This paper presents a Downsian model of political competition in which parties have incomplete but richer information than voters on policy effects. Each party can observe a private signal of the policy effects, while voters cannot. In this setting, voters infer the policy effects from the party platforms. In this political game with private information, we show that there exist weak perfect Bayesian equilibria (WPBEs) at which the parties play different strategies, and thus, announce different platforms even when their signals coincide. This result is in contrast with the conclusion of the Median Voter Theorem in the classical Downsian model. Our equilibrium analysis suggests similarity between the set of WPBEs in this model and the set of uniformly perfect equilibria of Harsanyi and Selten (1988) in the model with completely informed parties which we studied in a previous paper (Kikuchi, 2010).