Voters' voting decisions crucially depend on their information. Thus, it is an important question how much / what kind of information they should know, as a normative guidance of the optimal extent of transparency. We consider a simple two-alternative majority voting environment, and study the optimal information disclosure policy by a utilitarian social planner. Although full transparency is sometimes (informally) argued as ideal, we show that full transparency is often strictly suboptimal. This is basically because of the well-known potential mismatch between what a majority wants and what is socially optimal. Under certain conditions, in order to alleviate this mismatch, the optimal policy discloses just the ``anonymized'' information about the value of the alternatives to the voters, placing them effectively behind a partial ``veil of ignorance''.