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Social Learners Impact Outcome of Group Decision-making

By Jillian Kunze

Many people follow along with their family or friends to make voting decisions in a herd-following behavior called social learning, instead of evaluating the merits of different options on their own in individual learning. Online echo chambers—social media communities that continually reinforce one particular viewpoint—may exacerbate this kind of herding. “Many, if not most, of U.S. voters do not know basic facts about how the government functions and cannot tell you about the policies they're voting for,” Vicky Chuqiao Yang of the Santa Fe Institute said. During a minisymposium presentation at the 2021 SIAM Conference on Applications of Dynamical Systems, which took place virtually this week, Yang described her inquiry into whether a collective group of people can make good decisions when a certain proportion of the population is made up of social learners.

Figure 1. The proportion of a group that supports option X versus the proportion of social learners in the group, for a situation in which options X and Y have equal merit. The group remains at a 50-50 split of opinions when the proportion of social learners is low, but begins to overwhelmingly favor X or Y when the proportion of social learners becomes larger.
A number of previous studies have explored collective decision-making and come to somewhat contradictory conclusions. Some research has found that social learners hurt decision-making outcomes, since they act as free riders and do not add anything new to the conversation. Other studies have found that social learners help groups make cohesive decisions by talking to each other and spreading information and opinions. There have likely been such conflicting results because collective decisions are an outcome of very complex interactions that depend on many different factors, such as the number of social learners in a group. Researchers often study these factors in isolation, leading to vastly different outcomes from studies. 

Yang, herself an applied mathematician, worked with an interdisciplinary team to pursue this question: psychologist Mirta Galesic, economist Ani Harutyunyan, and undergraduate student Harvey McGuinness. “Our goal was to create a general mathematical framework that allows for studying the effects of multiple social and psychological factors simultaneously,” Yang said. She and her collaborators created a mathematical model with a well-mixed population of both social and individual learners who must make a binary choice between options X and Y. There is a relative merit to each option that is determined by how many people would choose that option if they evaluated all the relevant information. If 70% of the population would value option X if they had perfect information, for example, then X has a merit of 0.7. There is no single option that is universally the most meritorious, because people with the same information often come to different conclusions.

Figure 2. The proportion of a group that supports option X versus the proportion of social learners in the group, for a situation in which option X has more merit than option Y. If the proportion of social learners is low, the group favors option X. But if the proportion of social learners is high, the group may choose either outcome.
The social learners in the model had two possible motivations. Normative conformity is motivated by fitting in, while information conformity is motivated by finding the best option — like looking through a playlist of popular music to figure out what songs to play. The distinction between the two is important, since different mathematical functions govern the different motivations. 

Figure 1 shows the model’s predictions in the case where options X and Y have equal merit, and where the social learners are motivated by normative conformity. When the proportion of social learners is low, the group unsurprisingly stabilizes at a 50-50 split between both options. But when there is a large number of social learners, that 50-50 split becomes unstable, and group members begin to overwhelmingly favor one or the other option. Figure 2 shows a second situation in which option X has more merit than option Y. When the proportion of social learners is low in this scenario, the population always reaches the more meritorious decision. But with a higher number of social learners, the group is not guaranteed to reach the better outcome and could possibly decide on either option.

“A good thing about this model is that it's simple enough to be analytically tractable,” Yang said. It is possible to calculate the critical transition point at which the group switches from favoring one option to another, and the simplicity of the model also allows for extensions and adaptations. For example, it is possible to add an individual-social learning spectrum to the model in which a person is not strictly an individual or social learner, but somewhere on the continuum between them (see Figure 3). This analysis reveals that the bifurcating behavior seen in Figure 1 was not artificially created by the dichotomy between individual and social learners, but is actually generalizable.

Figure 3. One extension of the collective decision-making model was to allow individuals to sit somewhere on the spectrum between individual and social learners, instead of being strictly one or the other.
Overall, the model was able to characterize collective decision-making problems with three parameters: merit, conformity function, and proportion of social versus individual learners. These three parameters acting in combination created a broad variety of phenomena at the group level, indicating that the same model can explain the seemingly conflicting findings from earlier studies. Since this model is analytically tractable, it is also possible to expand its simulations and develop conclusions that would be applicable to many different behaviors. “The model offers a flexible mathematical framework that can be extended or adapted to study the interactions of a wide range of social and psychological factors,” Yang said.

Yang hopes to further test the model using real-world observations from the World Values Survey, which contains data on the levels of collectivism versus individualism across different countries. She may also add more interesting factors to the model such changes in merit association over time—possibly due to social media—and the presence of committed minority groups. Currently, Yang is collaborating with a psychologist to create online group experiments that will further explore the complicated process of collective decision-making. 

  Jillian Kunze is the associate editor of SIAM News