  In elections, the vote shares or turnout rates show a strong spatial
correlation. The logarithmic decay with distance suggests that a 2D noisy
diffusive equation describes the system. Based on the study of U.S.
presidential elections data, it was determined that the fluctuations of vote
shares also exhibit a strong and long-range spatial correlation. Previously, it
was considered difficult to induce strong and long-range spatial correlation of
the vote shares without breaking the empirically observed narrow distribution.
We demonstrate that a voter model on networks shows such a behavior. In the
model, there are many voters in a node who are affected by the agents in the
node and by the agents in the linked nodes. A multivariate Wright-Fisher
diffusion equation for the joint probability density of the vote shares is
derived. The stationary distribution is a multivariate generalization of the
beta distribution. In addition, we also estimate the equilibrium values and the
covariance matrix of the vote shares and obtain a correspondence with a
multivariate normal distribution. This approach largely simplifies the
calibration of the parameters in the modeling of elections.
