# The Permute-and-Flip Mechanism is Identical to Report-Noisy-Max with Exponential Noise

arXiv: https://arxiv.org/abs/2105.07260 · HTML: https://mlsanity.com/paper/2105.07260/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 May 2021.

## Built on by (most cited first, 14 of 14)

- [Privacy-Preserving In-Context Learning with Differentially Private Few-Shot Generation](https://mlsanity.com/paper/2309.11765/) (2023)
- [Permute-and-Flip: An optimally stable and watermarkable decoder for LLMs](https://mlsanity.com/paper/2402.05864/) (2024)
- [Adaptive Private-K-Selection with Adaptive K and Application to Multi-label PATE](https://mlsanity.com/paper/2203.16100/) (2022)
- [Unbounded Differentially Private Quantile and Maximum Estimation](https://mlsanity.com/paper/2305.01177/) (2023)
- [Differentially Private Top-k Selection via Canonical Lipschitz Mechanism](https://mlsanity.com/paper/2201.13376/) (2022)
- [Randomized algorithms for precise measurement of differentially-private, personalized recommendations](https://mlsanity.com/paper/2308.03735/) (2023)
- [Unleash the Power of Ellipsis: Accuracy-enhanced Sparse Vector Technique with Exponential Noise](https://mlsanity.com/paper/2407.20068/) (2024)
- [Faster Private Minimum Spanning Trees](https://mlsanity.com/paper/2408.06997/) (2024)
- [Differentially Private and Federated Structure Learning in Bayesian Networks](https://mlsanity.com/paper/2512.01708/) (2025)
- [Differentially Private Conditional Independence Testing](https://mlsanity.com/paper/2306.06721/) (2023)
- [Private Selection with Heterogeneous Sensitivities](https://mlsanity.com/paper/2501.05309/) (2025)
- [Differentially Private Selection using Smooth Sensitivity](https://mlsanity.com/paper/2504.08086/) (2025)
- [DPrivBench: Benchmarking LLMs' Reasoning for Differential Privacy](https://mlsanity.com/paper/2604.15851/) (2026)
- [ExpBoN: Exponential-Noise Best-of-n for Efficient Test-Time LLM Alignment](https://mlsanity.com/paper/2609.21899/) (2026)

## Abstract (arXiv)

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.