# Mean Field Voter Model of Election to the House of Representatives in Japan

## TL;DR

This paper introduces a mean field voter model for Japanese House of Representatives elections, capturing voter behavior with fixed supporters and herding voters, and successfully estimates voter composition and herding ratios from real election data.

## Contribution

It presents a novel mechanical model of plurality elections incorporating fixed supporters and herding voters, with empirical estimation from Japanese election data.

## Key findings

- Estimated herding ratio p aligns with survey data.
- Spatial inhomogeneity of fixed supporters explains correlations.
- Model accurately reproduces election vote-share distributions.

## Abstract

In this study, we propose a mechanical model of a plurality election based on a mean field voter model. We assume that there are three candidates in each electoral district, i.e., one from the ruling party, one from the main opposition party, and one from other political parties. The voters are classified as fixed supporters and herding (floating) voters with ratios of $1-p$ and $p$, respectively. Fixed supporters make decisions based on their information and herding voters make the same choice as another randomly selected voter. The equilibrium vote-share probability density of herding voters follows a Dirichlet distribution. We estimate the composition of fixed supporters in each electoral district and $p$ using data from elections to the House of Representatives in Japan (43rd to 47th). The spatial inhomogeneity of fixed supporters explains the long-range spatial and temporal correlations. The estimated values of $p$ are close to the estimates obtained from a survey.