In many economic and political settings, decisions are made collectively by committees. The committee members who participate in these decision-making processes are partly motivated by the quality of the decisions they reach, but they may additionally be concerned about the expost consequences of the way their votes are perceived. Moreover, in some of these scenarios the committee members would not like to be seen as voting in any particular way, and instead prefer to maintain an ambiguous perception of their vote. One might conjecture that for committees with such members, it would be desirable to institute voting procedures that hide some or all of the information about how the votes were cast. For instance, anonymous voting, in which only an anonymous tally of the votes is publicized, would be preferable to open voting, in which all individual votes are publicly disclosed. And secret voting, in which nothing beyond the final decision is revealed, would be best. This paper examines the validity of this conjecture by analyzing these three common disclosure rules|open, anonymous, and secret| when voters have a preference for strategic ambiguity. The main result is that the conjecture is false, and that restricting the amount of information disclosed about the votes may actually be harmful. More specifically, we consider a common-value setting, in which committee members receive signals about the state of the world, and in each state of the world there is a corresponding correct outcome that all members prefer most. The three disclosure rules are compared along two dimensions: The probability that the committee decides on the correct outcome, and the welfare of the committee members. In standard common-value voting models, in which voters do not have preferences over how their votes are perceived by others, the welfare of voters is maximized when the probability of correctness is maximized. In this paper, however, the two dimensions are not perfectly aligned, as welfare is impacted not only by the outcome, but also by the inferences that can be drawn by outsiders about committee members' votes. We show that the amount of information disclosed may have a non-monotonic effect on both the probability of correctness and on the welfare of the committee members. In particular, the first-best probability of correctness is often attained at the extremes|in open voting, when all information is disclosed, and in secret voting, when no information is disclosed|but is not attained in anonymous voting, when some but not all information is disclosed. Furthermore, the welfare of the committee members, while always minimal in open voting, is sometimes maximal in anonymous rather than secret voting.