This work provides a comprehensive study of trade-offs between communication complexity and distortion for voting rules, and reviewers were unanimously in favor of acceptance. Please take their constructive feedback into account for the final version, especially with regard to the exposition. While there were concerns as to the fit at NeurIPS given the topic of the paper, the paper is clearly is relevant to AI. (That said, to the extent that the authors can draw connections between their work and AI / ML explicitly, perhaps in the introduction, we would encourage them to do so.)