Voter model on networks and the multivariate beta distribution.

Area of Science:

• Computational Social Science
• Statistical Physics
• Political Science

Background:

• Electoral data, including vote shares and turnout, exhibit significant spatial correlations.
• Previous models struggled to explain strong, long-range spatial correlations in vote shares without disrupting observed distributions.

Purpose of the Study:

• To demonstrate that a voter model on networks can generate strong and long-range spatial correlations in vote shares.
• To develop a mathematical framework for understanding these correlations in electoral systems.

Main Methods:

• Utilized a voter model where agents within nodes and linked nodes influence each other.
• Derived a multivariate Wright-Fisher diffusion equation to model the joint probability density of vote shares.
• Estimated equilibrium values and the covariance matrix of vote shares.

Main Results:

• The voter model successfully reproduces strong and long-range spatial correlations in vote shares.
• The derived stationary distribution is a multivariate generalization of the beta distribution.
• A correspondence with a multivariate normal distribution was established, simplifying parameter calibration.

Conclusions:

• A network-based voter model provides a robust explanation for spatial correlations in election outcomes.
• The mathematical framework simplifies the analysis and calibration of electoral models.
• This approach offers new insights into the dynamics of political opinion formation and spatial dependence.