Abstract
In the voter and many other opinion formation models, agents are assumed to behave as congregators (also called the conformists); they are attracted to the opinions of others. In this study I investigate linear extensions of the voter model with contrarian agents. An agent is either congregator or contrarian and assumes a binary opinion. I investigate three models that differ in the behavior of the contrarian toward other agents. In model 1, contrarians mimic the opinions of other contrarians and oppose (i.e., try to select the opinion opposite to) those of congregators. In model 2, contrarians mimic the opinions of congregators and oppose those of other contrarians. In model 3, contrarians oppose anybody. In all models, congregators are assumed to like anybody. I show that even a small number of contrarians prohibits the consensus in the entire population to be reached in all three models. I also obtain the equilibrium distributions using the van Kampen small-fluctuation approximation and the Fokker-Planck equation for the case of many contrarians and a single contrarian, respectively. I show that the fluctuation around the symmetric coexistence equilibrium is much larger in model 2 than in models 1 and 3 when contrarians are rare.
Highlights
Dynamics of collective opinion formation is widely studied in various disciplines including statistical physics
The effects of contrarians have been examined in the so-called minority game [28]. In contrast to these nonlinear models, I focus on three linear extensions of the voter model with contrarian agents
Where ∗ denotes the values in the equilibrium
Summary
Dynamics of collective opinion formation is widely studied in various disciplines including statistical physics. The effects of contrarians have been examined in the so-called minority game [28] In contrast to these nonlinear models, I focus on three linear extensions of the voter model with contrarian agents (i.e., quenched randomness). Each contrarian in state 0 independently flips to state 1 with the rate equal to the sum of the number of 0 congregators and that of 1 contrarians. Each contrarian in state 0 flips to state 1 with the rate equal to the sum of the number of 1 congregators and that of 0 contrarians. Each contrarian in state 0 flips to state 1 with the rate equal to the sum of the number of 0 agents.
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