The paper addresses the problem of combining multiple uncertainty sets, such as confidence intervals or prediction sets, that are arbitrarily dependent. The authors propose a majority vote procedure to efficiently merge these sets into a single uncertainty set while maintaining nearly the same error guarantee. They extend this core idea in several ways: incorporating prior information through weighted averaging, achieving strictly smaller merged sets through randomization without altering coverage, and improving the method for exchangeable sets. The paper also demonstrates how modern methods like split conformal prediction, median of means, HuC, and cross-fitted "double machine learning" can be effectively derandomized using these ideas. The majority vote procedure is shown to be robust and versatile, providing a practical and efficient solution for combining uncertainty sets in various statistical and machine learning applications.The paper addresses the problem of combining multiple uncertainty sets, such as confidence intervals or prediction sets, that are arbitrarily dependent. The authors propose a majority vote procedure to efficiently merge these sets into a single uncertainty set while maintaining nearly the same error guarantee. They extend this core idea in several ways: incorporating prior information through weighted averaging, achieving strictly smaller merged sets through randomization without altering coverage, and improving the method for exchangeable sets. The paper also demonstrates how modern methods like split conformal prediction, median of means, HuC, and cross-fitted "double machine learning" can be effectively derandomized using these ideas. The majority vote procedure is shown to be robust and versatile, providing a practical and efficient solution for combining uncertainty sets in various statistical and machine learning applications.