Mathematical Models for Social Science Exploration

Matt Salganik
Graduate Student, Sociology, Columbia

Experiments on the collective generation of superstar cultural objects

Many cultural markets exhibit an extreme variation in the success of individual objects yet remain unpredictable. These two apparently contradictory aggregate-features are shown to be consistent with interdependence of decision-making at the individual level. These ideas are explored in a series of four web-based experiments involving a total of 27,379 subjects. We discuss implications for the sociology of culture as well as social science in general.

Tom Diprete
Professor, Sociology, Columbia

Cumulative Advantage as a Mechanism for Ineqaulity

While originally developed by Merton to explain advancement in scientific careers, cumulative advantage is a general mechanism for inequality across any temporal process (e.g. life course, family generations) in which a favorable relative position becomes a resource that produces further relative gains. We show that the term 'cumulative advantage' has come to have multiple meanings in the sociological literature. We distinguish between these alternative forms, discuss mechanisms that have been proposed in the literature that might produce cumulative advantage, and review the empirical literature in the areas of education, work careers, and related life course processes.

[diprete2005_cumulativeAdvantage.pdf]

Emily Erikson
Graduate Student, Sociology, Columbia

Note: There are two speakers on this date.

Malfeasance and the Foundations for Global Trade: The Structure of English Trade in the East Indies, 1601-1833

Drawing on a remarkable dataset compiled from ships' logs, journals, factory correspondence, ledgers, and reports that provide unusually precise information on each of the 4,572 voyages taken by English traders of the East India Company (hereafter EIC), we describe the EIC trade network over time, from 1601 to 1833. From structural images of voyages organized by shipping seasons, we map the (over time and space) emergence of dense, fully integrated, global trade networks: of globalization before globalization. We show that the integration of the world trade system under the aegis of the EIC was the unintended by-product of systematic individual malfeasance (private trading) on the part of ship captains seeking profit from internal Eastern trade.

[erikson2005_malfeasance.pdf]

Gueorgi Kossinets
Graduate Student, Sociology, Columbia

Note: There are two speakers on this date.

The Formation Processes in Social Networks

Using a unique network dataset, in which social interactions, affiliations and attributes are recorded over time, we study formation of social connections among individuals. First, we present an approach, based on a sliding window filter, for recovery of network structure from communication event history between members of some community or organization. We show that the results are robust for reasonable choices of parameters and also describe some results about stability of network properties. Second, building upon the notion of transitivity and Feld's theory of interaction foci, we develop and quantify the concepts of cyclic and focal closure. Focal closure refers to the process of formation of a new network tie between two individuals who share a common affiliation or group. Cyclic closure is our generalization of transitive closure and refers to formation of a new tie between individuals at an arbitrary network distance. Our results show that a single opportunity for interaction, whether it is a common acquaintance or a shared interaction focus, leads to developing a new network tie with a high probability. We conclude that even minimally accurate, generative models of evolving social networks would need to account for triadic closure (tie formation via a mutual acquaintance), focal closure (the formation via a shared focus), and the compounding effect of both processes together.

Ernest Drucker
PhD, Montefiore Medical Center

Population Effects of Individual Medical Interventions: The Origin of AIDS in Africa

Population cycles of periods longer than seasonal are common in the temporal patterns of many infections diseases, including endemic cholera. Evidence that environmental factors, particularly climatic ones, drive these cycles has been highly controversial because of the difficulty in isolating their contribution while also taking into account the non-linear population dynamics of the disease. I present a nonlinear time series model developed for this purpose and its recent application to temporal cholera patterns in Matlab (Bangladesh). Results show the critical interplay of population dynamics and environmental forcing, with strain-dependent responses and the existence of periods 'refractory' to climate variability. I discuss the challenges posed by pathogen diversity and changes in dominaint strain over time. I then address the limitations of 'mean-field' disease models that ignore the local nature of interaction and assume random mixing. With network models, I present results on scaling disease dynamics from individuals to populations via simple temporal models that parametrize the effects of distributed interations.

[drucker2001_injection.html] [drucker2002_cameroon.pdf] [drucker2005_transfusions.doc]

Peter S. Dodds
Associate Director, CDG, Columbia

Social Contagion on Networks

I'll present observations regarding a simple model of social contagion acting on a range of networks. In particular, I'll discuss how the model behaves on random networks with Poisson and skewed degree distributions; how to maximize the probability of triggering a global activation cascade when a network's structure is minimally understood; how group-based networks greatly facilitate spreading (in comparison to random networks); and how rapid spreading can occur on some networks even when nodes require multiple, (near) simultaneous `hits.' I'll also show that for response functions that lead to chaotic behavior in the mean-field version, period doubling can also be tuned by network connectivity. For chaotic maps, some preliminary results suggest that when individual response functions are deterministic, chaotic behavior is only transient and the system collapses to a low period behavior.

Alex Peterhansl
Graduate Student, Economics, Columbia

A Social Planning Approach to Coordination Failure

There is a class of problems in non-cooperative game theory that is subject to multiple, Pareto-ranked equilibria, where decision makers are faced with strategic uncertainty. In this paper, we investigate how a social planner can efficiently alter the incentives of a small subset of individuals to trigger system-wide coordination on the Pareto-superiour outcome. Our intervention strategy utilizes a Schelling-inspired tipping phenomenon.

Various

Note: This meeting will consist of attending the afternoon session of a one-day seminar to commemorate 'Personal Influence'.

Re-Reading 'Personal Influence': Retrospects and Prospects Fifty Years Later

The 50-year anniversary of the publication of Elihu Katz and Paul Lazarsfeld's 'Personal Influence' provides a fitting opportunity to revisit a classic text from varied contemporary horizons. Beyond its historical resonance, 'Personal Influence' addresses a number of issues that remain current today: the place of face-to-face conversation in a world crowded by media; the nature of social networks and their roles in the diffusion of information and beliefs; and the preferred methods and sociology of knowledge production within contemporary institutional contexts.

Jeffrey Nickerson
Stevens Institute of Technology

Defending the Spirit of the Web: Conflicts in the Internet Standards Process

The creation of Internet standards is a process in which people and ideas move across many venues. Some participants engage in design activities, and seek legitimacy for their ideas by establishing or joining working groups within specific standards bodies. Other participants act as officers and uphold the bylaws and culture of the standards bodies. A third group of participants observe the process and register opinions through public mailing lists, but do not engage in the process otherwise. The encounters between these groups sometimes produce standards, and sometimes produce movement, as participants seek alternative venues for their ideas. These observations are based on the study of 11 years of Web services choreography standards development, in which over 500 participants met in nine different standards venues. This paper explains the venue hopping we observed in the study. We show that the bylaws of the institutions have an important impact on the pattern of movement, and are used in some cases to oppose what some participants perceive as corporate self-interest. Out findings suggest that changes in the bylaws of standards bodies might alter the necessary conditions for the current way of developing standards.

[nickerson2003_internetStandards.pdf]

Dunia Lopez Pintado
Postdoctoral Fellow, ISERP, Columbia

Social Influence and Collective Decisions

In this paper we address the general question of how social influence determines collec- tive outcomes. First, we define conditions under which the behavior of individuals making binary decisions can be described in terms of what we call an influence response function: a one-dimensional function of the (weighted) number of individuals choosing each of the alternatives. We show the precise form of these influence response functions for a wide range of contexts, such as public good games, technology adoption, diffusion of information etc. Second, we demonstrate that, under the assumptions of global and anonymous inter- actions, general knowledge of the influence response functions is sufficient to compute the equilibrium, and even non-equilibrium properties of the collective dynamics.

Patrick Callahan
Professor, Mathematics, UCSD

California's Science and Mathematics Initiative: Issues of Quality and Capacity in Teacher Education

Mercedes Pascual
U. Mich

Note: This is a joint meeting with the Infectious Disease Working Group.

Porblems of scale in disease population dynamics: cholera, climate, and Ro

Population cycles of periods longer than seasonal are common in the temporal patterns of many infections diseases, including endemic cholera. Evidence that environmental factors, particularly climatic ones, drive these cycles has been highly controversial because of the difficulty in isolating their contribution while also taking into account the non-linear population dynamics of the disease. I present a nonlinear time series model developed for this purpose and its recent application to temporal cholera patterns in Matlab (Bangladesh). Results show the critical interplay of population dynamics and environmental forcing, with strain-dependent responses and the existence of periods 'refractory' to climate variability. I discuss the challenges posed by pathogen diversity and changes in dominaint strain over time. I then address the limitations of 'mean-field' disease models that ignore the local nature of interaction and assume random mixing. With network models, I present results on scaling disease dynamics from individuals to populations via simple temporal models that parametrize the effects of distributed interations.

Jeff Cares and David Jarvis
Alidade Corporation

A Methodology for Analyzing Complex Military Command and Control Networks

Military personnel are increasingly subject to multiple means of electronic communication for command and control (C2). The means are both synchronous and asynchronous and include email, chat, voice over IP and others. The analytical methodology offered through the study of complex networks such as the Internet, power grids, transportation networks, and patterns of social interaction can aid in the understanding of C2 systems used by military organizations. By analyzing the topologies of communication networks and developing metrics; leadership, patterns of communication, vulnerabilities, and the level of collaboration in the network can be discerned. This paper provides a condensed version of the results from a “discovery analysis” of a military email system used during a recent US/UK naval exercise. Additional topics for discussion include collaboration patterns between the two country’s networks, an analysis of various sub-network communication patterns, and questions regarding unique properties of military networks that are not seen in other social networks. This methodology can help engineers and knowledge managers design better C2 structures by incorporating information about how people actually use electronic communication networks.

Rajiv Sethi
Professor, Economics, Barnard

Inequality and Segregation

Despite declining group inequality and the rapid expansion of the black middle class in the United States, major urban centers with significant black populations continue to exhibit extreme racial sep- aration. Using a theoretical framework in which individuals care about both the affluence and the racial composition of neighborhoods, we show that lower inequality is consistent with extreme and even rising levels of segregation in cities in which the minority population is large. Our results can help explain why segregation continues to characterize the urban landscape even though survey evidence suggests that individuals favor more integration than they did in the past. We will also explore the dynamics of group inequality when segregation of social networks places the initially less a