content_image/306862.jpg
## Accept-Shift-Constrict Model of Opinion Dynamics 

The RPM model is simple and intuitive but does not describe the dynamical process by which proximate majorities form. To do so, we introduce the accept-shift-constrict model of opinion dynamics on networks in which majorities emerge and persist as a consequence of micro-level attitude change dynamics. 

The ASC model evolves both the positions and uncertainties of group members in response to their dyadic interactions. We consider position first, which can be a policy or, more generally, an opinion about some matter. A persuasive message sent by one group member to another must first be accepted by the recipient in order to shift their policy. While a number of factors can affect whether a message is accepted (McGuire 1985), the distance between the message’s rhetorical issue position and the receiver’s rhetorical issue position plays the key role in our model: if the distance is within the “latitude of acceptance” (LOA), a term borrowed from social judgment theory (Sherif and Hovland 1961), the message is likely to be accepted, but the acceptance probability rapidly decays beyond the LOA. If the message is accepted, then the receiver’s policy is shifted in proportion to its distance from the sender’s policy. 

Formally, we encode the above process as an ordinary differential equation for x$_{i}$ ( t ), the policy position of the i th group member at time t . For a group with N members, the rate of change of x$_{i}$ is given by 

<img src='content_image/306862.jpg'>

where κ$_{ij}$ is the coupling strength from j → i and λ$_{i}$ is i ’s LOA. The matrix formed by the coupling strengths defines a policy-independent network of influence. In general, κ$_{ij}$ depends on communication rate and other factors such as credibility and expertise 

