SIAM News Blog

Model Explores the Difference Between Private and Expressed Opinions

By Jillian Kunze

“Whenever we are in a social group—whether that is your local sports club, your workplace, or any other situation—we will often exert influence on others,” Mengbin Ye of Curtin University said during a minisymposium presentation at the SIAM Conference on Control and Its Applications, which took place virtually this week concurrently with the SIAM Annual Meeting. “And in turn, we can be influenced by others within the group.” People may feel motivated to say certain things or act a certain way due to group leaders, peer pressure, or the desire to fit in or make persuasive arguments. 

Figure 1. An example simulation from the expressed-private-opinion model, showing the evolution of private and expressed opinions for a group of individuals over time.
All of these influences can cause people to change their opinions over time or say things that they do not really believe. “In many different situations, we express a view which is different from our private view,” Ye said. “Sometimes that happens because we feel pressured as part of our group to say something that does not deviate much from the group opinion.” For example, someone might secretly believe that the Earth is flat, but not want to express that opinion while at a scientific conference. 

During his presentation, Ye described a mathematical model for the changes in private and expressed opinions based on external influences and explored its implications for the existing social psychology literature. “How can we mathematically model social influence in social networks, in the context of opinion formation?” he asked. “And how do individual-level dynamics determine the network-level phenomena?” Ye had investigated those questions in collaboration with Ming Cao (University of Groningen), Brian Anderson (Australian National University), Yuzhen Qin (University of California, Riverside), Alain Govaert (Lund University), Weiguo Xia (Dalian University of Technology), and Hong Liang (Dalian University of Technology).

The Friedkin-Johnsen model is a classical way to calculate the change in an individual’s opinion over time, including the influence that one individual exerts on another. This model includes a parameter for susceptibility, which shows the relative strength that social influence exerts over the individual’s own opinion. Individuals with a lower susceptibility are more tied to their initial stance and resistant to changing opinions. A strong diversity of opinions can emerge due to people’s attachment to their initial opinion, resulting in disagreement even when the model reaches a steady state.

Figure 2. A classical social psychology experiment asks participants to say whether the green line on the left is closest in length to line A, B, or C. C is the correct answer.
Ye built upon the Friedkin-Johnsen framework to develop a new model that could determine how both expressed and private opinions change. Qualitatively, the first step in the expressed-private-opinion model is for an individual to express an opinion and hear the expressed opinion of their neighbors. This individual then updates their private opinion, accounting for both their own thoughts and the expressed opinions of others. Finally, the individual accounts for group pressure effects to determine what their new expressed opinion should be. As this process iterates, private and expressed opinions evolve in a coupled manner. 

The calculations in the expressed-private-opinion model capture the individual’s resilience to social pressure — if their resilience is high, they are more likely to say exactly what they think. This stubbornness along with a pressure to conform can lead to the same individual eventually holding different private and expressed opinions. Figure 1 shows one example for the final results in a simulation, in which the expressed opinions fall within a comparatively smaller range that is enclosed by the private opinions. “There is always larger disagreement among the private opinions than what you can observe in the expressed opinions,” Ye said.

Figure 3. A recreation of one of the possible outcomes in the Asch conformity experiments using the expressed-private-opinion model. The participant started out believing that C is the correct answer, which is true. That remains their private belief, but as time progresses their expressed belief becomes closer to the wrong answer due to the pressure to conform.
Next, Ye described an application of this model to the Asch conformity experiments: a classic series of social psychology studies that demonstrated how group pressure can modify and distort an individual’s judgement, even in the face of overwhelming facts. In the scenario that Ye used to represent these experiments, a group of eight participants observe a line and decide which line from a set of three labeled A, B, and C it is most similar to in terms of length (see Figure 2). The participants discuss this question as a group, then each pick an answer and say it out loud. The correct answer is C, but there is a catch: seven out of the eight participants were told ahead of time to pick answer B. The question was then how this sense of consensus on the wrong answer would affect the eighth person.

Based on the Asch conformity experiments, there were three ways that the eighth participant may respond. They might remain insistent that C was the correct answer, or they might tell the group that B was the correct answer but later assert in a post-interview that C was actually true. Finally, that participant might also say B is the right answer in front of the group and stick with that statement in the post-interview. 

By adjusting the parameters for stubbornness and resilience, Ye was able to recreate all three of these outcomes in the expressed-private-opinion model. Figure 3 shows an example simulation of the second reaction. Here, the participant starts out believing that C is correct; however, the participant’s lack of resilience to social pressure leads them to express an opinion that is much closer to the wrong answer.

Figure 4. A simulation depicting pluralistic ignorance. Out of 200 total individuals in the network, there are five zealots with extreme views (in red). The zealots pull the expressed opinions of everyone else in the network (in green) closer to their own opinions over time, while the public’s private opinions (in blue) stay largely the same.
The model was also able to recreate the phenomenon of pluralistic ignorance. “Pluralistic ignorance is when the majority of a group privately hold one particular view, but mistakenly assume that the majority supports a different view,” Ye said. Figure 4 shows the results from a simulation of this effect. The presence of only five highly stubborn and resilient zealots with extreme views in a network of 200 people led to the development of pluralistic ignorance among the general population — the expressed opinions among the group grew to be closer to that of the zealots over time, while their private opinions stayed largely the same.

Ye is currently collaborating with social psychologists at the University of Groningen to gather field data on opinions regarding sustainable behavior in the local community that, in combination with the model, may lend more insight into opinion dynamics. A preliminary analysis of the questionnaires and surveys has already been able identify pluralistic ignorance, and further research in tandem with the expressed-private-opinion model will hopefully shed even more insight on the social phenomena of shared and private opinions. 

  Jillian Kunze is the associate editor of SIAM News


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