  Nonetheless it provides new insights into how elasticity and price dynamics arise from the aggregation of rhythms in the behavior of large numbers of people over long periods of time.

Periodicity is a focal point that is unexplored by economists, political scientists, and others.  It could serve as the foundation for a more complete empirical theory of the firm.

[First draft June 25, 2008. Revised on March 2, 2011. -MFM]

Hockey Helmets and Patent Markets

Years ago most hockey players did not wear helmets. Yet when privately polled, most hockey players said they would prefer to wear helmets for the extra safety that helmets would provide. Why the difference?

Economist Thomas Schelling pointed out the problem: when almost no player wears helmets, the player who does puts himself at a disadvantage in terms of peripheral vision. Although each player preferred the saftey of helmets, none was willing to accept the disadvantage in exchange for the extra safety. The answer: make helmets a league requirement. When everybody wears helmets, everyone is safer and everyone at the same disadvantage.

Patent buyers and sellers are in a similar position to hockey players right now. Although plenty of comparable patents are being licensed and assigned at any given moment, and public information about the terms of these licenses and assignments would make valuations considerably easier for everyone (saving some legal and expert witness fees at least), nobody alone would dream of doing so because of the advantage this would give competitors in terms of estimating costs of development and competition.

The soluton for patent buyers and sellers is as simple as the solution for hockey players -- require ALL patent license and assignment agreements to be disclosed. Everyone benefits from more accurate valuations. Nobody is at a competitive advantage in terms of disclosure.

Lemley and Myhrvold proposed this in an oped earlier this year.