Downsian competition in the absence of a condorcet winner

This paper studies studies two-party electoral competition in a setting where no policy is unbeatable. It is shown that if parties take turns in choosing platforms and observe each other's choises, altering one's platform so as to win is pointless since the other party never accepts an outcome where it is sure to loose. If there is any cost to changing platform, the prediction is that the game ends in the first period with the parties converging on whatever platform the incumbent chooses. If, however, there is a slight chance of a small mistake, the incumbent does best in choosing a local equilibrium platform. This suggest that local equilibrium policies can be the predicted outcome even if the voting process is not myopic in any way. -- Voting ; Downsian competition ; Local equilibrium ; Spatial trembles