Nonlinear models of distribution of talking in small groups |
| |
Affiliation: | 1. Center for Mathematics, Technische Universität München, Garching 85748, Germany;2. Section of Population Genetics, Center of Life and Food Sciences Weihenstephan, Technische Universität München, Freising 85354, Germany;3. Institute for Computational Biology, Helmholtz Center Munich, Neuherberg 85764, Germany;1. Department of Ecology & Evolutionary Biology, University of Tennessee, Knoxville, TN 37996, United States;2. National Institute for Mathematical and Biological Synthesis (NIMBioS), University of Tennessee, Knoxville, TN 37996, United States;3. Department of Entomology, University of Illinois at Urbana-Champaign, Urbana, IL 61801, United States;4. Department of Mathematics, University of San Diego, San Diego, CA 92110, United States;5. Department of Geography, University of Florida, Gainesville, FL 32611, United States;6. Emerging Pathogens Institute, University of Florida, Gainesville, FL 32611, United States;7. School of Life Sciences, University of KwaZulu-Natal, Durban, South Africa;8. Department of Math and Statistics,Washington State University, Pullman, WA, United States;9. Paul G. Allen School for Global Animal Health, Washington State University, Pullman, WA, United States;10. Department of Psychology, Princeton University, Princeton, NJ 08544, United States;11. Illinois Natural History Survey, University of Illinois at Urbana-Champaign, Champaign, IL 61820, United States;12. Center for Discrete Mathematics & Theoretical Computer Science (DIMACS), Rutgers University, Piscataway, NJ 08854, United States;13. Department of Mathematics, University of Tennessee, Knoxville, TN 37996, United States;1. University Medical Centre Groningen (UMCG), the Netherlands;2. Department of Human Resource Management & Organizational Behavior, University of Groningen, Nettelbosje 2, 9712 TS, Groningen, the Netherlands. |
| |
Abstract: | This paper develops a mathematical model of the distribution over time of talking in discussion groups. Researchers of small group processes and social inequality have long recognized that interaction in small discussion groups is usually not equally distributed and that being a person who talks more than others is associated with having higher status outside the group and greater prestige and influence within the group. There is also a history of mathematical approaches to describing this phenomenon. As an addition to this literature, here a nonlinear dynamical system model is presented and used to develop computer simulations that are compared with data from a laboratory study of real four-person discussion groups. The model is based on theoretical assumptions about group processes including individual differences in volubility, status generalization, deference hierarchies and norms of taking turns and of fairness. While none of these alone make predictions that match the data, when they are all combined simulations are produced that closely match the data in both changes over time and differentiation among members. The dynamical system using the parameters as estimated for these data reaches a fixed point, which may help understand how groups structures become stable under some conditions but not others. |
| |
Keywords: | Group processes Discussion groups Nonlinear dynamical systems Status generalization Contributive fairness |
本文献已被 ScienceDirect 等数据库收录! |
|