The continual improvement of 3D sensors has driven the development of algorithms to perform point cloud analysis. In fact, techniques for point cloud classification and segmentation have in recent years achieved incredible performance driven in part by leveraging large synthetic datasets. Unfortunately these same state-of-the-art approaches perform poorly when applied to incomplete point clouds. This limitation of existing algorithms is particularly concerning since point clouds generated by 3D sensors in the real world are usually incomplete due to perspective view or occlusion by other objects. This paper proposes a general model for partial point clouds analysis wherein the latent feature encoding a complete point clouds is inferred by applying a local point set voting strategy. In particular, each local point set constructs a vote that corresponds to a distribution in the latent space, and the optimal latent feature is the one with the highest probability. This approach ensures that any subsequent point cloud analysis is robust to partial observation while simultaneously guaranteeing that the proposed model is able to output multiple possible results. This paper illustrates that this proposed method achieves state-of-the-art performance on shape classification, part segmentation and point cloud completion.