Opinion dynamics

Spatial model of party competition (Hotelling-Downs)

Based on the paper by Christopher Campbell and Graeme J. Ackland

With the associated online game .

This model represents political competition in a two-dimensional opinion space. The axes correspond to two possible policy positions (e.g. economic and cultural) Each point in the square corresponds to a possible political position, and voters are distributed across that space according to one of several voter-density models.

Parties are also represented as points in the same opinion space. Each voter is assumed to support the nearest party. The total support for a party therefore comes from the region of opinion space for which that party is closest.

Turnout may depend on distance. When turnout weighting is active, voters who are further from the nearest party contribute less strongly than voters who are close to it. The parameter tau controls the strength of this effect.

Party movement is determined by a simple adaptive rule. In greedy mode, each party searches nearby positions and moves if a better one is found. In metropolis mode, parties make stochastic trial moves, so positions may sometimes change even when the move is not immediately beneficial. The parameter T_mc represents the volatility - large values mean the parties are more likely to make non-beneficial moves.

The parameter alpha determines how much a party values vote share relative to staying close to the centre of the voters assigned to it. When alpha = 1, parties care only about vote share. Smaller values of alpha introduce an attraction toward the centroid of their support.

Three voter distributions are available:

• flat: uniform voter density across the whole opinion space
• two_peak: two Gaussian concentrations of voters, separated by m
• covariant: an anisotropic Gaussian-like distribution with an additional correlation term, controlled by a_xy and alpha_xy

The figure shows the final partition of opinion space, density contours of the voter distribution, the trajectories of the parties during the simulation, and the marginal voter densities in the horizontal and vertical directions.

Adjust the controls and then click Run simulation to explore how the number of parties, turnout effects, voter distribution, and update rule affect the final political configuration.