The Permute-and-Flip Mechanism is Identical to Report-Noisy-Max with Exponential Noise. (arXiv:2105.07260v3 [cs.CR] UPDATED)

The permute-and-flip mechanism is a recently proposed differentially private
selection algorithm that was shown to outperform the exponential mechanism. In
this paper, we show that permute-and-flip is equivalent to the well-known
report noisy max algorithm with exponential noise.