Mystifying but Not Misleading: When does Political Ambiguity Not Confuse Voters?

The purpose of political campaigns in democracies is to provide voters with information that allows them to make ``correct'' choices, that is, vote for the party/candidate whose proposed policy or ``position'' is closest to their ideal position. In the world where political talks are often ambiguous and imprecise, it then becomes important to understand whether correct choices can still be made. In this paper we identify two elements of political culture that are key to answering this question: (i) whether or not political statements satisfy a so-called ``grain of truth'' assumption, and (ii) whether or not politicians make statements which are comparative, that is contain information about politicians' own position relative to that of their adversaries. The ``grain of truth'' assumption means that statements, even if vague, do not completely misrepresent the true positions of the parties. We find that only in case when political campaigning is comparative and has a grain of truth, voters will always make correct choices as if they were fully informed. Therefore, imprecision of political statements should not be a problem as long as comparative campaigning is in place.