A Spatial Theory of Ostracism

We investigate a variant of the Hotelling-Downs model where politicians choose their policies under ostracism with each voter voting for the politician whose policy is least preferable for him and the politician obtaining the most votes being expelled. We present a necessary and sufficient condition for a strategy tuple to be a Nash equilibrium and show that in any Nash equilibrium, politicians' policies are same. We identify the equilibrium policy set such that a politicians' policy tuple is a Nash equilibrium if and only if all policies in the tuple are the same policy in the equilibrium policy set. We also show that under mild assumptions, the equilibrium policy set is a superset of the set of medians in all directions, bounded, closed, convex, increasing in the number of politicians, convergent to the convex hull of the support of voters' ideal policy distribution as the number of politicians tends to infinity, and nonempty for a sufficiently large population of politicians.