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Register a new userThe ambiguous role of social influence on the wisdom of crowds: An analytic approach
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Wisdom of crowds refers to the phenomenon that the average opinion of a group of individuals on a given question can be very close to the true answer. It requires a large group diversity of opinions, but the collective error, the difference between the average opinion and the true value, has to be small. We consider a stochastic opinion dynamics where individuals can change their opinion based on the opinions of others (social influence $alpha$), but to some degree also stick to their initial opinion (individual conviction $beta$). We then derive analytic expressions for the dynamics of the collective error and the group diversity. We analyze their long-term behavior to determine the impact of the two parameters $(alpha,beta)$ and the initial opinion distribution on the wisdom of crowds. This allows us to quantify the ambiguous role of social influence: only if the initial collective error is large, it helps to improve the wisdom of crowds, but in most cases it deteriorates the outcome. In these cases, individual conviction still improves the wisdom of crowds because it mitigates the impact of social influence.
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We propose an agent-based model of collective opinion formation to study the wisdom of crowds under social influence. The opinion of an agent is a continuous positive value, denoting its subjective answer to a factual question. The wisdom of crowds states that the average of all opinions is close to the truth, i.e. the correct answer. But if agents have the chance to adjust their opinion in response to the opinions of others, this effect can be destroyed. Our model investigates this scenario by evaluating two competing effects: (i) agents tend to keep their own opinion (individual conviction $beta$), (ii) they tend to adjust their opinion if they have information about the opinions of others (social influence $alpha$). For the latter, two different regimes (full information vs. aggregated information) are compared. Our simulations show that social influence only in rare cases enhances the wisdom of crowds. Most often, we find that agents converge to a collective opinion that is even farther away from the true answer. So, under social influence the wisdom of crowds can be systematically wrong.
Pedestrians are often encountered walking in the company of some social relations, rather than alone. The social groups thus formed, in variable proportions depending on the context, are not randomly organised but exhibit distinct features, such as the well-known tendency of 3-member groups to be arranged in a V-shape. The existence of group structures is thus likely to impact the collective dynamics of the crowd, possibly in a critical way when emergency situations are considered. After turning a blind eye to these group aspects for years, endeavours to model groups in crowd simulation software have thrived in the past decades. This fairly short review opens on a description of their empirical characteristics and their impact on the global flow. Then, it aims to offer a pedagogical discussion of the main strategies to model such groups, within different types of models, in order to provide guidance for prospective modellers.
Human groups can perform extraordinary accurate estimations compared to individuals by simply using the mean, median or geometric mean of the individual estimations [Galton 1907, Surowiecki 2005, Page 2008]. However, this is true only for some tasks and in general these collective estimations show strong biases. The method fails also when allowing for social interactions, which makes the collective estimation worse as individuals tend to converge to the biased result [Lorenz et al. 2011]. Here we show that there is a bright side of this apparently negative impact of social interactions into collective intelligence. We found that some individuals resist the social influence and, when using the median of this subgroup, we can eliminate the bias of the wisdom of the full crowd. To find this subgroup of individuals more confident in their private estimations than in the social influence, we model individuals as estimators that combine private and social information with different relative weights [Perez-Escudero & de Polavieja 2011, Arganda et al. 2012]. We then computed the geometric mean for increasingly smaller groups by eliminating those using in their estimations higher values of the social influence weight. The trend obtained in this procedure gives unbiased results, in contrast to the simpler method of computing the median of the complete group. Our results show that, while a simple operation like the mean, median or geometric mean of a group may not allow groups to make good estimations, a more complex operation taking into account individuality in the social dynamics can lead to a better collective intelligence.
During the unfolding of a crisis, it is crucial to determine its severity, yet access to reliable data is challenging. We investigate the relation between geolocated Tweet Intensity of initial COVID-19 related tweet at the beginning of the pandemic across Italian, Spanish and USA regions and mortality in the region a month later. We find significant proportionality between early social media reaction and the cumulative number of COVID-19 deaths almost a month later. Our findings suggest that the crowds perceived the risk correctly. This is one of the few examples where the wisdom of crowds can be quantified and applied in practice. This can be used to create real-time alert systems that could be of help for crisis-management and intervention, especially in developing countries. Such systems could contribute to inform fast-response policy making at early stages of a crisis.
We show how the prevailing majority opinion in a population can be rapidly reversed by a small fraction p of randomly distributed committed agents who consistently proselytize the opposing opinion and are immune to influence. Specifically, we show that when the committed fraction grows beyond a critical value p_c approx 10%, there is a dramatic decrease in the time, T_c, taken for the entire population to adopt the committed opinion. In particular, for complete graphs we show that when p < p_c, T_c sim exp(alpha(p)N), while for p > p_c, T_c sim ln N. We conclude with simulation results for ErdH{o}s-Renyi random graphs and scale-free networks which show qualitatively similar behavior.
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