No place like home: Opinion formation with homophily and implications for policy decisions

ABSTRACT

We set up an opinion diffusion model with a local opinion leader, and using simulations we show the possibility of driving a significant wedge between the opinions of two groups that exhibit homophily although individuals are highly conformist. There exists an opinion gap between the group to which the opinion leader belongs and the other group. This opinion gap increases according to the relative size of the residence community. We show empirical traits related to our simulation: Employing Swiss national referenda data from 2008 to 2012, we show that members of parliament match referenda outcomes in their residence communities closer than they do in neighboring communities and that this wedge interacts significantly with the relative size of the residence community.

KEYWORDS:

• Opinion leadership
• diffusion
• homophily
• communication in networks
• voter preferences
• representation

Acknowledgements

We thank Ivo Bischoff, John Conley, Rainer Hegselmann, Linda G Veiga, Benno Torgler, and the participants of the 2015 Annual Meeting of the European Public Choice Society, the 2015 Congress of the International Institute of Public Finance, and the Joint Workshop on Political Economics organized by the Indiana University and the University of Bayreuth for discussion and helpful comments.

Notes

¹ See Friedkin and Johnsen (2011) for a detailed discussion on these pioneer models.

² Homophily as a term originates from Lazarsfeld and Merton (1954). See McPherson, Smith-Lovin, and Cook (2001) for a detailed overview and discussion.

³ Linking probability originites from the literature on noncooperative network formation games and it denotes the probability that any two randomly chosen nodes in the network are connected by a direct link with one another (or equivalently, they have a geodesic distance of one from each other). See e.g. Jackson (2008), Bala and Goyal (2000), or Slikker and Van Den Nouweland (2001) for detailed explanations.

⁴ Katz and Lazarsfeld (1955) and Merton (1968) put forward influence models where influentials act as intermediaries. Influentials are assumed to have a larger number of connections than an average citizen, and their opinions are valued for whatever reason by the public.

⁵ This structure of local connections generates a rooted directed spanning tree as shown by Lu et al. (2009) and discussed in detail by Wu (2005).

⁶ Functional forms of linking probabilities shown here are chosen in a way such that they embody our basic assumptions on linking probabilities as simple as possible. Aim of this section is not to investigate the exact functional form of linking probabilities but to help visualizing implications of our fundamental assumptions about the patterns of linking probabilities.

⁷ γ serves a purely technical purpose. Note that intra-community linking probabilities depend on community size, so that individuals in the smaller community will always have a smaller intra-community linking probability than inter-community, hence geographic homophily holds for individuals in the smaller community even if γ was equal one. The situation is different for individuals in the larger community: if γ was equal one, then there won’t be difference between their intra-community and inter-community linking probabilities, which would mean that there is no geographic homophily in linking probabilities of individuals residing in the larger community. Scaling the inter-community linking probability by γ∈(0,1) simply makes sure that geographic homophily holds.

⁸ Note that influentials may be linked to each other as well, but since this will not affect their opinion formation in our model, we leave this out for tractability.

⁹ See the appendix A.1 for the calculation of expected opinions and population shares. We run this analysis using R, and our source code is available upon request.

¹⁰ We take γ = 0.8 in our simulations, and other values of γ between zero and one don’t yield qualitatively different outcomes. Lower values of γ maintain the overall shape of the curves, making the opinion gap slightly more pronounced when the relative size of the residence community is smaller than 0.3 or greater than 0.7. Alternative figures with different γ values will be made available at request.

¹¹ A perfect setting would be one in which, on top of all mentioned above, individual opinions, individual communication connections, and exchange of opinions are observed.

¹² In addition to the majority of citizens, constitutional amendments require a double majority of citizens and cantons (so called Ständemehr).

¹³ MPs’ abstentions are excluded from the analysis.

¹⁴ Number of communities contained in each canton and distribution of population in communities are documented in Figure A1 and Table A1 in the appendix.

¹⁵ A complete list of proposals and initiatives taken to referenda between 2008 and 2012 (hence covered in our dataset) is shown in Table A2 in the appendix.

¹⁶ We further rule out such explanations in robustness tests by analyzing MPs who were born in their residence community.

¹⁷ There is rich literature documenting and discussing to what extend politicians fail to represent voters’ preferences, and how this can be explained (see Gerber & Lewis, 2004, for example). Ågren, Dahlberg, and Mörk (2006), Grofman (2004), Matsusaka (2010), Padovano (2013), Portmann, Stadelmann, and Eichenberger (2012), Giger and Klüver (2016), provide an overview of related literature in economics as well as in political science.

¹⁸ The Swiss National Parliament is located in Bern which can be reached from most parts of the country within two to three hours by train.

¹⁹ Instead of MP fixed effects, we use electoral district fixed (canton) in some estimations. MPs in our sample did not change their electoral district during the time period analyzed.

²⁰ We calculate discrete effects applying the Delta-Method as suggested by Ai, Norton, and Shvets (2003).

²¹ Synthetic communities as well as matching representative’s votes with local referenda outcomes are discussed in depth in Hermann and Leuthold (2007).

²² We provide further evidence on the significance of the opinion gap by using the actual share of votes in residence and neighbor communities that match MP’s vote instead of using the binary variable opinion match. Although point estimates for the coefficient of Residence Community are smaller than those in Table 1, they remain positive and significant. Estimation results are shown in Table A5 in the appendix.

²³ Cantons constitute MPs’ electoral districts, and it is quite possible that an MP is more responsive to her residence community if the neighbors lie outside the electoral district.

²⁴ As shown in detail in the appendix, using a percentage match variable (table A5) instead of a binary match indicator (Table 3) yields qualitatively very similar results.