title: The Undecided Have the Key: Interaction-Driven Opinion Dynamics in a Three State Model.
abstract: The effects of interpersonal interactions on individual's agreements result in a social aggregation process which is reflected in the formation of collective states, as for instance, groups of individuals with a similar opinion about a given issue. This field, which has been a longstanding concern of sociologists and psychologists, has been extended into an area of experimental social psychology, and even has attracted the attention of physicists and mathematicians. In this article, we present a novel model of opinion formation in which agents may either have a strict preference for a choice, or be undecided. The opinion shift emerges, in a threshold process, as a consequence of a cumulative persuasion for either one of the two opinions in repeated interactions. There are two main ingredients which play key roles in determining the steady states: the initial fraction of undecided agents and the change in agents' persuasion after each interaction. As a function of these two parameters, the model presents a wide range of solutions, among which there are consensus of each opinion and bi-polarization. We found that a minimum fraction of undecided agents is not crucial for reaching consensus only, but also to determine a dominant opinion in a polarized situation. In order to gain a deeper comprehension of the dynamics, we also present the theoretical framework of the model. The master equations are of special interest for their nontrivial properties and difficulties in being solved analytically.
authors.affiliation: Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires and IFIBA, CONICET, Buenos Aires, Argentina.
authors.forename: Pablo
authors.initials: P
authors.lastname: Balenzuela
authors.affiliation: Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires and IMAS UBA-CONICET, Buenos Aires, Argentina.
authors.forename: Juan Pablo
authors.initials: JP
authors.lastname: Pinasco
authors.affiliation: Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Buenos Aires, Argentina; Instituto Interdisciplinario de Economía Política de Buenos Aires (IIEP-BAIRES), Facultad de Ciencias Económicas, Universidad de Buenos Aires, Buenos Aires, Argentina.
authors.forename: Viktoriya
authors.initials: V
authors.lastname: Semeshenko
mesh_terms: D003657:Decision Making; D006126:Group Processes; D006801:Humans; D007398:Interpersonal Relations; D008960:Models, Psychological; D000067074:Peer Influence; D010565:Persuasive Communication