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We consider the problem of differentially private selection. Given a finiteset of candidate items and a quality score for each item, our goal is to designa differentially private mechanism that returns an item with a score that is ashigh as possible. The most commonly used mechanism for this task is theexponential mechanism. In this work, we propose a new mechanism for this taskbased on a careful analysis of the privacy constraints. The expected score ofour mechanism is always at least as large as the exponential mechanism, and canoffer improvements up to a factor of two. Our mechanism is simple to implementand runs in linear time.

Permute-and-Flip: A new mechanism for differentially private selection