We consider a framework where the optimal decision rule determining the collective choice depends in a simple way on the decision makers' posterior probabilities of a particular state of nature. Nevertheless, voting is generally an inefficient way to make collective choices and this paper sheds light on the relationship between the optimal decision rule and voting mechanisms. The paper derives the conditions under which the optimal decision rule is equivalent to some well-known voting procedure (weighted supermajority, weighted majority, and simple majority) and shows that these are very stringent. The paper also considers more general voting procedures, as for example allowing for abstentions, and shows that the conditions for reaching the optimal collective choice remain very stringent.