In this paper, we present PDP, a distributed polling protocol that enables a set of participants to gather their opinion on a common interest without revealing their point of view. PDP does not rely on any centralized authority or on heavyweight cryptography. PDP is an overlay-based protocol where a subset of participants may use a simple sharing scheme to express their votes. In a system of $M$ participants arranged in groups of size $N$ where at least $2k-1$ participants are honest, PDP bounds the probability for a given participant to have its vote recovered with certainty by a coalition of $B$ dishonest participants by $pi(B/N)^(k+1)$, where $pi$ is the proportion of participants splitting their votes, and $k$ a privacy parameter. PDP bounds the impact of dishonest participants on the global outcome by $2(k&alpha + BN), where represents the number of dishonest nodes using the sharing scheme.