We thank all reviewers for the valuable constructive feedback. $ Reviewer 1: --The assumption that $m I(\pi)$ tends to infinity is implied by the condition $\log k=o(m I(\pi))$ stated in Theorem 3.1. We are going to state it explicitly along with the Markov inequality in the revision. --$k$ does not have to be a constant. It is allowed to grow as long as $\log k=o(m I(\pi))$ is satisfied throughout the paper. The proof derives a lower bound $k^{-1}\exp(-(1+o(1))m I(\pi))$. Under the assumption $\log k=o(m I(\pi))$, the extra polynomial factor of $k$ can be absorbed into the $o(1)$ term on the exponent. --The results in this paper can be regarded as asymptotic in the sense that we let $m$ go to infinity. There is a typo in Line 625. The quantity $Q(S_m \leq L)$ should be $Q(S_m \geq L)$. Thank you for pointing that out. Reviewer 2: The main innovation in the proof lies in the lower bound for a large deviation probability. The classical lower bound results of Cramer-Chernoff and Sanov assume i.i.d. data with probability that does not depend on sample size. In terms of crowdsourcing, that implies $I(\pi)$ to be a constant. Unlike the classical lower bound results, our result additionally covers the case where $I(\pi)$ vanishes to zero. This is particularly meaningful in crowdsourcing since $I(\pi)$ vanishing to zero means that the number of experts is only at a smaller order compared to the total number of workers. We will include the above remark in the revised version, and also the interesting references listed in the feedback with discussions. Reviewer 3: Our work is restricted to the classic Dawid-Skene (DS) model in which, as you noted, the instances’ contexts and the corresponding label dependency are not modeled. Although it is simple, it does have nice empirical performance (see references) so we want to understand it better. It is definitely interesting to explore in the future how to extend the DS model such that the instances (even workers) contexts are incorporated, and how to extend the analysis here to such more general settings.