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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 conÞguration 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 equilibria in the above worst-case scenario, when n grows to inÞnity. 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.
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  • HAL Id : hal-01065582, version 1
  • SCIENCESPO : 2441/10277

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Hervé Crès, Utku Unver. Ideology and existence of 50% : Majority equilibria in multidimensional spatial voting models. 2005. ⟨hal-01065582⟩

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