Opinion evolution in closed community.

Opinion evolution in closed community.

17 Jan 2001 | Katarzyna Sznajd-Weron¹ and Józef Sznajd²
A simple Ising spin model is proposed to describe decision-making in a closed community. The model shows that simple rules lead to complex dynamics and a power-law distribution of decision times. In a closed community, the system evolves to either a dictatorship or a stalemate state, where no common decision can be made. A common decision can only be reached in an open community through a democratic process. The model uses Ising spins to represent opinions (A or B). Three stable states are considered: all A, all B, and 50-50 split. The dynamics are governed by rules that influence neighboring spins based on the opinion of a pair. These rules lead to the three steady states, with the 50-50 state being achieved through a special mechanism where neighbors disagree. Monte Carlo simulations show that the system relaxes to one of the three states, with the 50-50 state being more likely. The decision time (magnetization) follows a power-law distribution with an exponent of -3/2. The distribution of decision times is influenced by initial conditions and noise. The model also shows that small amounts of noise (representing an open community) can lead to disorder and prevent the system from reaching a steady state, allowing for democratic decision-making. The model is tested with different initial conditions and noise levels. It is found that the distribution of decision times follows a power-law regardless of initial conditions. The presence of noise affects the decision time distribution, with the distribution transitioning from a power-law to an exponential as noise increases. The model is discussed in terms of its implications for decision-making in closed communities. It suggests that in a closed community, the final state is either a dictatorship or a stalemate. However, with some noise, the system can reach a more democratic state. The model also shows that a small group can lead to a stalemate, but a larger group is needed to change the majority opinion. The model's results are compared to empirical data on social mood, showing similar patterns. The model is also compared to other Ising spin models, showing that different rules can lead to different outcomes. The model's results suggest that the decision-making process in closed communities is complex and can lead to different outcomes depending on initial conditions and noise levels. The model's findings have implications for understanding decision-making in social systems and the role of noise in influencing collective decisions.A simple Ising spin model is proposed to describe decision-making in a closed community. The model shows that simple rules lead to complex dynamics and a power-law distribution of decision times. In a closed community, the system evolves to either a dictatorship or a stalemate state, where no common decision can be made. A common decision can only be reached in an open community through a democratic process. The model uses Ising spins to represent opinions (A or B). Three stable states are considered: all A, all B, and 50-50 split. The dynamics are governed by rules that influence neighboring spins based on the opinion of a pair. These rules lead to the three steady states, with the 50-50 state being achieved through a special mechanism where neighbors disagree. Monte Carlo simulations show that the system relaxes to one of the three states, with the 50-50 state being more likely. The decision time (magnetization) follows a power-law distribution with an exponent of -3/2. The distribution of decision times is influenced by initial conditions and noise. The model also shows that small amounts of noise (representing an open community) can lead to disorder and prevent the system from reaching a steady state, allowing for democratic decision-making. The model is tested with different initial conditions and noise levels. It is found that the distribution of decision times follows a power-law regardless of initial conditions. The presence of noise affects the decision time distribution, with the distribution transitioning from a power-law to an exponential as noise increases. The model is discussed in terms of its implications for decision-making in closed communities. It suggests that in a closed community, the final state is either a dictatorship or a stalemate. However, with some noise, the system can reach a more democratic state. The model also shows that a small group can lead to a stalemate, but a larger group is needed to change the majority opinion. The model's results are compared to empirical data on social mood, showing similar patterns. The model is also compared to other Ising spin models, showing that different rules can lead to different outcomes. The model's results suggest that the decision-making process in closed communities is complex and can lead to different outcomes depending on initial conditions and noise levels. The model's findings have implications for understanding decision-making in social systems and the role of noise in influencing collective decisions.
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