Dynamics of Evolving Social Groups

Exclusive social groups are ones in which the group members decide whether or not to admit a candidate to the group. Examples of exclusive social groups include academic departments and fraternal organizations. In the present paper we introduce an analytic framework for studying the dynamics of exclusive social groups. In our model, every group member is characterized by his opinion, which is represented as a point on the real line. The group evolves in discrete time steps through a voting process carried out by the group's members. Due to homophily, each member votes for the candidate who is more similar to him (i.e., closer to him on the line). An admission rule is then applied to determine which candidate, if any, is admitted. We consider several natural admission rules including majority and consensus. We ask: how do different admission rules affect the composition of the group in the long term? We study both growing groups (where new members join old ones) and fixed-size groups (where new members replace those who quit). Our analysis reveals intriguing phenomena and phase transitions, some of which are quite counterintuitive.

[1]  M. Degroot.  Reaching a Consensus , 1974 .

[2]  Noah E. Friedkin,et al.  Social influence and opinions , 1990 .

[3]  F. C. Gamst.  Foundations of Social Theory , 1991 .

[4]  N. Wormald.  Differential Equations for Random Processes and Random Graphs , 1995 .

[5]  R. Axelrod.  The Dissemination of Culture , 1997 .

[6]  Karl-Martin Ehrhart,et al.  Série Scientifique Scientific Series Mobility and Cooperation: on the Run , 2022 .

[7]  Guillaume Deffuant,et al.  Mixing beliefs among interacting agents , 2000, Adv. Complex Syst..

[8]  M. McPherson,et al.  Birds of a Feather: Homophily in Social Networks , 2001 .

[9]  Rainer Hegselmann,et al.  Opinion dynamics and bounded confidence: models, analysis and simulation , 2002, J. Artif. Soc. Soc. Simul..

[10]  E. Ben-Naim,et al.  Bifurcations and patterns in compromise processes , 2002, cond-mat/0212313.

[11]  L. Putterman,et al.  Cooperation Under the Threat of Expulsion in a Public Goods Experiment , 2005 .

[12]  Partha Gangopadhyay.  Endogenous group formation , 2004 .

[13]  Sven E. Feldmann.  Political Competition: Theory and Applications , 2005, Perspectives on Politics.

[14]  Jon M. Kleinberg,et al.  Group formation in large social networks: membership, growth, and evolution , 2006, KDD '06.

[15]  Gerard Delanty.  The Foundations of Social Theory , 2009 .

[16]  Timothy C. Salmon,et al.  Coming and going: Experiments on endogenous group sizes for excludable public goods , 2009 .

[17]  Santo Fortunato,et al.  Community detection in graphs , 2009, ArXiv.

[18]  S. Fortunato,et al.  Statistical physics of social dynamics , 2007, 0710.3256.

[19]  Jon M. Kleinberg,et al.  How Bad is Forming Your Own Opinion? , 2011, 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science.

[20]  Kamesh Munagala,et al.  Coevolutionary opinion formation games , 2013, STOC '13.

[21]  Jon M. Kleinberg,et al.  Selection and influence in cultural dynamics , 2013, EC '13.

[22]  Jon M. Kleinberg,et al.  On discrete preferences and coordination , 2013, EC '13.

[23]  David Lee,et al.  Biased assimilation, homophily, and the dynamics of polarization , 2012, Proceedings of the National Academy of Sciences.

[24]  G. Charness,et al.  Journal of Economic Behavior & Organization Starting Small toward Voluntary Formation of Efficient Large Groups in Public Goods Provision , 2022 .

[25]  M. Macy,et al.  Local Convergence and Global Diversity: From Interpersonal to Social , 2016 .

[26]  Ohad N. Feldheim,et al.  Mean and minimum of independent random variables , 2016, Israel Journal of Mathematics.