<p>We investigate a variant of the Hotelling–Downs model where at least two politicians choose their policies in a general policy space under ostracism with each voter voting for the least preferred politician and the politician with the most votes being expelled. We show that if there are at least three politicians, or if the policy space is an inner product space and the support of the distribution of voters’ ideal policies is connected, it is necessary and sufficient for a Nash equilibrium that every politician chooses the same policy in a certain set. Furthermore, we show that under mild assumptions, there exists a Nash equilibrium for a sufficiently large population of politicians.</p>