Can Ambiguity in Electoral Competition be Explained by Projection Effects in Voters' Perceptions?

Studies in political science and psychology suggest that voters' perceptions of political positions depend on their personal views of the candidates. A voter who likes/dislikes a candidate will perceive his position as closer to/further from his own than it really is (projection). Clearly these effects should be most pronounced when candidate positions are ambiguous. Thus a generally well liked candidate will have an incentive to take an ambiguous position. In this paper we construct a simple model to see under which conditions this incentive survives in the strategic setting of electoral competition, even if voters dislike ambiguity per se.