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I know that perturbation should be proportional to the $\text{L}_1$-sensitivity of the function if someone wants ($\epsilon,0$)-differential privacy, and proportional to the $\text{L}_2$-sensitivity of the function if someone wants ($\epsilon, \delta$)-differential privacy for $\delta > 0$.

But why is that? Can anybody describe the intuition behind the use of these two norms? Or maybe share some resources?

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