Consistent correspondences between point clouds are vital to 3D vision tasks such as registration and recognition. In this paper, we present a mutual voting method for ranking 3D correspondences. The key insight is to achieve reliable scoring results for correspondences by refining both voters and candidates in a mutual voting scheme. First, a graph is constructed for the initial correspondence set with the pairwise compatibility constraint. Second, nodal clustering coefficients are introduced to preliminarily remove a portion of outliers and speed up the following voting process. Third, we model nodes and edges in the graph as candidates and voters, respectively. Mutual voting is then performed in the graph to score correspondences. Finally, the correspondences are ranked based on the voting scores and top-ranked ones are identified as inliers. Feature matching, 3D point cloud registration, and 3D object recognition experiments on various datasets with different nuisances and modalities verify that MV is robust to heavy outliers under different challenging settings, and can significantly boost 3D point cloud registration and 3D object recognition performance. Code will be available at: https://github.com/NWPU-YJQ-3DV/2022_Mutual_Voting.