# Solution of the multistate voter model and application to strong neutrals in the naming game.

@article{Pickering2015SolutionOT, title={Solution of the multistate voter model and application to strong neutrals in the naming game.}, author={William Pickering and Chjan C. Lim}, journal={Physical review. E}, year={2015}, volume={93 3}, pages={ 032318 } }

We consider the voter model with M states initially in the system. Using generating functions, we pose the spectral problem for the Markov transition matrix and solve for all eigenvalues and eigenvectors exactly. With this solution, we can find all future probability probability distributions, the expected time for the system to condense from M states to M-1 states, the moments of consensus time, the expected local times, and the expected number of states over time. Furthermore, when the…

## 12 Citations

### Multistate voter model with imperfect copying.

- MathematicsPhysical review. E
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A variant of the multistate voter model in mean field that incorporates a degree of imperfection or error in the copying process, which leaves the states of the two interacting individuals similar but not exactly equal is introduced.

### Zealots in multistate noisy voter models.

- MathematicsPhysical review. E
- 2021

It is found that the phase behavior diversifies, with up to six possible qualitatively different types of stationary states, and situations in which zealots affect the entire population, or only a fraction of agents, are analyzed, which corresponds to a single-community model with a fractional number of zealots.

### Finite-size effects on the convergence time in continuous-opinion dynamics.

- MathematicsPhysical review. E
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Finite-size effects on the convergence time in a continuous-opinion dynamics model finds that the characteristic time to the convergence increases as the system size increases according to a particular functional form in the case of lattice networks.

### Flocking dynamics with voter-like interactions

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We study the collective motion of a large set of self-propelled particles subject to voter-like interactions. Each particle moves on a 2D space at a constant speed in a direction that is randomly…

### Engineering Agreement: The Naming Game with Asymmetric and Heterogeneous Agents

- Computer ScienceAAAI
- 2017

It is shown that increasing asymmetry in network topology can improve convergence rates and how consensus can be manipulated when stubborn nodes are introduced at different points of the process is analyzed.

### Solution to urn models of pairwise interaction with application to social, physical, and biological sciences.

- MathematicsPhysical review. E
- 2017

The dynamics on uncorrelated heterogeneous degree sequence networks are analyzed and the convergence times to the moments of the degree sequences for various pairwise interaction mechanisms are related.

### Analysis of the high dimensional naming game with committed minorities

- PhysicsPhysical review. E
- 2016

The results suggest that committed minorities can more easily conquer highly diverse systems, showing them to be inherently unstable.

### Filter bubble effect in the multistate voter model.

- Computer ScienceChaos
- 2022

A multistate voter model where, with a given probability λ, a user interacts with "personalized information," suggesting the opinion most frequently held in the past is investigated, showing the existence of a nontrivial transition between a region where a consensus is reached and a region (above a threshold λc) where the system gets polarized and clusters of users with different opinions persist indefinitely.

### Solution of urn models by generating functions with applications to social, physical, biological, and network sciences

- Mathematics
- 2016

The method of solution given in this thesis easily solves the Ehrenfest model, where the original generating function method of Kac does not solve the general urn models easily.

### Opinion Diversity and the Stability of Social Systems: Implications from a Model of Social Influence

- Economics
- 2015

The results suggest that committed minorities can more easily conquer highly diverse systems, showing them to be inherently unstable.

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