Mixed equilibrium in a Downsian model with a favored candidate. (English) Zbl 1050.91028

Two candidates simultaneously choose positions on a finite set of points in a one-dimensional policy space. A voter votes for the candidate closest to his or her ideal policy position. If there are no extraneous factors, both candidates adopt a median position and each has a \(\frac{1}{2}\) probability of winning. However, in normal elections, extraneous factors do intrude. In this paper the authors analyze the situation where one candidate enjoys an ‘image’ advantage over the other. The advantage is taken to be constant for all voters. The principal focus of the authors is the situation where the image advantage is small (less than the distance between the points in the policy-space). The authors show that under certain assumptions, the candidate with the advantage chooses a centralist policy stance, but the equilibrium strategy is mixed, while the disadvantaged candidate chooses a mixed U-shaped strategy to establish the distance from the advantaged candidate. The pure strategy result when there is no advantage is shown to be a degenerate limiting case as the advantage tends to zero.


91B12 Voting theory
91B72 Spatial models in economics
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