In this paper we study a model of political competition where citizens vote
sincerely and candidates may be either citizens or Downsian politicians.
The model extends the citizen-candidate model proposed by Osborne and
Slivinski [1996] by including Downsian politicians similar to those studied
by Osborne [1993]. We give necessary and sufficient conditions for existence,
together with complete characterisation, of one party and two party Nash
equilibria in our model. An important feature, in view of the Duverger's
Law, of the two-party equilibrium is that these equilibria cannot have any
Downsian contestant. Moreover, we compare our model with that studied
by Osborne and Slivinski [1996], showing that in both cases there exist po-
litical configurations that can appear in one of the models only. We show
also that in our settings it is possible to have Nash equilibria with Downsian
candidates, without requiring to have very restrictive constraints on the dis-
tribution function. We also argue that as the number of parties in equilibrium
increases, the `likelihood' of an ideology driven citizen-candidate winning the
elections and running the government falls. Finally we argue that in any
equilibrium extremist parties proposing their policies uniquely are typically
ideology-driven as well.