Ideology and existence of 50%-majority equilibria in multidimensional spatial voting models

When aggregating individual preferences through the majority rule in an n-dimensional spatial voting model, the "worst-case" scenario is a social choice configuration where no political equilibrium exists unless a super majority rate as high as 1-1/n is adopted. In this paper the authors assume that a lower d-dimensional (d<n)linear map spans the possible candidates plateforms. These d "ideological" dimensions imply some linkages between the n political issues. The authors randomize over these linkages and show that there almost surely exists a50%-majority equilibria in the above worst-case scenario, when n grows to infinity.Moreover the equilibrium is the mean voter. The speed of convergence (toward 50%)of the super majority rate guaranteeing existence of equilibrium is computed for d= 1 and 2.