We define and instantiate a cryptographic scheme called “private counters”, which can be used in applications such as preferential voting to express and update preferences (or any secret) privately and non-interactively. A private counter consists of an encrypted value together with rules for updating that value if certain events occur. Updates are private: the rules do not reveal how the value of the counter is updated, nor even whether it is updated for a certain event. Updates are non-interactive: a counter can be updated without communicating with its creator. A private counter also contains an encrypted bit indicating if the current value in the counter is within a pre-specified range. We also define a privacy model for private counters and prove that our construction satisfies this notion of privacy. As an application of private counters, we present an efficient protocol for preferential voting that hides the order in which voters rank candidates, and thus offers greater privacy guarantees than any other preferential voting scheme.