This paper introduces a method for merging K different uncertainty sets (e.g., prediction sets or confidence sets) that are arbitrarily dependent, to produce a single uncertainty set with nearly the same coverage. The method is based on a simple majority vote procedure, which can be extended to incorporate prior information and produce smaller sets without altering the coverage guarantee. The paper also shows that the method can be used to derandomize statistical procedures based on data splitting, such as median-of-means and HulC. The majority vote procedure is shown to have a coverage guarantee of 1-2α, and can be improved by using randomization or permutation techniques. The paper also discusses the application of the method to differentially private confidence sets and conformal inference, and shows that it can be extended to other bounded loss functions beyond coverage. The method is shown to be effective in both theoretical and practical settings, and provides a simple and broadly applicable way to combine uncertainty sets.This paper introduces a method for merging K different uncertainty sets (e.g., prediction sets or confidence sets) that are arbitrarily dependent, to produce a single uncertainty set with nearly the same coverage. The method is based on a simple majority vote procedure, which can be extended to incorporate prior information and produce smaller sets without altering the coverage guarantee. The paper also shows that the method can be used to derandomize statistical procedures based on data splitting, such as median-of-means and HulC. The majority vote procedure is shown to have a coverage guarantee of 1-2α, and can be improved by using randomization or permutation techniques. The paper also discusses the application of the method to differentially private confidence sets and conformal inference, and shows that it can be extended to other bounded loss functions beyond coverage. The method is shown to be effective in both theoretical and practical settings, and provides a simple and broadly applicable way to combine uncertainty sets.