This paper studies a continuous one-dimensional spatial model of electoral competition
with two office-motivated candidates differentiated by their “intensity” valence.
All voters agree that one candidate will implement more intensively his announced
policy than his opponent. However, and contrary to existing models, the
intensity valence has a different impact on the utility of voters according to their
position in the policy space. The assumption that voters have utility functions with
intensity valence, an assumption which has been found to be grounded empirically,
generates very different results than those obtained with traditional utility functions
with additive valence. First, the candidate with low intensity valence is supported
by voters whose ideal points are on both extremes of the policy space. Second,
there exist pure strategy Nash equilibria in which the winner is the candidate with
high intensity if the distribution of voters in the policy space is sufficiently homogeneous.
On the contrary, if the distribution of voters in the policy space is very
heterogeneous, there are pure strategy Nash equilibria in which the candidate with
low intensity wins. For moderate heterogeneity of the distribution of voters, there
is no pure strategy Nash equilibrium.