In the context of communication complexity I see a definition of differential privacy which isn't totally clear to me as to why it makes sense. So the two parties $A$ and $B$ draw two strings $X$ and $Y$ from the set $S^n$ where $S$ is some finite set. Let $P$ be the protocol. Now if $z_1 = (X_1,Y_1)$ and $z_2 = (X_2,Y_2)$ are two instances drawn with a probability distribution $\mu$ over the set $S^n \times S^n$ then the protocol $P$ is called $\epsilon$-differentially private if the following holds: $$e^{-2 \epsilon n}  \leq  \Pr[P(z_1) = p]  /  \Pr[P(z_2) = p]   \leq e^{2 \epsilon n}$$Now why does this make sense? What's the intuition? How is this related to the bounded derivative definition? 
About the definition of differential privacy in communication complexity
complexity theory;terminology;cryptography;communication complexity