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Dynamics of majority rule with differential latencies
1IRIDIA, CoDE, Université Libre de Bruxelles, Brussels, B-1050 Belgium. ascheidler@iridia.ulb.ac.be
Summary
This study explores opinion formation with voter latency, finding that shorter opinion adoption times create a bias toward consensus. The research quantifies consensus dynamics in voter systems.
Area of Science:
- Social dynamics and opinion formation modeling.
- Statistical physics of social systems.
- Agent-based modeling and simulation.
Background:
- The majority-rule opinion formation model is a key framework for understanding social consensus.
- Voter latency, where individuals are temporarily excluded from decision-making, is a realistic factor not typically included.
- Differential latencies, varying by opinion, can introduce biases into consensus-building processes.
Purpose of the Study:
- To investigate the impact of differential voter latencies on the majority-rule opinion formation model.
- To analyze how varying durations of latent states influence the speed and outcome of consensus.
- To mathematically characterize the consensus dynamics and time to consensus in such systems.
Main Methods:
- Extension of the standard majority-rule model to incorporate differential voter latencies.
- Calculation of exit probabilities and time to consensus for finite systems of N voters.
- Derivation of an asymptotic characterization using a continuum model for large systems.
Main Results:
- Differential latencies introduce a bias towards consensus on the opinion with the shorter associated latency.
- The study provides quantitative measures for the exit probability and time to reach consensus.
- An asymptotic analysis offers insights into consensus dynamics in large-scale systems.
Conclusions:
- Voter latency, particularly when differential, significantly alters opinion formation dynamics.
- The model predicts a predictable bias in consensus based on latency durations.
- The findings have implications for understanding opinion spread and convergence in networks with communication delays.
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