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Social Choice and Welfare

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26-10-2020 | Original Paper

Social Capital, Communication Channels and Opinion Formation

Authors: Christos Mavridis, Nikolas Tsakas

Published in: Social Choice and Welfare | Issue 4/2021

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Abstract

We study how different forms of social capital lead to different distributions of multidimensional opinions by affecting the channels through which individuals communicate. We develop a model to compare and contrast the evolution of opinions between societies whose members communicate through bonding associations (i.e., which bond similar people together) and societies where communication is through bridging associations (i.e., which bridge the gap among different people). Both processes converge towards opinion distributions where there are groups within which there is consensus in all issues. Bridging processes are more likely to lead to society-wide consensus and converge to distributions that have, on average, fewer opinion groups. The latter result holds even when the confidence bound that allows successful communication in the bridging process is much smaller than the respective bound in the bonding process.

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This is in fact a recurrent result in this type of processes, see Deffuant et al. (2000) and Lorenz (2005).

See Bala and Goyal (1998); Gale and Kariv (2003); Banerjee and Fudenberg (2004); Acemoglu and Ozdaglar (2011); DeMarzo et al. (2003); Golub and Jackson (2010); Mueller-Frank (2013,2015) and also Golub and Sadler (2017) for an excellent review of the different branches of literature on learning on networks.

For other definitions of social capital and for a research survey on the topic see Durlauf and Fafchamps (2005). For an empirical decomposition of the concept see Bjørnskov (2006).

There are also two forms of “bridging”, internal and external. Internal bridging brings together the members of a given association, whereas external bridging brings together members of different associations (see Geys and Murdoch 2008). Moreover, Geys and Murdoch (2010) discuss how the bridging and bonding nature of networks can be measured. Following the discussion on social capital and redistribution, Borisova et al. (2015) show that it is in fact the bridging social capital that has positive effects on redistribution.

For an excellent survey on opinion dynamics and bounded confidence see Lorenz (2007) and for some empirical evidence see Lorenz (2017). Moreover, a stream of the literature on average-based updating looks at the shape of persisting disagreement without considering bounded confidence (see DeMarzo et al. 2003; Louis et al. 2017).

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We focus on the variable that indicates whether or not someone has provided voluntary work for the given organization, rather than just having participated, as this provides a stronger indication on the extent of involvement in the organization.

The choice of twenty observations as a threshold is obviously ad hoc, as there is not standard way of making this choice. The idea is that on the one hand a small number of observations induces a lot of noise in the ELF, on the other hand setting a high threshold will lead us to drop too many observations, thus altering the nature of the total sample.

The complete table of regression results is available upon request.

In a different set of regressions we found the same result to be true if one looks at partisanship levels instead of the ELF. By partisanship level we mean the average absolute distance from the average opinion of 5.5. This result could be connected with the findings of Satyanath et al. (2017) where the authors find participation in associations to be linked with increased entry level in the Nazi party before WWII.

Alternatively, one could think that two citizens with very distant opinions can never be chosen to interact. The qualitative results of this alternative mechanism are identical and the only feature that is affected is the speed of convergence and some increased consistency of extreme opinions.

There might be cases where these two opinions might be ex-ante correlated, but this would not add anything to our model.

Later in the paper, for some results we will impose the normalization \(k=\frac{1}{2}-\sqrt{\frac{1}{4}-d^2}\) which ensures that the areas within which successful communication is possible cover the same area in each case. Observing at Fig. 1 the area in which a citizen may find others to agree is \(4d^2\) in the bonding case and \(2\cdot 2k-4k^2\) in the bridging case. Equating the two quantities yields the normalized value of the parameter k.

We consider that the citizens discuss a single issue at a time, however all results directly extend to the case in which both issues are discussed simultaneously. Such an assumption would only speed up the convergence of the process.

The proofs of these arguments are omitted as they are rather straightforward and well–established in the literature and are available upon request.

A short discussion on why focusing on the interior of the neighboring area is provided in the Appendix after the proof of the proposition.

The proof is readily available upon request.

The choices regarding the confidence bounds are made in order to have a unique expression for the probabilities we calculate. Our analysis allows us to calculate the respective probabilities for larger values as well, but that would induce a larger computational cost without adding much to the intuition. The assumption regarding successful communication does not affect the result; it just eliminates all interactions that lead to no update which affect only the speed of convergence.

A simple Taylor expansion gives \(\frac{1}{2}-\sqrt{\frac{1}{4}-d^2}=d^2+d^4+2d^6+5d^8+O[d^{10}]\).

We use as conditions for stabilization those of Propositions 2 and 3, which are sufficient for us to count the number of islands, as explained in Remark 3.

As a reminder, \(ELF=1-\sum s_i^2\) and \(GI=\sum \sum s_i s_j d_{ij}\), where \(s_i\) and \(s_j\) are shares of distinct opinion islands, and \(d_{ij}\) is the Euclidean distance between opinion islands i and j.

Lorenz (2005) states the result focusing on the limit of the backward product of transition matrices, which is equivalent to the consensus argument we present here.

Otherwise, if at least two of the citizens are sufficiently close to interact successfully, this will be true in all subsequent periods and hence by Proposition 1 there will be at most two islands in the long run.

In order to have two or fewer islands, at least two citizens must have exactly the same initial opinions, which has probability zero of occurring given the assumed distribution initial opinions are drawn from.

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Title: Social Capital, Communication Channels and Opinion Formation
Authors: Christos Mavridis
Nikolas Tsakas
Publication date: 26-10-2020
Publisher: Springer Berlin Heidelberg
Published in: Social Choice and Welfare / Issue 4/2021
Print ISSN: 0176-1714
Electronic ISSN: 1432-217X
DOI: https://doi.org/10.1007/s00355-020-01297-5

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