Ideology and Existence of 50%-Majority Equilibria in Multidimensional Spatial Voting Models

Abstract:     
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 we assume that a lower d-dimensional (d < n) linear map spans the possible candidates' platforms. These d 'ideological' dimensions imply some linkages between the n political issues. We randomize over these linkages and show that there almost surely exists a 50%-majority equilibrium 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.

Number of Pages in PDF File: 22

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