Social interaction radius effects on three-state consensus resilience*

The underlying mechanisms of human group behavior drive several aspects of social relations, organization, and dynamics, often exhibiting emergent properties that result from joint interactions. This work investigates collective decision-making processes via a three-state opinion formation model within the continuous network framework. We randomly place individuals as nodes on a unit square area with links representing social interactions within an influence radius, which we relate to the average connectivity 〈k〉 of the network. We implement a majority-vote dynamics in which individuals may assume one of three distinct opinions regarding a social subject under the influence of a social anxiety level q. We find a consensus-dissensus continuous transition responsive to the individual's social interaction radius. Using Monte Carlo simulations and finite-size scaling analysis, we obtain the order-disorder phase diagram q versus〈k〉and the critical exponents. Our findings suggest that larger communities exhibit greater resilience against the disruptive impact of disorder caused by social anxiety.