Funded Grants

Modeling social dynamics in competitive systems

In 1942, biochemist and writer Isaac Asimov published the first chapters of what would become his well-known Foundation Series. In that series of novels, Dr. Asimov imagined a new branch of science that he dubbed "psychohistory"-a theory of mathematical sociology whereby the large-scale behavior of human societies could be predicted.

While the idea of psychohistory remains mostly in the realm of science fiction, simple mathematical models of various aspects of human behavior have appeared in the scientific literature with increasing frequency in recent years. Though still few in number, successful examples demonstrate that analytically tractable systems of equations can usefully capture important aspects of the way humans behave in groups. Furthermore, the very process of paring down a complex system in order to create a simplified mathematical model gives insight into the critical components that most strongly determine how such a system behaves.

This proposal consists of a variety of projects connected by the common theme of group behavior: all of the proposed topics can be seen as systems with two or more groups competing for members. In the past, limitations on data made it difficult to test mathematical models such as these, discouraging their development. Today, a growing set of large historical databases is available, making it possible for the first time to quantitatively test many predictions of theoretical models of social behavior. I believe that the projects proposed below are only the tip of the iceberg for convincing dynamical representations of human social systems. Other approaches to social systems, such as agent-based modeling or econometric analysis, reveal that many systems obey understandable rules and are statistically predictable to varying extents. The addition of rigorous dynamical models would be of great benefit both for their predictive power and the insight gained into fundamental aspects of these complex problems.

The big questions to be addressed include:

1. Can religious shifts be predicted?

The 2008 American Religious Identification Survey by Trinity College found that Americans who don't identify with any particular religious group are the fastest growing religious minority and currently comprise about 15% of the population; a 2010 Pew survey found that more than 25% of Americans born after 1980 are religiously unaffiliated. Many other countries have experienced similar shifts in religious beliefs during the past half century: in the Netherlands, for example, those who affiliate with a religious group are now in the minority. What is driving this rapid and historically unprecedented movement away from organized religion? Is it likely to continue or reverse? Can we make any predictions about the future of religious identification?

This project would be based on a model of competition between religious groups and the "unaffiliated" group for adherents. Previous research has shown that this type of model can be analyzed mathematically with only minimal information about the response of individuals to social pressure, giving deep insight into underlying causes. Quantitative predictions will depend on construction of sufficiently large historical data sets, which are available through government census records for a significant number of countries worldwide.

2. What drives language death?

In recent years a disturbing trend had become increasingly difficult to ignore: languages around the world are dying. The last speaker has already been born for an estimated 90% of world languages. The typical case is that a so-called "killer" language (e.g., English, French, Russian, Spanish, Portuguese, or Mandarin Chinese) takes root in a region where the native language is not protected by political borders, and, through economic or political influence, gradually becomes the dominant regional language. The time scale for a shift in regional language can be as short as 50 years. In such cases, it is not uncommon for children to be unable to communicate fluently with their grandparents. Previous models of this phenomenon have identified two key factors driving language change. The first factor is a majority effect: individuals have an advantage if they can communicate with a larger fraction of their peers, and therefore gain by switching to a majority language. The second factor is a socalled "status" effect: society may provide greater benefits (e.g., economic, political) to speakers of a language perceived to have higher status, and thus individuals have an incentive to switch to that language to gain the benefits. A typical example might be university education available only in a higher prestige language.

The author published a simple mathematical model incorporating these two key factors in 2003. Subject to very mild assumptions, the model made the surprising and disheartening prediction that, in the long run, only a single language can persist, with the bilingual society unstable. Furthermore, numerical simulation of the model matched historical data for a variety of declining world languages.

A caveat to the pessimistic predictions of the 2003 model, however, is its limited applicability: the numerical fits worked best for very small regions. Real human populations consist of a social network linking various members of the community. Because the model assumed that all members of society interact equally with one another, it couldn't be applied well to large distributed populations. So-called "small-world" networks have been shown to be good models for human societies. Understanding how the social structure of a society can promote or discourage language change is an important step in building useful strategies for language preservation. This project will incorporate network effects mathematically, as well as through data collected as part of field research in the Peruvian Andes to be conducted in 2010.

3. Will obesity rates continue to rise or level off?

Between 1980 and 2008, overall U.S. adult obesity rates increased from 15% to 30%, with even more dramatic increases concentrated in some regions of the country. In 2007 Nicholas Christakis and James Fowler used data from the Framingham Heart Study (a 32-year longitudinal study tracking weights and social connections for 12,067 individuals) to show that the chance of an individual becoming obese was strongly correlated with obesity rates among neighbors in his or her the social network. Besides having important clinical implications, this discovery provides an ideal basis for a dynamical model of obesity. Such a model would be of great use in understanding the key factors underlying the current epidemic and in highlighting changes that may affect the future prevalence of obesity.

The proposed project entails creation of both a "compartmental" and a "continuous" competitive model, in which individuals shift weights with probabilities dependent on both intrinsic biological parameters and social factors. The goal is to explain today's distribution of weights in the US population as a steady-state of the model, and then to extend predictions to the future. Parameters for the model will be kept to a minimum, and focus made on mathematically rigorous statements about behavior of the model.

4. Why do left-handers constitute about 10% of the populations?

The percentage of the population that is left-handed (about 10%) is very consistent among world cultures today, and studies of skeletal remains indicate that it has remained fairly constant since prehistoric times. This suggests that there may be an inherent advantage to the rarity of left-handers. The percentage left-handed changes considerably in the world of professional sports, however, approaching 50% among leading baseball players or boxers. The traditional explanation for this observation is that sports focused on individual physical competition yield an advantage for the competitor who is different. For example, a single left-handed boxer in an otherwise right-handed league would have the advantage of extensive experience against right-handers, but opponents would have no experience against left-handers.

If competition were the only effect at play, then we would expect to see a human population with approximately 50% left-handed and 50% right-handed, since a competitive advantage would lead to relative growth of the left-handed population until the advantage disappeared. The fact that left-handers are indeed rare implies that there is some evolutionary disadvantage to nonconformity. The observed fraction of left-handers must represent a balance between the competing influences of conformity and competition.

A successful model of this phenomenon would give insight into factors affecting human evolutionary history. The problem will be approached in a manner similar to others previously described, imagining a "lefty" group and a "righty" group competing for members on evolutionary time scales. Individual competitive fitness would necessarily increase with membership in the minority group, but overall group fitness would favor conformity.