The Downsian model predicts divergence

The 'Downsian' model is widely held to predict the convergence of parties t o the median in two-party systems with unidimensional policy spaces. We sho w this is not true, if voters are uncertain. This paper gives an exposition of the two-party divergence results, including (1) if both candidates are free to move, but the incumbent has lower variance of policy action as perc eived by voters, then there is no equilibrium, even if preferences are 'sin gle-peaked'; (2) if the lower-variance candidate is forced to run on a fixe d record, then an equilibrium platform exists for the challenger, but it al ways diverges from incumbent's platform; (3) if the incumbent's perceived p olicy once in office has a lower variance than any prospective challenger, the incumbent may win each of a long series of elections even if the incumb ent's policy choices diverge from the underlying median of the distribution of voter preferences.