Agent-Based Modeling of Consensus Group Formation with Complex Webs of Beliefs
Round 1
Reviewer 1 Report
This is an interesting paper that extends the standard “linear” approach to beliefs in opinion dynamics and proposes to represent such beliefs as complex webs. However, similarity updates in the model are based on set operations on the collection of nodes and vertices, which is as mechanistic as the standard opinion dynamics models. My comments are as follows:
1o. A weakness of the approach is how to model such webs of beliefs in a way that represent mental coherence of the adopting individuals. I invite the author to investigate recent developments in the social science literature that have dealt with similar concerns in a more realistic way, and connect them to his model—not necessarily modifying the model but putting upfront limitations of the WoBs approach.
An important concern of opinion dynamics models is that of the coherence of the structure of beliefs. Edmonds (2020) proposes a structural approach to beliefs where belief dissonance influences the probability of belief change itself. Shaw (2020) presents a model with Bayesian updating, showing that belief dynamics are “path dependent” on prior belief knowledge. Leon-Medina et al (2020) also highlights the importance of coherence heuristics in the adoption of opinions. I also believe that processes of cognitive alignment are important, especially in the context of the emergence of scholarly groups, as highlighted by the author (cf. Falandays and Smaldino, 2022).
Incorporating such aspects will open room to more interesting results, beyond the trivial one of stabilizing similarity / formation of clusters as a by-product of interaction. Please elaborate on the above aspects.
2o. Although the author provides an explanation at the beginning of section 2.3, it is not fully clear what the rationale is behind equations 4 and 5. Please provide a more complete explanation for equations 4 and 5 and, perhaps, add a numerical example to understand the dynamics of WoBs updating.
3o. Minor points / typos:
Line 67, there is a missing space in “firstthe”
Line 82: consider revising the following sentence “In constructing the generic networks are pruned…”
Equation 4: revise location of agents’ indices
Equation 5: there is a missing parenthesis—the one that closes the Max function.
References:
Edmonds, B. (2020). Co-developing beliefs and social influence networks—towards understanding socio-cognitive processes like Brexit. Quality & Quantity, 54(2), 491-515.
Falandays, J. B., & Smaldino, P. E. (2022). The emergence of cultural attractors: how dynamic populations of learners achieve collective cognitive alignment. Cognitive Science, 46(8), e13183.
León-Medina, F. J., Tena-Sánchez, J., & Miguel, F. J. (2020). Fakers becoming believers: how opinion dynamics are shaped by preference falsification, impression management and coherence heuristics. Quality & Quantity, 54(2), 385-412.
Shaw, L. A. (2020). Something out of nothing: a Bayesian learning computational model for the social construction of value. The Journal of Mathematical Sociology, 44(2), 65-89.
Author Response
Please, see the attachment. Responses to reviews are in attached pdf-file.
Author Response File: 
Author Response.pdf
Reviewer 2 Report
The paper presents an ABM where influence each other's beliefs based on similarity. In interactions the beliefs are altered when agents seek consensus and consensus groups are formed. The authors claim that their results resemble the formation of disciplinary, scholarly consensus groups.
(1) The introduction describes the model at a high level and related work. However, the paper would be improved if the paper presented an actual research questions with a testable hypothesis. The authors are attempting to formalize and a grow an explanation related to web of beliefs in disciplinary, scholarly consensus groups. Identifying some observed data or characteristics that could be statistically tested to prove / answer this reserach question would increase the scientific soundness of the paper.
(2) There are a number of related paper focusing on the general dyanmics of interactions based around similarity to formulate concensus groups in ABMs. See below for an overview of these papers. Citing/referencing/reviewing them would improve the quality of the submission:
Social influence is an important factor in human interaction. In encounters, individuals can modify their opinions, attitudes, beliefs, or behavior to mimic or to oppose those they interact with. These modifications can be the result of persuasion, uncertainty or peer pressure (Flache et al. 2017).
FLACHE, A., Mäs, M., Feliciani, T., Chattoe-Brown, E., Deffuant, G., Huet, S. & Lorenz, J. (2017). Models of social influence: Towards the next frontiers. Journal of Artificial Societies and Social Simulation, 20(4), 2: https://www.jasss.org/20/4/2.html. [doi:10.18564/jasss.3521 ]
Initial social influence models included actors whose opinion on a position was socially influenced on a continuous spectrum (Abelson 1967; Berger 1981; DeGroot 1974; Lehrer 1975). Examples of these models include agents determining the appropriate speed on an interstate. Later, modelers assumed that opinions did not vary on a continuous scale but instead reflected a choice between mutually exclusive options (Axelrod 1997; Latané 1996; Liggett 2012; Sznajd-Weron & Sznajd 2000).
ABELSON, R. P. (1967). Mathematical models in social psychology. Advances in Experimental Social Psychology, 3, 1-54. [doi:10.1016/S0065-2601(08)60341-X ]
BERGER, R. L. (1981). A necessary and sufficient condition for reaching a consensus using Degroot’s method. Journal of the American Statistical Association, 76(374), 415-418. [doi:10.1080/01621459.1981.10477662 ]
DEGROOT, M. H. (1974). Reaching a consensus. Journal of the American Statistical Association, 69(345), 118-121. [doi:10.1080/01621459.1974.10480137 ]
LEHRER, K. (1975). Social consensus and rational agnoiology. Synthese, 31(1), 141-160. [doi:10.1007/BF00869475 ]
AXELROD, R. (1997). The dissemination of culture a model with local convergence and global polarization. Journal of Conflict Resolution, 41(2), 203-226.
LATANÉ, B. (1996). Dynamic social impact: The creation of culture by communication. Journal of Communication, 46(4), 13-25.
LIGGETT, T. (2012). Interacting particle systems. New York, NY: Springer.
SZNAJD-WERON, K. & Sznajd, J. (2000). Opinion evolution in closed community. International Journal of Modern Physics C, 11(06), 1157-1165. [doi:10.1142/S0129183100000936 ]
Recently, researchers have identified three classes of social-influence models that are the most popular in agent-based modeling. These classes of social influence models are: (1) assimilative social influence (Durkheim 2014; Myers 1982; Vinokur & Burnstein 1978; Akers et al. 1979), (2) similarity biased influence (Axelrod 1997; Carley 1991; Deffuant et al. 2000; Hegselmann et al. 2002; Mark 1998) and (3) repulsive influence (Jager & Amblard 2005; Macy et al. 2003; Mark 2003).
VINOKUR, A. & Burnstein, E. (1978). Depolarization of attitudes in groups. Journal of Personality and Social Psychology, 36(8), 872.
DURKHEIM, E. [1901] (2014). The rules of sociological method: and selected texts on sociology and its method. New York, NY: Free Press.
MYERS, D. G. (1982). Polarizing effects of social interaction. Group Decision Making, 26(4), 187–193.
CARLEY, K. (1991). A theory of group stability. American Sociological Review, 56, 331-354. [doi:10.2307/2096108 ]
DEFFUANT, G., Neau, D., Amblard, F. & Weisbuch, G. (2000). Mixing beliefs among interacting agents. Advances in Complex Systems, 3(01n04), 87-98.
HEGSELMANN, R., Krause, U. et al. (2002). Opinion dynamics and bounded confidence models, analysis, and simulation. Journal of Artificial Societies and Social Simulation, 5(3), 2: https://www.jasss.org/5/3/2.html.
AKERS, R. L., Krohn, M. D., Lanza-Kaduce, L. & Radosevich, M. (1979). Social learning and deviant behavior: A specific test of a general theory. American Sociological Review, 44(4), 636-55.
HEGSELMANN, R., Krause, U. et al. (2002). Opinion dynamics and bounded confidence models, analysis, and simulation. Journal of Artificial Societies and Social Simulation, 5(3), 2: https://www.jasss.org/5/3/2.html.
JAGER, W. & Amblard, F. (2005). Uniformity, bipolarization and pluriformity captured as generic stylized behavior with an agent-based simulation model of attitude change. Computational & Mathematical Organization Theory, 10(4), 295-303. [doi:10.1007/s10588-005-6282-2 ]
MACY, M. W., Kitts, J. A., Flache, A. & Benard, S. (2003). 'Polarization in dynamic networks: A Hopfield model of emergent structure.' In R. Breiger, K. Carley & P. Pattison (Eds.), Dynamic Social Network Modeling and Analysis: Workshop Summary and Papers. Washington, DC: The National Academies Press, pp. 162–173.
MARK, N. (1998). Beyond individual differences: Social differentiation from first principles. American Sociological Review, 63, 309–330. [doi:10.2307/2657552 ]
MARK, N. P. (2003). Culture and competition: Homophily and distancing explanations for cultural niches. American sociological review, 68(3), 319-345.
In assimilative social influence models, individuals are connected by a structural relationship and always influence each other to reduce opinion differences. Here, if the network is connected the influence dynamics eventually create consensus (Flache et al. 2017).
For models with similarity biased influence, only sufficiently similar individuals can influence each other to reduce opinion differences. How much similarity is sufficient depends on other mechanisms included in the model (e.g. social identity, confidence in others, etc). With similarity based influence consensus can be avoided. However, if the similarity bias is sufficiently strong, then multiple homogenous but distinct clusters of individuals emerge. Opinions, however, never leave the initial range (Deffuant et al. 2000; Hegselmann et al. 2002; Flache et al. 2017).
In models with repulsive influence, when individuals are too dissimilar they can influence each other to increase opinion differences. The amount of dissimilarity needed to trigger repulsive influence depends on other mechanisms included in the model (e.g. social identity, ego-involvement). Here, consensus can be avoided. Also, clusters can form and adopt maximally opposing views (bi-polarization). These dynamics allow opinions to leave the initial range (Flache et al. 2017).
It is important to note that most social influence models represent opinions as a one-dimensional variable. However, recent research has shown the importance of using a multidimensional model to study opinion polarization (Li & Xiao 2017). We employ this multi-dimensional representation in our representation of religiosity.
LI, J. & Xiao, R. (2017). Agent-based modelling approach for multidimensional opinion polarization in collective behaviour. Journal of Artificial Societies & Social Simulation, 20(2), 4: https://www.jasss.org/20/2/4.html. [doi:10.18564/jasss.3385 ]
Finally, two recent papers haved shown how similarity based groups can form concensus related to opinions and schloarly discipline formation. These are (Gore et al. 2016) and (Diallo et al. 205)
Diallo, Saikou Y., et al. "An overview of modeling and simulation using content analysis." Scientometrics 103.3 (2015): 977-1002.
Gore, Ross, et al. "Forecasting changes in religiosity and existential security with an agent-based model." Journal of Artificial Societies and Social Simulation 21.1 (2018).
(3) The visualization in Figure 1 does not illuminate the data. While it is obvious that V increases it is difficult to tell which links were added / removed / remained in the networks. Either using color of simply presenting the data tabularly with these aspects sub-sectioned would improve the paper.
(4) The authors indicate that sharing data and code for their paper is not applicable. In the replication crisis era, especially when an ABM is being presented, sharing the code and data for the model, as well as all data and code used to produce the visualizations and results is paramount.
Author Response
Please, see the attachment. Responses to reviews are in attached pdf-file.
Author Response File: Author Response.pdf
Round 2
Reviewer 2 Report
My concerns have been sufficiently addressed. The paper is now suitable for publication.
