Numerical Analyses of Collective Opinions in Social Networks and Digital Democracy

In big data engineering and digital democracy, modern mathematical means and methodologies may be introduced into voting and election data analyses in order to gain rigorous perspectives and insights of data implications. This paper formally analyzes the nature and mechanisms of voting systems and the derivation of collective opinion equilibrium. A set of numerical technologies for collective opinions analyses is presented in social networks, online voting, and general elections. The conventional methods such as those of simple max finding, average weighted sum, and statistics are enhanced by rigorous numerical regressions and weighted opinion integrations. These novel methodologies lead to the finding of a key concept known as collective opinion equilibrium implied in any voting and election, which denotes the representative centriod elicited from the spectrum of opinion distribution. A set of case studies on real-world general electron data is rigorously analyzed for demonstrating the value-added applications of the formal methods in poll data mining, collective opinion determination, and quantitative election data processing.