We thank all reviewers for helpful comments and suggestions! We will follow reviewers’ suggestions, especially adding formal statements about the moment conditions for our GMM.$ Reviewer 3: We will add the statement of Corollary 3 by Allman et al. We appreciate the reviewer for the reminder of the work by Chierichetti et al. Actually we are aware of this closely-related work and discussed it in a previous version, but accidentally removed it in the submission. We will definitely fix this in a future version. Reviewer 4: Our GMM algorithm works for k=2 and any m>=4 (we focused on m=4 for illustration). It can also be used for other combinations of k and m, but we haven’t obtained theoretical guarantee on identifiability yet. We are working on more experimental comparisons between GMM and EMM (with various combinations of iterations in MM and in EM), and extending our GMM to partial rankings. Thanks for the suggestions! By “logistic regression” we meant “multinomial logistic regression”. We will make this clear. Reviewer 5: Thanks for the suggestions!