This is a theory-focused paper that analyzes the relations between prediction sets, confidence intervals and calibration in a distribution-free setting. Reviewers were unanimous in supporting the acceptance of this paper to the conference. Since the topic has been extensively researched before they had some difficulty teasing apart the unique contributions of this paper. Authors have promised to clarify this in the final version. Reviewers were also keen on seeing better illustration and description of the intuitions behind the theorems. That would help the paper have a wider impact in the community.