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The Undecided Have the Key: Interaction-Driven Opinion Dynamics in a Three State Model.

Balenzuela P, Pinasco JP, Semeshenko V - PLoS ONE (2015)

Bottom Line: 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.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.The master equations are of special interest for their nontrivial properties and difficulties in being solved analytically.

View Article: PubMed Central - PubMed

Affiliation: Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires and IFIBA, CONICET, Buenos Aires, Argentina.

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.

No MeSH data available.


Fundamental Phase Diagram.Dominant steady state solution as a function of P0 and Δ. We identify three different regions: region T0, convergence of undecided; region T+T−, consensus of opinions +1/-1 and region Tbp, bi-polarization. In the simulations CT = 1, k = 2, Cmax = 3 were used.
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pone.0139572.g002: Fundamental Phase Diagram.Dominant steady state solution as a function of P0 and Δ. We identify three different regions: region T0, convergence of undecided; region T+T−, consensus of opinions +1/-1 and region Tbp, bi-polarization. In the simulations CT = 1, k = 2, Cmax = 3 were used.

Mentions: Fig 2 shows the Fundamental Phase Diagram (FPD) that depicts existence of different regions of the system under equilibrium. In this Phase Diagram we analyse the prevalence of each equilibria for every pair of values of P0 and Δ within the specific range.


The Undecided Have the Key: Interaction-Driven Opinion Dynamics in a Three State Model.

Balenzuela P, Pinasco JP, Semeshenko V - PLoS ONE (2015)

Fundamental Phase Diagram.Dominant steady state solution as a function of P0 and Δ. We identify three different regions: region T0, convergence of undecided; region T+T−, consensus of opinions +1/-1 and region Tbp, bi-polarization. In the simulations CT = 1, k = 2, Cmax = 3 were used.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4593537&req=5

pone.0139572.g002: Fundamental Phase Diagram.Dominant steady state solution as a function of P0 and Δ. We identify three different regions: region T0, convergence of undecided; region T+T−, consensus of opinions +1/-1 and region Tbp, bi-polarization. In the simulations CT = 1, k = 2, Cmax = 3 were used.
Mentions: Fig 2 shows the Fundamental Phase Diagram (FPD) that depicts existence of different regions of the system under equilibrium. In this Phase Diagram we analyse the prevalence of each equilibria for every pair of values of P0 and Δ within the specific range.

Bottom Line: 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.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.The master equations are of special interest for their nontrivial properties and difficulties in being solved analytically.

View Article: PubMed Central - PubMed

Affiliation: Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires and IFIBA, CONICET, Buenos Aires, Argentina.

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.

No MeSH data available.