Downsian Competition When No Policy is Unbeatable

This paper studies two-party electoral competition in a setting where 1 no policy is unbeatable. It is shown that if parties take turns in choosing policy 2 platforms and observe eachother’s choices, for one party to change position so 3 as to win is pointless since the other party never accepts an outcome where it is 4 sure to loose. If there is any cost to changing platform, the prediction is that the 5 game ends in the first period with the parties converging on whatever platform 6 the incumbent chooses. If, however, there is a slight chance of a small mistake, 7 the incumbent does best in choosing a local equilibrium platform. This suggests 8 that local equilibrium policies can be the predicted outcome even if the voting 9 process is not myopic in any way. 10