Reinforcement in opinion dynamics
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I consider the evolution and acceptance of a new opinion in a population of unaware agents by using physics-based models of contagion spread. These models rely upon agentbased dynamics, in which an agent changes opinion by interactions with neighbors according to specific interactions. Most of these models have the feature that only a single input is required to change the opinion of an agent - an agent has no commitment to its current opinion and accepts a new idea at the slightest provocation. These single-input models fail to account for people's confidence in their own beliefs. Thus I study the concept of social reinforcement - that an agent adopts a new opinion only after multiple reinforcing prompts. Building on single-input models, I introduce two models of opinion spreading that incorporate a social reinforcement mechanism. (a) In the irreversible innovation and in the transient fad spreading models, a development is initially known only to a small portion of the population and subsequently spreads. An individual requires M > 1 interactions with an adopter before adopting the development. The ultimate extent of a transient fad depends critically on the characteristic time the fad keeps the attention of an adopting agent. (b) In the confident voter model, a voter can be in one of two opinion states and can additionally have two levels of commitment to an opinion: confident and vacillating. Upon interacting with an agent of a different opinion, a confident voter becomes less committed, or vacillating, but does not change opinion. However, a vacillating agent changes opinion by interacting with an agent of a different opinion. In two dimensions, the distribution of consensus times is characterized by two distinct times one that scales linearly with N and another that appears to scale as N^3/2. The longer time arises from configurations that fall into long-lived states that consist of multiple single-opinion stripes before consensus is reached.
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